| Title: | Markov Chain Gaussian Fields Simulation and Parameter Estimation |
|---|---|
| Description: | Simulating and estimating (regime-switching) Markov chain Gaussian fields with covariance functions of the Gneiting class (Gneiting 2002) <doi:10.1198/016214502760047113>. It supports parameter estimation by weighted least squares and maximum likelihood methods, and produces Kriging forecasts and intervals for existing and new locations. |
| Authors: | Tianxia Jia [aut, cre, cph] |
| Maintainer: | Tianxia Jia <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.1.0.9000 |
| Built: | 2025-03-25 04:05:24 UTC |
| Source: | https://github.com/tianxia-jia/mcgf |
Calculate regime-switching auto-correlation
acf_rs(x, label, lag_max, demean = TRUE)acf_rs(x, label, lag_max, demean = TRUE)
x |
A univariate numeric time series. |
label |
A factor of regime labels. |
lag_max |
Maximum lag at which to calculate the acf. |
demean |
Logical. Should the covariances be about the sample means? |
Mean auto-correlations for each group in label.
set.seed(123) x <- rnorm(100) label <- sample(1:2, 100, replace = TRUE) acf_rs(x, label = factor(label), lag_max = 3)set.seed(123) x <- rnorm(100) label <- sample(1:2, 100, replace = TRUE) acf_rs(x, label = factor(label), lag_max = 3)
Generic function for calculating autocorrelation
acfs(x, ...)acfs(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to acfs.mcgf() and acfs.mcgf_rs() for more details.
A vector of mean auto-correlations for mcgf objects, or that plus
a list of regime-switching mean auto-correlations for mcgf_rs objects.
mcgf or
mcgf_rs objectExtract, calculate, or assign mean auto-correlations for an mcgf or
mcgf_rs object
## S3 method for class 'mcgf' acfs(x, lag_max, replace = FALSE, ...) ## S3 method for class 'mcgf_rs' acfs(x, lag_max, replace = FALSE, ...) acfs(x) <- value add_acfs(x, lag_max, ...)## S3 method for class 'mcgf' acfs(x, lag_max, replace = FALSE, ...) ## S3 method for class 'mcgf_rs' acfs(x, lag_max, replace = FALSE, ...) acfs(x) <- value add_acfs(x, lag_max, ...)
x |
An |
lag_max |
Maximum lag at which to calculate the acf. |
replace |
Logical; if TRUE, |
... |
Additional parameters or attributes. |
value |
A Vector of mean of auto-correlations for time lags starting from 0. |
For mcgf objects, acfs() computes mean auto-correlations for each time
lag across locations. The output is a vector of acfs.
For mcgf_rs objects, acfs() computes regime-switching mean
auto-correlations for each time lag across locations. The output is a list of
vectors of acfs, where each vector in the list corresponds to the acfs for
a regime.
acfs<- assigns acfs to x.
add_acfs() adds acfs to x.
acfs() returns (regime-switching) mean auto-correlations.
add_acfs() returns the same object with additional attributes of
(regime-switching) mean auto-correlations.
# Calculate acfs for 'sim1' data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) acfs(sim1_mcgf, lag_max = 5) # Add acfs to 'sim1_mcgf' sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) print(sim1_mcgf, "acfs") # Calculate acfs for 'sim2' data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) acfs(sim2_mcgf, lag_max = 5) # Add acfs to 'sim2_mcgf' sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) print(sim2_mcgf, "acfs")# Calculate acfs for 'sim1' data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) acfs(sim1_mcgf, lag_max = 5) # Add acfs to 'sim1_mcgf' sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) print(sim1_mcgf, "acfs") # Calculate acfs for 'sim2' data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) acfs(sim2_mcgf, lag_max = 5) # Add acfs to 'sim2_mcgf' sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) print(sim2_mcgf, "acfs")
Generic function for adding a base model
add_base(x, ...)add_base(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to add_base.mcgf() and add_base.mcgf_rs() for more details.
x with the newly added base model.
fit_base() to an mcgf object.Add base model outputted from fit_base() to an mcgf object.
## S3 method for class 'mcgf' add_base(x, fit_base, fit_s, fit_t, sep = FALSE, old = FALSE, ...) base(x) <- value## S3 method for class 'mcgf' add_base(x, fit_base, fit_s, fit_t, sep = FALSE, old = FALSE, ...) base(x) <- value
x |
An |
fit_base |
Output from the |
fit_s |
Pure spatial model outputted from the |
fit_t |
Pure temporal model outputted from the |
sep |
Logical; TRUE if spatial and temporal models are fitted separately. |
old |
Logical; TRUE if the old base model needs to be kept. |
... |
Additional arguments. Not in use. |
value |
A list containing the base model as well as its parameters. It
must contains the same output as |
After fitting the base model by fit_base(), the results can be added to
x by add_base(). To supply the base model directly, use base<- to
add the base model; the value must contain model, par_base, cor_base,
lag, and horizon.
x with newly added attributes of the base model.
Other functions on fitting an mcgf:
add_lagr.mcgf(),
fit_base.mcgf(),
fit_lagr.mcgf(),
krige.mcgf(),
krige_new.mcgf()
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a pure spatial model fit_spatial <- fit_base( sim1_mcgf, model = "spatial", lag = 5, par_init = c(c = 0.001, gamma = 0.5), par_fixed = c(nugget = 0) ) # Fit a pure temporal model fit_temporal <- fit_base( sim1_mcgf, model = "temporal", lag = 5, par_init = c(a = 0.3, alpha = 0.5) ) # Store the fitted models to 'sim1_mcgf' sim1_mcgf <- add_base(sim1_mcgf, fit_s = fit_spatial, fit_t = fit_temporal, sep = TRUE ) # Fit a separable model fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) # Store the newly fitted model, and keep the old fit sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep, old = TRUE) model(sim1_mcgf, model = "base", old = TRUE)data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a pure spatial model fit_spatial <- fit_base( sim1_mcgf, model = "spatial", lag = 5, par_init = c(c = 0.001, gamma = 0.5), par_fixed = c(nugget = 0) ) # Fit a pure temporal model fit_temporal <- fit_base( sim1_mcgf, model = "temporal", lag = 5, par_init = c(a = 0.3, alpha = 0.5) ) # Store the fitted models to 'sim1_mcgf' sim1_mcgf <- add_base(sim1_mcgf, fit_s = fit_spatial, fit_t = fit_temporal, sep = TRUE ) # Fit a separable model fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) # Store the newly fitted model, and keep the old fit sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep, old = TRUE) model(sim1_mcgf, model = "base", old = TRUE)
fit_base() to an mcgf_rs object.Add base model outputted from fit_base() to an mcgf_rs object.
## S3 method for class 'mcgf_rs' add_base(x, fit_base_ls, fit_s_ls, fit_t_ls, sep = FALSE, old = FALSE, ...)## S3 method for class 'mcgf_rs' add_base(x, fit_base_ls, fit_s_ls, fit_t_ls, sep = FALSE, old = FALSE, ...)
x |
An mcgf_rs' object. |
fit_base_ls |
Output from the |
fit_s_ls |
Pure spatial model outputted from the |
fit_t_ls |
Pure temporal model outputted from the |
sep |
Logical; TRUE if spatial and temporal models are fitted separately. |
old |
Logical; TRUE if the old base model needs to be kept. The lag and horizon of the new model are assumed to be the same as that of the old model. |
... |
Additional arguments. Not in use. |
After fitting the base model by fit_base(), the results can be added to
x by add_base(). To supply the base model directly, use base<- to
add the base model; the value must contain the same output as
add_base.mcgf() or add_base.mcgf_rs().
x with newly added attributes of the base model.
Other functions on fitting an mcgf_rs:
add_lagr.mcgf_rs(),
fit_base.mcgf_rs(),
fit_lagr.mcgf_rs(),
krige.mcgf_rs(),
krige_new.mcgf_rs()
data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching pure spatial model fit_spatial <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "spatial", par_init_ls = list(c(c = 0.00005, gamma = 0.5)), par_fixed_ls = list(c(nugget = 0)) ) # Fit a regime-switching pure temporal model fit_temporal <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "temporal", par_init_ls = list( list(a = 0.8, alpha = 0.8), list(a = 0.1, alpha = 0.1) ) ) # Store the fitted models to 'sim2_mcgf' sim2_mcgf <- add_base(sim2_mcgf, fit_s_ls = fit_spatial, fit_t_ls = fit_temporal, sep = TRUE ) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) # Store the newly fitted model, and keep the old fit sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep, old = TRUE) model(sim2_mcgf, model = "base", old = TRUE)data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching pure spatial model fit_spatial <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "spatial", par_init_ls = list(c(c = 0.00005, gamma = 0.5)), par_fixed_ls = list(c(nugget = 0)) ) # Fit a regime-switching pure temporal model fit_temporal <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "temporal", par_init_ls = list( list(a = 0.8, alpha = 0.8), list(a = 0.1, alpha = 0.1) ) ) # Store the fitted models to 'sim2_mcgf' sim2_mcgf <- add_base(sim2_mcgf, fit_s_ls = fit_spatial, fit_t_ls = fit_temporal, sep = TRUE ) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) # Store the newly fitted model, and keep the old fit sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep, old = TRUE) model(sim2_mcgf, model = "base", old = TRUE)
Generic function for adding a Lagrangian model
add_lagr(x, ...)add_lagr(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to add_lagr.mcgf() and add_lagr.mcgf_rs() for more details.
x with the newly added Lagrangian model.
fit_lagr() to a mcgf object.Add lagr model outputted from fit_lagr() to a mcgf object.
## S3 method for class 'mcgf' add_lagr(x, fit_lagr, ...) lagr(x) <- value## S3 method for class 'mcgf' add_lagr(x, fit_lagr, ...) lagr(x) <- value
x |
An |
fit_lagr |
Output from the |
... |
Additional arguments. Not in use. |
value |
A list containing the lagr model as well as its parameters. It
must contains |
x with newly added attributes of the Lagrangian model.
Other functions on fitting an mcgf:
add_base.mcgf(),
fit_base.mcgf(),
fit_lagr.mcgf(),
krige.mcgf(),
krige_new.mcgf()
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) # Store the fitted Lagrangian model to 'sim1_mcgf' sim1_mcgf <- add_lagr(sim1_mcgf, fit_lagr = fit_lagr) model(sim1_mcgf, old = TRUE)data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) # Store the fitted Lagrangian model to 'sim1_mcgf' sim1_mcgf <- add_lagr(sim1_mcgf, fit_lagr = fit_lagr) model(sim1_mcgf, old = TRUE)
fit_lagr() to a mcgf_rs object.Add lagr model outputted from fit_lagr() to a mcgf_rs object.
## S3 method for class 'mcgf_rs' add_lagr(x, fit_lagr_ls, ...)## S3 method for class 'mcgf_rs' add_lagr(x, fit_lagr_ls, ...)
x |
An |
fit_lagr_ls |
Output from the |
... |
Additional arguments. Not in use. |
After fitting the Lagrangian model by fit_lagr(), the results can be
added to x by add_base(). To supply the Lagrangian model directly,
use lagr<- to add the Lagrangian model; the value must contain the same
output as add_lagr.mcgf() or add_lagr.mcgf_rs().
x with newly added attributes of the Lagrangian model.
Other functions on fitting an mcgf_rs:
add_base.mcgf_rs(),
fit_base.mcgf_rs(),
fit_lagr.mcgf_rs(),
krige.mcgf_rs(),
krige_new.mcgf_rs()
data(sim3) sim3_mcgf <- mcgf_rs(sim3$data, dists = sim3$dists, label = sim3$label) sim3_mcgf <- add_acfs(sim3_mcgf, lag_max = 5) sim3_mcgf <- add_ccfs(sim3_mcgf, lag_max = 5) # Fit a fully symmetric model with known variables fit_fs <- fit_base( sim3_mcgf, lag_ls = 5, model_ls = "fs", rs = FALSE, par_init_ls = list(list(beta = 0)), par_fixed_ls = list(list( nugget = 0, c = 0.05, gamma = 0.5, a = 0.5, alpha = 0.2 )) ) # Set beta to 0 to fit a separable model with known variables fit_fs[[1]]$fit$par <- 0 # Store the fitted separable model to 'sim3_mcgf' sim3_mcgf <- add_base(sim3_mcgf, fit_base_ls = fit_fs) # Fit a regime-switching Lagrangian model. fit_lagr_rs <- fit_lagr( sim3_mcgf, model_ls = list("lagr_tri"), par_init_ls = list( list(v1 = -50, v2 = 50), list(v1 = 100, v2 = 100) ), par_fixed_ls = list(list(lambda = 0.2, k = 2)) ) # Store the fitted Lagrangian model to 'sim3_mcgf' sim3_mcgf <- add_lagr(sim3_mcgf, fit_lagr_ls = fit_lagr_rs) model(sim3_mcgf)data(sim3) sim3_mcgf <- mcgf_rs(sim3$data, dists = sim3$dists, label = sim3$label) sim3_mcgf <- add_acfs(sim3_mcgf, lag_max = 5) sim3_mcgf <- add_ccfs(sim3_mcgf, lag_max = 5) # Fit a fully symmetric model with known variables fit_fs <- fit_base( sim3_mcgf, lag_ls = 5, model_ls = "fs", rs = FALSE, par_init_ls = list(list(beta = 0)), par_fixed_ls = list(list( nugget = 0, c = 0.05, gamma = 0.5, a = 0.5, alpha = 0.2 )) ) # Set beta to 0 to fit a separable model with known variables fit_fs[[1]]$fit$par <- 0 # Store the fitted separable model to 'sim3_mcgf' sim3_mcgf <- add_base(sim3_mcgf, fit_base_ls = fit_fs) # Fit a regime-switching Lagrangian model. fit_lagr_rs <- fit_lagr( sim3_mcgf, model_ls = list("lagr_tri"), par_init_ls = list( list(v1 = -50, v2 = 50), list(v1 = 100, v2 = 100) ), par_fixed_ls = list(list(lambda = 0.2, k = 2)) ) # Store the fitted Lagrangian model to 'sim3_mcgf' sim3_mcgf <- add_lagr(sim3_mcgf, fit_lagr_ls = fit_lagr_rs) model(sim3_mcgf)
Calculate regime-switching cross-correlation
ccf_rs(x, y, label, lag_max)ccf_rs(x, y, label, lag_max)
x, y
|
A univariate numeric time series. |
label |
A factor of regime labels. |
lag_max |
Maximum lag at which to calculate the ccf. |
Cross-correlations for each group in label.
set.seed(123) x <- rnorm(100) y <- rnorm(100) label <- sample(1:2, 100, replace = TRUE) ccf_rs(x, y, label = factor(label), lag_max = 3)set.seed(123) x <- rnorm(100) y <- rnorm(100) label <- sample(1:2, 100, replace = TRUE) ccf_rs(x, y, label = factor(label), lag_max = 3)
Generic function for calculating cross-correlation
ccfs(x, ...)ccfs(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to ccfs.mcgf() and ccfs.mcgf_rs() for more details.
An array of cross-correlations for mcgf objects, or that plus
a list of regime-switching cross-correlations for mcgf_rs objects.
mcgf or mcgf_rs
objectExtract, calculate, or assign cross-correlations for an mcgf or mcgf_rs
object
## S3 method for class 'mcgf' ccfs(x, lag_max, ncores = 1, replace = FALSE, ...) ## S3 method for class 'mcgf_rs' ccfs(x, lag_max, ncores = 1, replace = FALSE, ...) ccfs(x) <- value add_ccfs(x, lag_max, ncores = 1, ...)## S3 method for class 'mcgf' ccfs(x, lag_max, ncores = 1, replace = FALSE, ...) ## S3 method for class 'mcgf_rs' ccfs(x, lag_max, ncores = 1, replace = FALSE, ...) ccfs(x) <- value add_ccfs(x, lag_max, ncores = 1, ...)
x |
An |
lag_max |
Maximum lag at which to calculate the ccfs. |
ncores |
Number of cpu cores used for computing. The |
replace |
Logical; if TRUE, |
... |
Additional parameters or attributes. Not in use. |
value |
Cross-correlations. |
For mcgf objects, ccfs() computes cross-correlations for each time
lag. The output is an array of matrices where each matrix corresponds to the
cross-correlation for a time lag.
For mcgf_rs objects, ccfs() computes regime-switching
cross-correlations for each time lag. The output is a list of array of
matrices where each array in the list corresponds to the cross-correlation
for a regime.
ccfs<- assigns ccfs to x.
add_ccfs() adds ccfs and sds to x.
ccfs() returns (regime-switching) cross-correlations.
add_ccfs() returns the same object with additional attributes of
(regime-switching) cross-correlations and (regime-switching) empirical
standard deviations.
# Calculate ccfs for 'sim1' data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) ccfs(sim1_mcgf, lag_max = 5) # To use multiple cores, use the `ncores` argument ccfs(sim1_mcgf, lag_max = 5, ncores = 2) # Add ccfs and sds to 'sim1_mcgf' sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) print(sim1_mcgf, "ccfs") print(sim1_mcgf, "sds") # Calculate ccfs for 'sim2' data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) ccfs(sim2_mcgf, lag_max = 5) # Add ccfs and sds to 'sim2_mcgf' sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) print(sim2_mcgf, "ccfs") print(sim2_mcgf, "sds")# Calculate ccfs for 'sim1' data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) ccfs(sim1_mcgf, lag_max = 5) # To use multiple cores, use the `ncores` argument ccfs(sim1_mcgf, lag_max = 5, ncores = 2) # Add ccfs and sds to 'sim1_mcgf' sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) print(sim1_mcgf, "ccfs") print(sim1_mcgf, "sds") # Calculate ccfs for 'sim2' data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) ccfs(sim2_mcgf, lag_max = 5) # Add ccfs and sds to 'sim2_mcgf' sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) print(sim2_mcgf, "ccfs") print(sim2_mcgf, "sds")
Generic functions for calculating joint covariance/correlation matrix for mcgf objects
ccov(x, ...)ccov(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to ccov.mcgf() and ccov.mcgf_rs() for more details.
Joint correlation/covariance matrix.
mcgf objectCovariance/correlation for joint distribution of an mcgf object
## S3 method for class 'mcgf' ccov(x, model = c("all", "base", "empirical"), cor = FALSE, ...)## S3 method for class 'mcgf' ccov(x, model = c("all", "base", "empirical"), cor = FALSE, ...)
x |
An |
model |
Which model to use. One of |
cor |
Logical; if TRUE, correlation is outputted. |
... |
Additional arguments. Not in use. |
Joint covariance/correlation matrix.
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) ccov(sim1_mcgf, model = "base")data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) ccov(sim1_mcgf, model = "base")
mcgf_rsobjectCovariance/correlation for joint distribution of an mcgf_rsobject
## S3 method for class 'mcgf_rs' ccov(x, model = c("all", "base", "empirical"), cor = FALSE, ...)## S3 method for class 'mcgf_rs' ccov(x, model = c("all", "base", "empirical"), cor = FALSE, ...)
x |
An |
model |
Which model to use. One of |
cor |
Logical; if TRUE, correlation is returned |
... |
Additional arguments. Not in use. |
A list of joint covariance/correlation matrix.
data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.000001, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep) ccov(sim2_mcgf, model = "base")data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.000001, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep) ccov(sim2_mcgf, model = "base")
Calculate Cauchy correlation
cor_cauchy(x, a, alpha, nu = 1, nugget = 0, is.dist = FALSE)cor_cauchy(x, a, alpha, nu = 1, nugget = 0, is.dist = FALSE)
x |
A numeric vector, matrix, or array. |
a |
Smooth parameter, |
alpha |
Scale parameter, |
nu |
Power parameter, |
nugget |
The nugget effect |
is.dist |
Logical; if TRUE, |
The Cauchy correlation function with scale parameter and
smooth parameter has the form
where is 1 when and 0 otherwise.
Correlations of the same dimension as x.
Gneiting, T., and Schlather, M. (2004). Stochastic Models That Separate Fractal Dimension and the Hurst Effect. SIAM Review, 46(2), 269–282.
Other correlation functions:
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_sep(),
cor_stat(),
cor_stat_rs()
x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_cauchy(x, a = 1, alpha = 0.5) x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_cauchy(x, a = 1, alpha = 0.5, nugget = 0.3, is.dist = TRUE)x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_cauchy(x, a = 1, alpha = 0.5) x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_cauchy(x, a = 1, alpha = 0.5, nugget = 0.3, is.dist = TRUE)
Calculate exponential correlation
cor_exp(x, c, gamma = 1/2, nugget = 0, is.dist = FALSE)cor_exp(x, c, gamma = 1/2, nugget = 0, is.dist = FALSE)
x |
A numeric vector, matrix, or array. |
c |
Smooth parameter, |
gamma |
Scale parameter, |
nugget |
The nugget effect |
is.dist |
Logical; if TRUE, |
The exponential correlation function with scale parameter
and smooth parameter has the form
where is 1 when and 0 otherwise.
Correlations of the same dimension as x.
Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-Based Geostatistics. Journal of the Royal Statistical Society. Series C (Applied Statistics), 47(3), 299–350.
Other correlation functions:
cor_cauchy(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_sep(),
cor_stat(),
cor_stat_rs()
x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_exp(x, c = 0.01, gamma = 0.5) x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_exp(x, c = 0.01, gamma = 0.5, nugget = 0.3, is.dist = TRUE)x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_exp(x, c = 0.01, gamma = 0.5) x <- matrix(c(0, 5, 5, 0), nrow = 2) cor_exp(x, c = 0.01, gamma = 0.5, nugget = 0.3, is.dist = TRUE)
Calculate correlation for fully symmetric model
cor_fs(nugget = 0, c, gamma = 1/2, a, alpha, beta = 0, h, u)cor_fs(nugget = 0, c, gamma = 1/2, a, alpha, beta = 0, h, u)
nugget |
The nugget effect |
c |
Scale parameter of |
gamma |
Smooth parameter of |
a |
Scale parameter of |
alpha |
Smooth parameter of |
beta |
Interaction parameter, |
h |
Euclidean distance matrix or array. |
u |
Time lag, same dimension as |
The fully symmetric correlation function with interaction parameter
has the form
where is the Euclidean distance, and is 1
when and 0 otherwise. Here and
. By default beta = 0 and it reduces to the separable
model.
Correlations of the same dimension as h and u.
Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space–Time Data, Journal of the American Statistical Association, 97:458, 590-600.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_sep(),
cor_stat(),
cor_stat_rs()
h <- matrix(c(0, 5, 5, 0), nrow = 2) u <- matrix(0, nrow = 2, ncol = 2) cor_fs(c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.5, h = h, u = u) h <- array(c(0, 5, 5, 0), dim = c(2, 2, 3)) u <- array(rep(0:2, each = 4), dim = c(2, 2, 3)) cor_fs(c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.5, h = h, u = u)h <- matrix(c(0, 5, 5, 0), nrow = 2) u <- matrix(0, nrow = 2, ncol = 2) cor_fs(c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.5, h = h, u = u) h <- array(c(0, 5, 5, 0), dim = c(2, 2, 3)) u <- array(rep(0:2, each = 4), dim = c(2, 2, 3)) cor_fs(c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.5, h = h, u = u)
Calculate Lagrangian correlation of the Askey form
cor_lagr_askey(v1, v2, k = 2, h1, h2, u)cor_lagr_askey(v1, v2, k = 2, h1, h2, u)
v1 |
Prevailing wind, u-component. |
v2 |
Prevailing wind, v-component. |
k |
Scale parameter of |
h1 |
Horizontal distance matrix or array. |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
The Lagrangian correlation function of the Askey form with parameters
has the form
where is the Euclidean distance, ,
and is the scale parameter controlling the magnitude of
asymmetry in correlation.
Correlations of the same dimension as h1.
Askey, R. (1973). Radial characteristic functions, Tech. Report No. 1262, Math. Research Center, University of Wisconsin-Madison.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_sep(),
cor_stat(),
cor_stat_rs()
h1 <- matrix(c(0, -5, 5, 0), nrow = 2) h2 <- matrix(c(0, -8, 8, 0), nrow = 2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_lagr_askey(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u) h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_lagr_askey(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)h1 <- matrix(c(0, -5, 5, 0), nrow = 2) h2 <- matrix(c(0, -8, 8, 0), nrow = 2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_lagr_askey(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u) h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_lagr_askey(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)
Calculate Lagrangian correlation of the exponential form
cor_lagr_exp(v1, v2, k = 2, h1, h2, u)cor_lagr_exp(v1, v2, k = 2, h1, h2, u)
v1 |
Prevailing wind, u-component. |
v2 |
Prevailing wind, v-component. |
k |
Scale parameter of |
h1 |
Horizontal distance matrix or array. |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
The Lagrangian correlation function of the exponential form with parameters
has the form
where is the Euclidean distance,
,
and is the scale parameter controlling the magnitude of
asymmetry in correlation.
Correlations of the same dimension as h1.
Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-Based Geostatistics. Journal of the Royal Statistical Society. Series C (Applied Statistics), 47(3), 299–350.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_tri(),
cor_sep(),
cor_stat(),
cor_stat_rs()
h1 <- matrix(c(0, -5, 5, 0), nrow = 2) h2 <- matrix(c(0, -8, 8, 0), nrow = 2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_lagr_exp(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u) h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_lagr_exp(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)h1 <- matrix(c(0, -5, 5, 0), nrow = 2) h2 <- matrix(c(0, -8, 8, 0), nrow = 2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_lagr_exp(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u) h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_lagr_exp(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)
Calculate Lagrangian correlation of the triangular form
cor_lagr_tri(v1, v2, k = 2, h1, h2, u)cor_lagr_tri(v1, v2, k = 2, h1, h2, u)
v1 |
Prevailing wind, u-component. |
v2 |
Prevailing wind, v-component. |
k |
Scale parameter of |
h1 |
Horizontal distance matrix or array. |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
The Lagrangian correlation function of the triangular form with parameters
has the form
where is the Euclidean distance, ,
and is the scale parameter controlling the magnitude of
asymmetry in correlation.
Correlations of the same dimension as h1.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_sep(),
cor_stat(),
cor_stat_rs()
h1 <- matrix(c(0, -5, 5, 0), nrow = 2) h2 <- matrix(c(0, -8, 8, 0), nrow = 2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_lagr_tri(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u) h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_lagr_tri(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)h1 <- matrix(c(0, -5, 5, 0), nrow = 2) h2 <- matrix(c(0, -8, 8, 0), nrow = 2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_lagr_tri(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u) h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3)) u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_lagr_tri(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)
Calculate correlation for separable model
cor_sep( spatial = c("exp", "cauchy"), temporal = c("exp", "cauchy"), par_s, par_t, h, u )cor_sep( spatial = c("exp", "cauchy"), temporal = c("exp", "cauchy"), par_s, par_t, h, u )
spatial |
Pure spatial model, |
temporal |
Pure temporal model, |
par_s |
Parameters for the pure spatial model. Nugget effect supported. |
par_t |
Parameters for the pure temporal model. |
h |
Euclidean distance matrix or array. |
u |
Time lag, same dimension as |
The separable model is the product of a pure temporal model, ,
and a pure spatial model, . It is of the form
where is 1 when and 0 otherwise. Here
and . Now only
exponential and Cauchy correlation models are available.
Correlations of the same dimension as h and u.
Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space–Time Data, Journal of the American Statistical Association, 97:458, 590-600.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_stat(),
cor_stat_rs()
h <- matrix(c(0, 5, 5, 0), nrow = 2) par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) u <- matrix(0, nrow = 2, ncol = 2) par_t <- list(a = 1, alpha = 0.5) cor_sep( spatial = "exp", temporal = "cauchy", par_s = par_s, par_t = par_t, h = h, u = u ) h <- array(c(0, 5, 5, 0), dim = c(2, 2, 3)) par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) u <- array(rep(0:2, each = 4), dim = c(2, 2, 3)) par_t <- list(a = 1, alpha = 0.5) cor_sep( spatial = "exp", temporal = "cauchy", par_s = par_s, par_t = par_t, h = h, u = u )h <- matrix(c(0, 5, 5, 0), nrow = 2) par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) u <- matrix(0, nrow = 2, ncol = 2) par_t <- list(a = 1, alpha = 0.5) cor_sep( spatial = "exp", temporal = "cauchy", par_s = par_s, par_t = par_t, h = h, u = u ) h <- array(c(0, 5, 5, 0), dim = c(2, 2, 3)) par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) u <- array(rep(0:2, each = 4), dim = c(2, 2, 3)) par_t <- list(a = 1, alpha = 0.5) cor_sep( spatial = "exp", temporal = "cauchy", par_s = par_s, par_t = par_t, h = h, u = u )
Calculate general stationary correlation.
cor_stat( base = c("sep", "fs"), lagrangian = c("none", "lagr_tri", "lagr_askey"), par_base, par_lagr, lambda, h, h1, h2, u, base_fixed = FALSE )cor_stat( base = c("sep", "fs"), lagrangian = c("none", "lagr_tri", "lagr_askey"), par_base, par_lagr, lambda, h, h1, h2, u, base_fixed = FALSE )
base |
Base model, |
lagrangian |
Lagrangian model, |
par_base |
Parameters for the base model (symmetric), used only when
|
par_lagr |
Parameters for the Lagrangian model. Used only when
|
lambda |
Weight of the Lagrangian term, |
h |
Euclidean distance matrix or array, used only when
|
h1 |
Horizontal distance matrix or array, same dimension as |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
base_fixed |
Logical; if TRUE, |
The general station model, a convex combination of a base model and a Lagrangian model, has the form
where is the weight of the Lagrangian term.
If base_fixed = TRUE, the correlation is of the form
where base is a correlation matrix/array and par_base and h are not
used.
When lagrangian = "none", lambda must be 0.
Correlations for the general stationary model. Same dimension of
base if base_fixed = FALSE.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_sep(),
cor_stat_rs()
par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) par_lagr <- list(v1 = 5, v2 = 10) h1 <- matrix(c(0, 5, -5, 0), nrow = 2) h2 <- matrix(c(0, 8, -8, 0), nrow = 2) h <- sqrt(h1^2 + h2^2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_stat( base = "sep", lagrangian = "lagr_tri", par_base = par_base, par_lagr = par_lagr, lambda = 0.8, h = h, h1 = h1, h2 = h2, u = u ) h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3)) h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3)) h <- sqrt(h1^2 + h2^2) u <- array(rep(c(0.1, 0.2, 0.3), each = 4), dim = c(2, 2, 3)) fit_base <- cor_fs( nugget = 0.5, c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.0, h = h, u = u ) par_lagr <- list(v1 = 5, v2 = 10) cor_stat( base = fit_base, lagrangian = "lagr_askey", par_lagr = par_lagr, h1 = h1, h2 = h2, u = u, lambda = 0.8, base_fixed = TRUE )par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) par_lagr <- list(v1 = 5, v2 = 10) h1 <- matrix(c(0, 5, -5, 0), nrow = 2) h2 <- matrix(c(0, 8, -8, 0), nrow = 2) h <- sqrt(h1^2 + h2^2) u <- matrix(0.1, nrow = 2, ncol = 2) cor_stat( base = "sep", lagrangian = "lagr_tri", par_base = par_base, par_lagr = par_lagr, lambda = 0.8, h = h, h1 = h1, h2 = h2, u = u ) h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3)) h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3)) h <- sqrt(h1^2 + h2^2) u <- array(rep(c(0.1, 0.2, 0.3), each = 4), dim = c(2, 2, 3)) fit_base <- cor_fs( nugget = 0.5, c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.0, h = h, u = u ) par_lagr <- list(v1 = 5, v2 = 10) cor_stat( base = fit_base, lagrangian = "lagr_askey", par_lagr = par_lagr, h1 = h1, h2 = h2, u = u, lambda = 0.8, base_fixed = TRUE )
Calculate general stationary correlation.
cor_stat_rs( n_regime, base_ls, lagrangian_ls, par_base_ls, par_lagr_ls, lambda_ls, h_ls, h1_ls, h2_ls, u_ls, base_fixed = FALSE )cor_stat_rs( n_regime, base_ls, lagrangian_ls, par_base_ls, par_lagr_ls, lambda_ls, h_ls, h1_ls, h2_ls, u_ls, base_fixed = FALSE )
n_regime |
Integer, number of regimes. |
base_ls |
List of base model, |
lagrangian_ls |
List of Lagrangian model, |
par_base_ls |
List of parameters for the base model, used only when
|
par_lagr_ls |
List of parameters for the Lagrangian model. Used only
when |
lambda_ls |
List of weight of the Lagrangian term,
|
h_ls |
List of Euclidean distance matrix or array,
used only when |
h1_ls |
List of horizontal distance matrix or array, same dimension as
|
h2_ls |
List of vertical distance matrix or array, same dimension as
|
u_ls |
List of time lag, same dimension as |
base_fixed |
Logical; if TRUE, |
It gives a list of general stationary correlation for n_regime
regimes. See cor_stat for the model details. Model parameters are lists of
length 1 or n_regime. When length is 1, same values are used for all
regimes. If base_fixed = TRUE, the base is a list of correlation and
par_base_ls and h_ls are not used.
Correlations for the general stationary model. Same dimension of
base_ls if base_fixed = TRUE.
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_lagr_tri(),
cor_sep(),
cor_stat()
# Fit general stationary model with sep base. par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3)) h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3)) h <- sqrt(h1^2 + h2^2) u <- array(rep(c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_stat_rs( n_regime = 2, base_ls = list("sep"), lagrangian_ls = list("none", "lagr_tri"), par_base_ls = list(par_base), par_lagr_ls = list(NULL, list(v1 = 10, v2 = 20)), lambda_ls = list(0, 0.2), h_ls = list(h), h1_ls = list(NULL, h1), h2_ls = list(NULL, h2), u_ls = list(u, u + 1) ) # Fit general stationary model given fs as the base model. h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3)) h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3)) h <- sqrt(h1^2 + h2^2) u <- array(rep(c(0.1, 0.2, 0.3), each = 4), dim = c(2, 2, 3)) fit_base <- cor_fs( nugget = 0.5, c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.0, h = h, u = u ) par_lagr <- list(v1 = 5, v2 = 10) cor_stat_rs( n_regime = 2, par_lagr_ls = list(par_lagr), h1_ls = list(h1), h2_ls = list(h2), u_ls = list(u, u + 1), lambda_ls = list(0, 0.8), base_ls = list(fit_base), lagrangian = list("lagr_tri", "lagr_askey"), base_fixed = TRUE )# Fit general stationary model with sep base. par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3)) h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3)) h <- sqrt(h1^2 + h2^2) u <- array(rep(c(1, 2, 3), each = 4), dim = c(2, 2, 3)) cor_stat_rs( n_regime = 2, base_ls = list("sep"), lagrangian_ls = list("none", "lagr_tri"), par_base_ls = list(par_base), par_lagr_ls = list(NULL, list(v1 = 10, v2 = 20)), lambda_ls = list(0, 0.2), h_ls = list(h), h1_ls = list(NULL, h1), h2_ls = list(NULL, h2), u_ls = list(u, u + 1) ) # Fit general stationary model given fs as the base model. h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3)) h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3)) h <- sqrt(h1^2 + h2^2) u <- array(rep(c(0.1, 0.2, 0.3), each = 4), dim = c(2, 2, 3)) fit_base <- cor_fs( nugget = 0.5, c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.0, h = h, u = u ) par_lagr <- list(v1 = 5, v2 = 10) cor_stat_rs( n_regime = 2, par_lagr_ls = list(par_lagr), h1_ls = list(h1), h2_ls = list(h2), u_ls = list(u, u + 1), lambda_ls = list(0, 0.8), base_ls = list(fit_base), lagrangian = list("lagr_tri", "lagr_askey"), base_fixed = TRUE )
Convert correlation to covariance
cor2cov(V, sd, empirical = FALSE) cor2cov_ar(V, sd, empirical = FALSE)cor2cov(V, sd, empirical = FALSE) cor2cov_ar(V, sd, empirical = FALSE)
V |
A correlation matrix, usually positive semi-definite. |
sd |
A vector of standard deviations. |
empirical |
Logical; TRUE if V is empirical correlation. |
cor2cov converts a matrix. cor2cov_ar converts an 3-D array.
A correlation matrix.
V <- matrix(c(1, 0.5, 0.5, 1), ncol = 2) sd <- 1:2 cor2cov(V, sd) V_ar <- array(c(1, 0.5, 0.5, 1), dim = c(2, 2, 2)) cor2cov_ar(V_ar, sd)V <- matrix(c(1, 0.5, 0.5, 1), ncol = 2) sd <- 1:2 cor2cov(V, sd) V_ar <- array(c(1, 0.5, 0.5, 1), dim = c(2, 2, 2)) cor2cov_ar(V_ar, sd)
Generic function for calculating distance matrices
dists(x, ...)dists(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
A list of signed distance matrices: h (Euclidean), h1
(horizontal), and h2 (vertical) with the same dimensions.
mcgf objectCalculating distance matrices for an mcgf object
## S3 method for class 'mcgf' dists(x, return_grid = FALSE, ...) dists(x) <- value## S3 method for class 'mcgf' dists(x, return_grid = FALSE, ...) dists(x) <- value
x |
An |
return_grid |
Logical; used when |
... |
Additional parameters or attributes. |
value |
List of signed distance matrices, outputted from |
If the dists attribute is available in x, it will be printed. Otherwise
dists will be calculated based on the locations attribute.
A list of signed distance matrices: h (Euclidean), h1
(horizontal), and h2 (vertical).
data <- cbind(S1 = 1:5, S2 = 4:8, S3 = 5:9) lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) # if locations are longitudes and latitudes obj <- mcgf(data = data, locations = locations) obj dists(obj) dists(obj) <- dists(obj) obj # if locations are just coordinates in a 2D plane: obj <- mcgf(data = data, locations = locations, longlat = FALSE) obj # calculate distances dists(obj) # add distances to the `mcgf` object dists(obj) <- dists(obj) objdata <- cbind(S1 = 1:5, S2 = 4:8, S3 = 5:9) lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) # if locations are longitudes and latitudes obj <- mcgf(data = data, locations = locations) obj dists(obj) dists(obj) <- dists(obj) obj # if locations are just coordinates in a 2D plane: obj <- mcgf(data = data, locations = locations, longlat = FALSE) obj # calculate distances dists(obj) # add distances to the `mcgf` object dists(obj) <- dists(obj) obj
Calculate (signed) distances between coordinates
find_dists(locations, longlat = TRUE, origin = 1L, return_grid = FALSE, ...)find_dists(locations, longlat = TRUE, origin = 1L, return_grid = FALSE, ...)
locations |
A matrix or data.frame of 2D points, the first column is x/longitude, and the second column is y/latitude. |
longlat |
Logical, if TURE Great Circle (WGS84 ellipsoid) distance; if FALSE, Euclidean distance. |
origin |
Optional; used when |
return_grid |
Logical; used when |
... |
Optional arguments passed to |
locations must be a matrix or data.frame containing 2 columns,
first column x/longitude, and second column y/latitude. The row names of
locations are used as the names of the locations.
If longlat is TRUE, the original coordinates are mapped to a 2D Euclidean
plane given the reference location. First, the Great Circle (WGS84 ellipsoid)
signed distance matrices are calculated, where the original latitudes are
replaced by the the mean of them to find the signed longitudinal
distances and the original longitudes are replaced by the the mean of them
to find the signed latitudinal distances. Then given the index of a
reference location origin, a new set of coordinates in a 2D plane is
generated where the coordinates are determined by the signed distances
between the locations and the reference location. Finally distance matrices
of the new coordinates are outputted.
A list of distance matrices. If return_grid is TRUE, a list
consists of a list of distance matrices, the mapped 2D grid, and the origin
is returned.
lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) rownames(locations) <- paste("Site", 1:3) find_dists(locations)lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) rownames(locations) <- paste("Site", 1:3) find_dists(locations)
Calculate (signed) distances between coordinates
find_dists_new( locations, locations_new, longlat = TRUE, origin = 1L, return_grid = FALSE, ... )find_dists_new( locations, locations_new, longlat = TRUE, origin = 1L, return_grid = FALSE, ... )
locations |
A matrix or data.frame of 2D points, the first column is x/longitude, and the second column is y/latitude. |
locations_new |
A matrix or data.frame of 2D points, the first column is x/longitude, and the second column is y/latitude. |
longlat |
Logical, if TURE Great Circle (WGS84 ellipsoid) distance; if FALSE, Euclidean distance. |
origin |
Optional; used when |
return_grid |
Logical; used when |
... |
Optional arguments passed to |
locations and locations_new must be matrices or data.frames containing
2 columns, first column x/longitude, and second column y/latitude. The row
names of locations and locations_new are used as the names of the
locations.
If longlat is TRUE, the original coordinates are mapped to a 2D Euclidean
plane given the reference location from locations. First, the Great Circle
(WGS84 ellipsoid) signed distance matrices are calculated, where the original
latitudes are replaced by the the mean of latitudes in locations to find
the signed longitudinal distances and the original longitudes are replaced by
the the mean of longitudes in locations to find the signed latitudinal
distances. Then given the index of a reference location origin, a new set
of coordinates in a 2D plane is generated where the coordinates are
determined by the signed distances between the locations and the reference
location. Finally distance matrices of the new coordinates for all stations
are outputted.
A list of distance matrices for all locations. If return_grid is
TRUE, a list consists of a list of distance matrices for all locations,
the mapped 2D grid for all locations, and the origin is returned.
lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) rownames(locations) <- paste("Site", 1:3) find_dists(locations) locations_new <- c(115, 55) find_dists_new(locations, locations_new)lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) rownames(locations) <- paste("Site", 1:3) find_dists(locations) locations_new <- c(115, 55) find_dists_new(locations, locations_new)
Fit correlation base models
fit_base(x, ...)fit_base(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to fit_base.mcgf() and fit_base.mcgf_rs() for more details.
A vector of estimated parameters.
mcgf
object.Parameter estimation for symmetric correlation functions for an mcgf
object.
## S3 method for class 'mcgf' fit_base( x, lag, horizon = 1, model = c("spatial", "temporal", "sep", "fs", "none"), method = c("wls", "mle"), optim_fn = c("nlminb", "optim", "other"), par_fixed = NULL, par_init, lower = NULL, upper = NULL, other_optim_fn = NULL, dists_base = NULL, scale_time = 1, ... )## S3 method for class 'mcgf' fit_base( x, lag, horizon = 1, model = c("spatial", "temporal", "sep", "fs", "none"), method = c("wls", "mle"), optim_fn = c("nlminb", "optim", "other"), par_fixed = NULL, par_init, lower = NULL, upper = NULL, other_optim_fn = NULL, dists_base = NULL, scale_time = 1, ... )
x |
An |
lag |
Integer time lag. |
horizon |
Integer forecast horizon. |
model |
Base model, one of |
method |
Parameter estimation methods, weighted least square ( |
optim_fn |
Optimization functions, one of |
par_fixed |
Fixed parameters. |
par_init |
Initial values for parameters to be optimized. |
lower |
Optional; lower bounds of parameters. |
upper |
Optional: upper bounds of parameters. |
other_optim_fn |
Optional, other optimization functions. The first two
arguments must be initial values for the parameters and a function to be
minimized respectively (same as that of |
dists_base |
List of distance matrices. If NULL, |
scale_time |
Scale of time unit, default is 1. |
... |
Additional arguments passed to |
This function fits the separable and fully symmetric models using weighted
least squares and maximum likelihood estimation. Optimization functions such
as nlminb and optim are supported. Other functions are also supported by
setting optim_fn = "other" and supplying other_optim_fn. lower and
upper are lower and upper bounds of parameters in par_init and default
bounds are used if they are not specified.
Note that both wls and mle are heuristic approaches when x contains
observations from a subset of the discrete spatial domain, though estimation
results are close to that using the full spatial domain for large sample
sizes.
A list containing outputs from optimization functions of optim_fn.
Other functions on fitting an mcgf:
add_base.mcgf(),
add_lagr.mcgf(),
fit_lagr.mcgf(),
krige.mcgf(),
krige_new.mcgf()
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a pure spatial model fit_spatial <- fit_base( sim1_mcgf, model = "spatial", lag = 5, par_init = c(c = 0.001, gamma = 0.5), par_fixed = c(nugget = 0) ) fit_spatial$fit # Fit a pure temporal model fit_temporal <- fit_base( sim1_mcgf, model = "temporal", lag = 5, par_init = c(a = 0.3, alpha = 0.5) ) fit_temporal$fit # Fit a separable model fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) fit_sep$fitdata(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a pure spatial model fit_spatial <- fit_base( sim1_mcgf, model = "spatial", lag = 5, par_init = c(c = 0.001, gamma = 0.5), par_fixed = c(nugget = 0) ) fit_spatial$fit # Fit a pure temporal model fit_temporal <- fit_base( sim1_mcgf, model = "temporal", lag = 5, par_init = c(a = 0.3, alpha = 0.5) ) fit_temporal$fit # Fit a separable model fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) fit_sep$fit
mcgf_rs
object.Parameter estimation for symmetric correlation functions for an mcgf_rs
object.
## S3 method for class 'mcgf_rs' fit_base( x, lag_ls, horizon = 1, model_ls, method_ls = "wls", optim_fn_ls = "nlminb", par_fixed_ls = list(NULL), par_init_ls, lower_ls = list(NULL), upper_ls = list(NULL), other_optim_fn_ls = list(NULL), dists_base_ls = list(NULL), scale_time = 1, rs = TRUE, ... )## S3 method for class 'mcgf_rs' fit_base( x, lag_ls, horizon = 1, model_ls, method_ls = "wls", optim_fn_ls = "nlminb", par_fixed_ls = list(NULL), par_init_ls, lower_ls = list(NULL), upper_ls = list(NULL), other_optim_fn_ls = list(NULL), dists_base_ls = list(NULL), scale_time = 1, rs = TRUE, ... )
x |
An |
lag_ls |
List of integer time lags. |
horizon |
Integer forecast horizon. |
model_ls |
List of base models, each element must be one of |
method_ls |
List of parameter estimation methods, weighted least square
( |
optim_fn_ls |
List of optimization functions, each element must be one
of |
par_fixed_ls |
List of fixed parameters. |
par_init_ls |
List of initial values for parameters to be optimized. |
lower_ls |
Optional; list of lower bounds of parameters. |
upper_ls |
Optional: list of upper bounds of parameters. |
other_optim_fn_ls |
Optional, list of other optimization functions. The
first two arguments must be initial values for the parameters and a function
to be minimized respectively (same as that of |
dists_base_ls |
List of lists of distance matrices. If NULL, |
scale_time |
Scale of time unit, default is 1. |
rs |
Logical; if TRUE |
... |
Additional arguments passed to all |
This functions is the regime-switching variant of fit_base.mcgf().
Arguments are in lists. The length of arguments that end in _ls must be 1
or the same as the number of regimes in x. If the length of an argument is
1, then it is set the same for all regimes. Refer to fit_base.mcgf() for
more details of the arguments.
Note that both wls and mle are heuristic approaches when x contains
observations from a subset of the discrete spatial domain, though estimation
results are close to that using the full spatial domain for large sample
sizes.
A list containing outputs from optimization functions of optim_fn
for each regime.
Other functions on fitting an mcgf_rs:
add_base.mcgf_rs(),
add_lagr.mcgf_rs(),
fit_lagr.mcgf_rs(),
krige.mcgf_rs(),
krige_new.mcgf_rs()
data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching pure spatial model fit_spatial <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "spatial", par_init_ls = list(c(c = 0.00005, gamma = 0.5)), par_fixed_ls = list(c(nugget = 0)) ) lapply(fit_spatial[1:2], function(x) x$fit) # Fit a regime-switching pure temporal model fit_temporal <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "temporal", par_init_ls = list( list(a = 0.8, alpha = 0.8), list(a = 0.1, alpha = 0.1) ) ) lapply(fit_temporal[1:2], function(x) x$fit) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) lapply(fit_sep[1:2], function(x) x$fit)data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching pure spatial model fit_spatial <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "spatial", par_init_ls = list(c(c = 0.00005, gamma = 0.5)), par_fixed_ls = list(c(nugget = 0)) ) lapply(fit_spatial[1:2], function(x) x$fit) # Fit a regime-switching pure temporal model fit_temporal <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "temporal", par_init_ls = list( list(a = 0.8, alpha = 0.8), list(a = 0.1, alpha = 0.1) ) ) lapply(fit_temporal[1:2], function(x) x$fit) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) lapply(fit_sep[1:2], function(x) x$fit)
Fit correlation Lagrangian models
fit_lagr(x, ...)fit_lagr(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to fit_lagr.mcgf() and fit_lagr.mcgf_rs() for more details.
A vector of estimated parameters.
mcgf
object.Parameter estimation for Lagrangian correlation functions for an mcgf
object.
## S3 method for class 'mcgf' fit_lagr( x, model = c("lagr_tri", "lagr_askey", "lagr_exp", "none"), method = c("wls", "mle"), optim_fn = c("nlminb", "optim", "other"), par_fixed = NULL, par_init, lower = NULL, upper = NULL, other_optim_fn = NULL, dists_base = FALSE, dists_lagr = NULL, ... )## S3 method for class 'mcgf' fit_lagr( x, model = c("lagr_tri", "lagr_askey", "lagr_exp", "none"), method = c("wls", "mle"), optim_fn = c("nlminb", "optim", "other"), par_fixed = NULL, par_init, lower = NULL, upper = NULL, other_optim_fn = NULL, dists_base = FALSE, dists_lagr = NULL, ... )
x |
An |
model |
Base model, one of |
method |
Parameter estimation methods, weighted least square ( |
optim_fn |
Optimization functions, one of |
par_fixed |
Fixed parameters. |
par_init |
Initial values for parameters to be optimized. |
lower |
Optional; lower bounds of parameters lambda, v1, v2, and k. |
upper |
Optional: upper bounds of parameters lambda, v1, v2, and k. |
other_optim_fn |
Optional, other optimization functions. The first two
arguments must be initial values for the parameters and a function to be
minimized respectively (same as that of |
dists_base |
Logical; if TRUE |
dists_lagr |
List of distance matrices/arrays. Used when |
... |
Additional arguments passed to |
This function fits the Lagrangian models using weighted least squares and
maximum likelihood estimation. The base model must be fitted first using
add_base() or base<-. Optimization functions such as nlminb and optim
are supported. Other functions are also supported by setting
optim_fn = "other" and supplying other_optim_fn. lower and upper are
lower and upper bounds of parameters in par_init and default bounds are
used if they are not specified.
Note that both wls and mle are heuristic approaches when x contains
observations from a subset of the discrete spatial domain, though estimation
results are close to that using the full spatial domain for large sample
sizes.
Since parameters for the base model and the Lagrangian model are estimated sequentially, more accurate estimation may be obtained if the full model is fitted all at once.
A list containing outputs from optimization functions of optim_fn.
Other functions on fitting an mcgf:
add_base.mcgf(),
add_lagr.mcgf(),
fit_base.mcgf(),
krige.mcgf(),
krige_new.mcgf()
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) fit_lagr$fitdata(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) fit_lagr$fit
mcgf_rs
object.Parameter estimation for Lagrangian correlation functions for an mcgf_rs
object.
## S3 method for class 'mcgf_rs' fit_lagr( x, model_ls, method_ls = "wls", optim_fn_ls = "nlminb", par_fixed_ls = list(NULL), par_init_ls, lower_ls = list(NULL), upper_ls = list(NULL), other_optim_fn_ls = list(NULL), dists_base_ls, dists_lagr_ls = list(NULL), rs = TRUE, ... )## S3 method for class 'mcgf_rs' fit_lagr( x, model_ls, method_ls = "wls", optim_fn_ls = "nlminb", par_fixed_ls = list(NULL), par_init_ls, lower_ls = list(NULL), upper_ls = list(NULL), other_optim_fn_ls = list(NULL), dists_base_ls, dists_lagr_ls = list(NULL), rs = TRUE, ... )
x |
An |
model_ls |
List of base models, each element must be one of |
method_ls |
List of parameter estimation methods, weighted least square
( |
optim_fn_ls |
List of optimization functions, each element must be one
of |
par_fixed_ls |
List of fixed parameters. |
par_init_ls |
List of initial values for parameters to be optimized. |
lower_ls |
Optional; list of lower bounds of parameters. |
upper_ls |
Optional: list of upper bounds of parameters. |
other_optim_fn_ls |
Optional, list of other optimization functions. The
first two arguments must be initial values for the parameters and a function
to be minimized respectively (same as that of |
dists_base_ls |
List of lists of distance matrices. If NULL, |
dists_lagr_ls |
List of distance matrices/arrays. Used when
|
rs |
Logical; if TRUE |
... |
Additional arguments passed to |
This functions is the regime-switching variant of fit_lagr.mcgf().
Arguments are in lists. The length of arguments that end in _ls must be 1
or the same as the number of regimes in x. If the length of an argument is
1, then it is set the same for all regimes. Refer to fit_lagr.mcgf() for
more details of the arguments.
Note that both wls and mle are heuristic approaches when x contains
observations from a subset of the discrete spatial domain, though estimation
results are close to that using the full spatial domain for large sample
sizes.
Since parameters for the base model and the Lagrangian model are estimated sequentially, more accurate estimation may be obtained if the full model is fitted all at once.
A list containing outputs from optimization functions of optim_fn.
Other functions on fitting an mcgf_rs:
add_base.mcgf_rs(),
add_lagr.mcgf_rs(),
fit_base.mcgf_rs(),
krige.mcgf_rs(),
krige_new.mcgf_rs()
data(sim3) sim3_mcgf <- mcgf_rs(sim3$data, dists = sim3$dists, label = sim3$label) sim3_mcgf <- add_acfs(sim3_mcgf, lag_max = 5) sim3_mcgf <- add_ccfs(sim3_mcgf, lag_max = 5) # Fit a fully symmetric model with known variables fit_fs <- fit_base( sim3_mcgf, lag_ls = 5, model_ls = "fs", rs = FALSE, par_init_ls = list(list(beta = 0)), par_fixed_ls = list(list( nugget = 0, c = 0.05, gamma = 0.5, a = 0.5, alpha = 0.2 )) ) # Set beta to 0 to fit a separable model with known variables fit_fs[[1]]$fit$par <- 0 # Store the fitted separable model to 'sim3_mcgf' sim3_mcgf <- add_base(sim3_mcgf, fit_base_ls = fit_fs) # Fit a regime-switching Lagrangian model. fit_lagr_rs <- fit_lagr( sim3_mcgf, model_ls = list("lagr_tri"), par_init_ls = list( list(v1 = -50, v2 = 50), list(v1 = 100, v2 = 100) ), par_fixed_ls = list(list(lambda = 0.2, k = 2)) ) lapply(fit_lagr_rs[1:2], function(x) x$fit)data(sim3) sim3_mcgf <- mcgf_rs(sim3$data, dists = sim3$dists, label = sim3$label) sim3_mcgf <- add_acfs(sim3_mcgf, lag_max = 5) sim3_mcgf <- add_ccfs(sim3_mcgf, lag_max = 5) # Fit a fully symmetric model with known variables fit_fs <- fit_base( sim3_mcgf, lag_ls = 5, model_ls = "fs", rs = FALSE, par_init_ls = list(list(beta = 0)), par_fixed_ls = list(list( nugget = 0, c = 0.05, gamma = 0.5, a = 0.5, alpha = 0.2 )) ) # Set beta to 0 to fit a separable model with known variables fit_fs[[1]]$fit$par <- 0 # Store the fitted separable model to 'sim3_mcgf' sim3_mcgf <- add_base(sim3_mcgf, fit_base_ls = fit_fs) # Fit a regime-switching Lagrangian model. fit_lagr_rs <- fit_lagr( sim3_mcgf, model_ls = list("lagr_tri"), par_init_ls = list( list(v1 = -50, v2 = 50), list(v1 = 100, v2 = 100) ), par_fixed_ls = list(list(lambda = 0.2, k = 2)) ) lapply(fit_lagr_rs[1:2], function(x) x$fit)
mcgf object.Check if an object is an mcgf object.
is.mcgf(x)is.mcgf(x)
x |
An Object. |
Logical; TRUE if x is of the mcgf class
data(sim1) is.mcgf(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) is.mcgf(sim1_mcgf)data(sim1) is.mcgf(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) is.mcgf(sim1_mcgf)
mcgf_rs object..Check if an object is an mcgf_rs object..
is.mcgf_rs(x) as.mcgf_rs(x, label, ncores = 1)is.mcgf_rs(x) as.mcgf_rs(x, label, ncores = 1)
x |
An Object. |
label |
A vector of regime labels. Its length must be the same as
the number rows in |
ncores |
Number of cpu cores used for computing in |
is.mcgf_rs returns a logical valud; TRUE if x is of the mcgf_rs
class. as.mcgf_rs coerces an mcgf object to an mcgf_rs object by adding
regime labels. Fitted base or Lagrangian models in x are kept.
data(sim2) is.mcgf_rs(sim2) sim2_mcgf <- mcgf(sim2$data, dists = sim2$dists) is.mcgf_rs(sim2_mcgf) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) is.mcgf_rs(sim2_mcgf) data(sim2) sim2_mcgf <- mcgf(sim2$data, dists = sim2$dists) sim2_mcgf <- as.mcgf_rs(sim2_mcgf, label = sim2$label)data(sim2) is.mcgf_rs(sim2) sim2_mcgf <- mcgf(sim2$data, dists = sim2$dists) is.mcgf_rs(sim2_mcgf) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) is.mcgf_rs(sim2_mcgf) data(sim2) sim2_mcgf <- mcgf(sim2$data, dists = sim2$dists) sim2_mcgf <- as.mcgf_rs(sim2_mcgf, label = sim2$label)
Generic function for computing kriging forecasts
krige(x, ...)krige(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to krige.mcgf() and krige.mcgf_rs() for more details.
Kriging results of x.
Generic function for computing kriging forecasts for new locations
krige_new(x, ...)krige_new(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to krige_new.mcgf() and krige_new.mcgf_rs() for more details.
Kriging results of x.
mcgf object.Obtain kriging forecasts for new locations for an mcgf object.
## S3 method for class 'mcgf' krige_new( x, newdata = NULL, locations_new = NULL, dists_new = NULL, newdata_new = NULL, sds_new = 1, model = c("all", "base"), interval = FALSE, level = 0.95, dists_new_base, ... )## S3 method for class 'mcgf' krige_new( x, newdata = NULL, locations_new = NULL, dists_new = NULL, newdata_new = NULL, sds_new = 1, model = c("all", "base"), interval = FALSE, level = 0.95, dists_new_base, ... )
x |
An |
newdata |
A data.frame with the same column names as |
locations_new |
A matrix of data.frame of 2D points of new locations,
first column longitude, second column latitude, both in decimal degrees.
Supply only if |
dists_new |
List of signed distance matrices (vectors) with names |
newdata_new |
Optional; a data.frame with the same number of rows as
|
sds_new |
The standard deviations of the new locations. Default is 1. |
model |
Which model to use. One of |
interval |
Logical; if TRUE, prediction intervals are computed. |
level |
A numeric scalar between 0 and 1 giving the confidence level for
the intervals (if any) to be calculated. Used when |
dists_new_base |
Optional; a distance array for all locations for the base model, with new locations in the end. Used for the base model. |
... |
Additional arguments. Not in use. |
It produces simple kriging forecasts for a zero-mean mcgf for new locations
given their coordinates or relative distances. It supports kriging for the
base model and the all model which is the general stationary model with
the base and Lagrangian model from x.
Users can either supply the coordinates via locations_new, or a list of
distance for all locations via dists_new, with new locations at the
end. dists_new will be used to calculate the new covariance matrices.
When locations_new is used, make sure x contains the attribute
locations of the coordinates of the old locations. When dists_new is
used, it should be a list of signed distance matrices of the same dimension,
where each row corresponds to the relative distances between a new location
and old locations in the same order as they appear in x.
If data for the new locations are available, use newdata_new to include
them and they will be used to calculate the kriging forecasts for the new
locations; otherwise only data of the old locations will be used via
newdata.
When interval = TRUE, confidence interval for each forecasts and each
horizon is given. Note that it does not compute confidence regions.
A list of kriging forecasts (and prediction intervals) for all locations.
Other functions on fitting an mcgf:
add_base.mcgf(),
add_lagr.mcgf(),
fit_base.mcgf(),
fit_lagr.mcgf(),
krige.mcgf()
data(sim1) sim1_mcgf <- mcgf(sim1$data, locations = sim1$locations) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) # Store the fitted Lagrangian model to 'sim1_mcgf' sim1_mcgf <- add_lagr(sim1_mcgf, fit_lagr = fit_lagr) # Calculate the simple kriging predictions and intervals for all locations locations_new <- rbind(c(-110, 55), c(-109, 54)) sim1_krige <- krige_new(sim1_mcgf, locations_new = locations_new, interval = TRUE )data(sim1) sim1_mcgf <- mcgf(sim1$data, locations = sim1$locations) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) # Store the fitted Lagrangian model to 'sim1_mcgf' sim1_mcgf <- add_lagr(sim1_mcgf, fit_lagr = fit_lagr) # Calculate the simple kriging predictions and intervals for all locations locations_new <- rbind(c(-110, 55), c(-109, 54)) sim1_krige <- krige_new(sim1_mcgf, locations_new = locations_new, interval = TRUE )
mcgf_rs object.Obtain kriging forecasts for new locations for an mcgf_rs object.
## S3 method for class 'mcgf_rs' krige_new( x, newdata = NULL, locations_new = NULL, dists_new_ls = NULL, newdata_new = NULL, sds_new_ls = 1, newlabel, soft = FALSE, prob, dists_new_base, model = c("all", "base"), interval = FALSE, level = 0.95, ... )## S3 method for class 'mcgf_rs' krige_new( x, newdata = NULL, locations_new = NULL, dists_new_ls = NULL, newdata_new = NULL, sds_new_ls = 1, newlabel, soft = FALSE, prob, dists_new_base, model = c("all", "base"), interval = FALSE, level = 0.95, ... )
x |
An |
newdata |
A data.frame with the same column names as |
locations_new |
A matrix of data.frame of 2D points of new locations,
first column longitude, second column latitude, both in decimal degrees.
Supply only if |
dists_new_ls |
List of signed distance matrices (vectors) with names |
newdata_new |
Optional; a data.frame with the same number of rows as
|
sds_new_ls |
List of the standard deviations of the new locations for
each regime. Format must be the same as the output from |
newlabel |
A vector of new regime labels. |
soft |
Logical; if true, soft forecasts (and bounds) are produced. |
prob |
Matrix with simplex rows. Number of columns must be the same as
unique labels in |
dists_new_base |
Optional, list of distance matrices for the base
model. Used when the base model is non-regime switching. Default is |
model |
Which model to use. One of |
interval |
Logical; if TRUE, prediction intervals are computed. |
level |
A numeric scalar between 0 and 1 giving the confidence level for
the intervals (if any) to be calculated. Used when |
... |
Additional arguments. |
It produces simple kriging forecasts for a zero-mean mcgf for new locations
given theri coordinates or relative distances. It supports kriging for the
base model and the all model which is the general stationary model with
the base and Lagrangian model from x.
Users can either supply the coordinates via locations_new, or a list of
distance for all locations via dists_new_ls, with new locations at the
end. dists_new_ls will be used to calculate the new covariance matrices.
When locations_new is used, make sure x contains the attribute
locations of the coordinates of the old locations. When dists_new_ls is
used, it should be a list of a list of signed distance matrices of the same
dimension, where each row corresponds to the relative distances between a new
location and old locations in the same order as they appear in x. If only
one list is provided, it will be used for all regimes.
When soft = TRUE, prob will be used to compute the soft forecasts
(weighted forecasts). The number of columns must match the number of unique
levels in x. The column order must be the same as the order of regimes as
in levels(attr(x, "label", exact = TRUE)). If not all regimes are seen in
newlabel, then only relevant columns in prob are used.
When interval = TRUE, confidence interval for each forecasts and each
horizon is given. Note that it does not compute confidence regions.
A list of kriging forecasts (and prediction intervals) for all locations.
Other functions on fitting an mcgf_rs:
add_base.mcgf_rs(),
add_lagr.mcgf_rs(),
fit_base.mcgf_rs(),
fit_lagr.mcgf_rs(),
krige.mcgf_rs()
data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, locations = sim2$locations, label = sim2$label ) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) # Store the fitted separable models to 'sim2_mcgf' sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep) # Calculate the simple kriging predictions and intervals for all locations locations_new <- rbind(c(-110, 55), c(-109, 54)) sim2_krige <- krige_new(sim2_mcgf, locations_new = locations_new, model = "base", interval = TRUE )data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, locations = sim2$locations, label = sim2$label ) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) # Store the fitted separable models to 'sim2_mcgf' sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep) # Calculate the simple kriging predictions and intervals for all locations locations_new <- rbind(c(-110, 55), c(-109, 54)) sim2_krige <- krige_new(sim2_mcgf, locations_new = locations_new, model = "base", interval = TRUE )
mcgf object.Obtain kriging forecasts for an mcgf object.
## S3 method for class 'mcgf' krige( x, newdata = NULL, model = c("all", "base", "empirical"), interval = FALSE, level = 0.95, ... )## S3 method for class 'mcgf' krige( x, newdata = NULL, model = c("all", "base", "empirical"), interval = FALSE, level = 0.95, ... )
x |
An |
newdata |
A data.frame with the same column names as |
model |
Which model to use. One of |
interval |
Logical; if TRUE, prediction intervals are computed. |
level |
A numeric scalar between 0 and 1 giving the confidence level for
the intervals (if any) to be calculated. Used when |
... |
Additional arguments. Give |
It produces simple kriging forecasts for a zero-mean mcgf. It supports
kriging for the empirical model, the base model, and the all model
which is the general stationary model with the base and Lagrangian model
from x.
When interval = TRUE, confidence interval for each forecasts and each
horizon is given. Note that it does not compute confidence regions.
A list of kriging forecasts (and prediction intervals).
Other functions on fitting an mcgf:
add_base.mcgf(),
add_lagr.mcgf(),
fit_base.mcgf(),
fit_lagr.mcgf(),
krige_new.mcgf()
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) # Store the fitted Lagrangian model to 'sim1_mcgf' sim1_mcgf <- add_lagr(sim1_mcgf, fit_lagr = fit_lagr) # Calculate the simple kriging predictions and intervals sim1_krige <- krige(sim1_mcgf, interval = TRUE) # Calculate RMSE for each location rmse <- sqrt(colMeans((sim1_mcgf - sim1_krige$fit)^2, na.rm = TRUE)) rmse # Calculate MAE for each location mae <- colMeans(abs(sim1_mcgf - sim1_krige$fit), na.rm = TRUE) mae # Calculate POPI for each location popi <- colMeans( sim1_mcgf < sim1_krige$lower | sim1_mcgf > sim1_krige$upper, na.rm = TRUE ) popidata(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5) sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5) # Fit a separable model and store it to 'sim1_mcgf' fit_sep <- fit_base( sim1_mcgf, model = "sep", lag = 5, par_init = c( c = 0.001, gamma = 0.5, a = 0.3, alpha = 0.5 ), par_fixed = c(nugget = 0) ) sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep) # Fit a Lagrangian model fit_lagr <- fit_lagr( sim1_mcgf, model = "lagr_tri", par_init = c(v1 = 300, v2 = 300, lambda = 0.15), par_fixed = c(k = 2) ) # Store the fitted Lagrangian model to 'sim1_mcgf' sim1_mcgf <- add_lagr(sim1_mcgf, fit_lagr = fit_lagr) # Calculate the simple kriging predictions and intervals sim1_krige <- krige(sim1_mcgf, interval = TRUE) # Calculate RMSE for each location rmse <- sqrt(colMeans((sim1_mcgf - sim1_krige$fit)^2, na.rm = TRUE)) rmse # Calculate MAE for each location mae <- colMeans(abs(sim1_mcgf - sim1_krige$fit), na.rm = TRUE) mae # Calculate POPI for each location popi <- colMeans( sim1_mcgf < sim1_krige$lower | sim1_mcgf > sim1_krige$upper, na.rm = TRUE ) popi
mcgf_rs object.Obtain kriging forecasts for an mcgf_rs object.
## S3 method for class 'mcgf_rs' krige( x, newdata = NULL, newlabel = NULL, soft = FALSE, prob, model = c("all", "base", "empirical"), interval = FALSE, level = 0.95, ... )## S3 method for class 'mcgf_rs' krige( x, newdata = NULL, newlabel = NULL, soft = FALSE, prob, model = c("all", "base", "empirical"), interval = FALSE, level = 0.95, ... )
x |
An |
newdata |
A data.frame with the same column names as |
newlabel |
A vector of new regime labels. |
soft |
Logical; if true, soft forecasts (and bounds) are produced. |
prob |
Matrix with simplex rows. Number of columns must be the same as
unique labels in |
model |
Which model to use. One of |
interval |
Logical; if TRUE, prediction intervals are computed. |
level |
A numeric scalar between 0 and 1 giving the confidence level for
the intervals (if any) to be calculated. Used when |
... |
Additional arguments. Give |
It produces simple kriging forecasts for a zero-mean mcgf. It supports
kriging for the empirical model, the base model, and the all model
which is the general stationary model with the base and Lagrangian model
from x.
When soft = TRUE, prob will be used to compute the soft forecasts
(weighted forecasts). The number of columns must match the number of unique
levels in x. The column order must be the same as the order of regimes as
in levels(attr(x, "label", exact = TRUE)). If not all regimes are seen in
newlabel, then only relevant columns in prob are used.
When interval = TRUE, confidence interval for each forecasts and each
horizon is given. Note that it does not compute confidence regions.
A list of kriging forecasts (and prediction intervals).
Other functions on fitting an mcgf_rs:
add_base.mcgf_rs(),
add_lagr.mcgf_rs(),
fit_base.mcgf_rs(),
fit_lagr.mcgf_rs(),
krige_new.mcgf_rs()
data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) # Store the fitted separable models to 'sim2_mcgf' sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep) # Calculate the simple kriging predictions and intervals sim2_krige <- krige(sim2_mcgf, model = "base", interval = TRUE) # Calculate RMSE for each location rmse <- sqrt(colMeans((sim2_mcgf - sim2_krige$fit)^2, na.rm = TRUE)) rmse # Calculate MAE for each location mae <- colMeans(abs(sim2_mcgf - sim2_krige$fit), na.rm = TRUE) mae # Calculate POPI for each location popi <- colMeans( sim2_mcgf < sim2_krige$lower | sim2_mcgf > sim2_krige$upper, na.rm = TRUE ) popidata(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5) sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5) # Fit a regime-switching separable model fit_sep <- fit_base( sim2_mcgf, lag_ls = 5, model_ls = "sep", par_init_ls = list(list( c = 0.00005, gamma = 0.5, a = 0.5, alpha = 0.5 )), par_fixed_ls = list(c(nugget = 0)) ) # Store the fitted separable models to 'sim2_mcgf' sim2_mcgf <- add_base(sim2_mcgf, fit_base_ls = fit_sep) # Calculate the simple kriging predictions and intervals sim2_krige <- krige(sim2_mcgf, model = "base", interval = TRUE) # Calculate RMSE for each location rmse <- sqrt(colMeans((sim2_mcgf - sim2_krige$fit)^2, na.rm = TRUE)) rmse # Calculate MAE for each location mae <- colMeans(abs(sim2_mcgf - sim2_krige$fit), na.rm = TRUE) mae # Calculate POPI for each location popi <- colMeans( sim2_mcgf < sim2_krige$lower | sim2_mcgf > sim2_krige$upper, na.rm = TRUE ) popi
Create mcgf object
mcgf(data, locations, dists, time, longlat = TRUE, origin = 1L)mcgf(data, locations, dists, time, longlat = TRUE, origin = 1L)
data |
Time series data set in space-wide format. |
locations |
A matrix of data.frame of 2D points, first column
x/longitude, second column y/latitude. Required when |
dists |
List of signed distance matrices on a 2D Euclidean Plane.
Required when |
time |
Optional, a vector of equally spaced time stamps. |
longlat |
Logical, if TURE |
origin |
Optional; used when |
An mcgf object extends the S3 class data.frame.
For inputs, data must be in space-wide format where rows correspond to
different time stamps and columns refer to spatial locations. Supply either
locations or dists. locations is a matrix or data.frame of 2D points
with first column x/longitude and second column y/latitude. By default it is
treated as a matrix of Earth's coordinates in decimal degrees. Number of rows
in locations must be the same as the number of columns of data. dists
must be a list of signed distance matrices with names h1, h2, and h.
If h is not given, it will be calculated as the Euclidean distance of h1
and h2. time is a vector of equally spaced time stamps. If it is not
supplied then data is assumed to be temporally equally spaced.
An mcgf object extends the S3 class data.frame, all methods remain valid
to the data part of the object.
An S3 object of class mcgf. As it inherits and extends the
data.frame class, all methods remain valid to the data part of the
object. Additional attributes may be assigned and extracted.
data <- cbind(S1 = 1:5, S2 = 4:8, S3 = 5:9) lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) obj <- mcgf(data, locations = locations) print(obj, "locations")data <- cbind(S1 = 1:5, S2 = 4:8, S3 = 5:9) lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) obj <- mcgf(data, locations = locations) print(obj, "locations")
Create mcgf_rs object
mcgf_rs(data, locations, dists, label, time, longlat = TRUE, origin = 1L)mcgf_rs(data, locations, dists, label, time, longlat = TRUE, origin = 1L)
data |
Time series data set in space-wide format. |
locations |
A matrix of data.frame of 2D points, first column
longitude, second column latitude, both in decimal degrees. Required when
|
dists |
List of signed distance matrices. Required when |
label |
A vector of regime labels. Its length must be the same as
the number rows in |
time |
Optional, a vector of equally spaced time stamps. |
longlat |
Logical, if TURE |
origin |
Optional; used when |
An mcgf_rs object extends the S3 classes mcgf and data.frame.
For inputs, data must be in space-wide format where rows correspond to
different time stamps and columns refer to spatial locations. Supply either
locations or dists. locations is a matrix or data.frame of 2D points
with first column x/longitude and second column y/latitude. By default it is
treated as a matrix of Earth's coordinates in decimal degrees. Number of rows
in locations must be the same as the number of columns of data. dists
must be a list of signed distance matrices with names h1, h2, and h.
If h is not given, it will be calculated as the Euclidean distance of h1
and h2. time is a vector of equally spaced time stamps. If it is not
supplied then data is assumed to be temporally equally spaced. label must
be a vector containing regime labels, and its length must be the same as the
number of rows in x.
An mcgf_rs object extends the S3 classes mcgf and data.frame, all
methods remain valid to the data part of the object.
An S3 object of class mcgf_rs. As it inherits and extends the
mcgf and then thedata.frame class, all methods remain valid to the
data part of the object. Additional attributes may be assigned and
extracted.
data <- cbind(S1 = 1:5, S2 = 4:8, S3 = 5:9) lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) label <- c(1, 1, 2, 2, 2) obj <- mcgf_rs(data, locations = locations, label = label) print(obj, "locations") print(obj, "label")data <- cbind(S1 = 1:5, S2 = 4:8, S3 = 5:9) lon <- c(110, 120, 130) lat <- c(50, 55, 60) locations <- cbind(lon, lat) label <- c(1, 1, 2, 2, 2) obj <- mcgf_rs(data, locations = locations, label = label) print(obj, "locations") print(obj, "label")
Simulate regime-switching Markov chain Gaussian field
mcgf_rs_sim( N, label, base_ls, lagrangian_ls, par_base_ls, par_lagr_ls, lambda_ls, dists_ls, sd_ls, lag_ls, scale_time = 1, init = 0, mu_c_ls = list(0), mu_p_ls = list(0), return_all = FALSE )mcgf_rs_sim( N, label, base_ls, lagrangian_ls, par_base_ls, par_lagr_ls, lambda_ls, dists_ls, sd_ls, lag_ls, scale_time = 1, init = 0, mu_c_ls = list(0), mu_p_ls = list(0), return_all = FALSE )
N |
Sample size. |
label |
Vector of regime labels of the same length as |
base_ls |
List of base model, |
lagrangian_ls |
List of Lagrangian model, "none" or |
par_base_ls |
List of parameters for the base model. |
par_lagr_ls |
List of parameters for the Lagrangian model. |
lambda_ls |
List of weight of the Lagrangian term,
|
dists_ls |
List of distance matrices or arrays. |
sd_ls |
List of standard deviation for each location. |
lag_ls |
List of time lags. |
scale_time |
Scale of time unit, default is 1. Elements in |
init |
Initial samples, default is 0. |
mu_c_ls, mu_p_ls
|
List of means of current and past. |
return_all |
Logical; if TRUE the joint covariance matrix, arrays of distances and time lag are returned. |
Simulated regime-switching Markov chain Gaussian field with
user-specified covariance structures. The simulation is done by kriging.
The output data is in space-wide format. Each element in dists_ls must
contain h for symmetric models, and h1 and h2 for general stationary
models. init can be a scalar or a vector of appropriate size.
List elements in sd_ls, mu_c_ls, and mu_p_ls must be vectors of
appropriate sizes.
Other simulations of Markov chain Gaussian fields:
mcgf_sim()
par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) par_lagr <- list(v1 = 5, v2 = 10) h1 <- matrix(c(0, 5, -5, 0), nrow = 2) h2 <- matrix(c(0, 8, -8, 0), nrow = 2) h <- sqrt(h1^2 + h2^2) dists <- list(h = h, h1 = h1, h2 = h2) set.seed(123) label <- sample(1:2, 1000, replace = TRUE) X <- mcgf_rs_sim( N = 1000, label = label, base_ls = list("sep"), lagrangian_ls = list("none", "lagr_tri"), lambda_ls = list(0, 0.5), par_base_ls = list(par_base), par_lagr_ls = list(NULL, par_lagr), dists_ls = list(dists, dists) ) # plot.ts(X[, -1])par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) par_lagr <- list(v1 = 5, v2 = 10) h1 <- matrix(c(0, 5, -5, 0), nrow = 2) h2 <- matrix(c(0, 8, -8, 0), nrow = 2) h <- sqrt(h1^2 + h2^2) dists <- list(h = h, h1 = h1, h2 = h2) set.seed(123) label <- sample(1:2, 1000, replace = TRUE) X <- mcgf_rs_sim( N = 1000, label = label, base_ls = list("sep"), lagrangian_ls = list("none", "lagr_tri"), lambda_ls = list(0, 0.5), par_base_ls = list(par_base), par_lagr_ls = list(NULL, par_lagr), dists_ls = list(dists, dists) ) # plot.ts(X[, -1])
Simulate Markov chain Gaussian field
mcgf_sim( N, base = c("sep", "fs"), lagrangian = c("none", "lagr_tri", "lagr_askey"), par_base, par_lagr, lambda, dists, sd = 1, lag = 1, scale_time = 1, horizon = 1, init = 0, mu_c = 0, mu_p = 0, return_all = FALSE )mcgf_sim( N, base = c("sep", "fs"), lagrangian = c("none", "lagr_tri", "lagr_askey"), par_base, par_lagr, lambda, dists, sd = 1, lag = 1, scale_time = 1, horizon = 1, init = 0, mu_c = 0, mu_p = 0, return_all = FALSE )
N |
Sample size. |
base |
Base model, |
lagrangian |
Lagrangian model, "none" or |
par_base |
Parameters for the base model (symmetric). |
par_lagr |
Parameters for the Lagrangian model. |
lambda |
Weight of the Lagrangian term, |
dists |
Distance matrices or arrays. |
sd |
Standard deviation for each location. |
lag |
Time lag. |
scale_time |
Scale of time unit, default is 1. |
horizon |
Forecast horizon, default is 1. |
init |
Initial samples, default is 0. |
mu_c, mu_p
|
Means of current and past. |
return_all |
Logical; if TRUE the joint covariance matrix, arrays of distances and time lag are returned. |
Simulated Markov chain Gaussian field with user-specified covariance
structure. The simulation is done by kriging. The output data is in
space-wide format. dists must contain h for symmetric models, and h1
and h2 for general stationary models. horizon controls forecasting
horizon. sd, mu_c, mu_p, and init must be vectors of appropriate
sizes.
Other simulations of Markov chain Gaussian fields:
mcgf_rs_sim()
par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) par_lagr <- list(v1 = 5, v2 = 10) h1 <- matrix(c(0, 5, -5, 0), nrow = 2) h2 <- matrix(c(0, 8, -8, 0), nrow = 2) h <- sqrt(h1^2 + h2^2) dists <- list(h = h, h1 = h1, h2 = h2) set.seed(123) X <- mcgf_sim( N = 1000, base = "sep", lagrangian = "lagr_tri", lambda = 0.5, par_base = par_base, par_lagr = par_lagr, dists = dists ) plot.ts(X)par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5) par_t <- list(a = 1, alpha = 0.5) par_base <- list(par_s = par_s, par_t = par_t) par_lagr <- list(v1 = 5, v2 = 10) h1 <- matrix(c(0, 5, -5, 0), nrow = 2) h2 <- matrix(c(0, 8, -8, 0), nrow = 2) h <- sqrt(h1^2 + h2^2) dists <- list(h = h, h1 = h1, h2 = h2) set.seed(123) X <- mcgf_sim( N = 1000, base = "sep", lagrangian = "lagr_tri", lambda = 0.5, par_base = par_base, par_lagr = par_lagr, dists = dists ) plot.ts(X)
mcgf objectsGeneric function for displaying fitted models for mcgf objects
model(x, ...)model(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to model.mcgf() and model.mcgf_rs() for more details.
Details of the fitted models.
mcgf or mcgf_rs objectDisplay fitted models for an mcgf or mcgf_rs object
## S3 method for class 'mcgf' model( x, model = c("all", "base", "lagrangian"), old = FALSE, print_model = TRUE, ... ) ## S3 method for class 'mcgf_rs' model( x, model = c("all", "base", "lagrangian"), old = FALSE, print_model = TRUE, ... )## S3 method for class 'mcgf' model( x, model = c("all", "base", "lagrangian"), old = FALSE, print_model = TRUE, ... ) ## S3 method for class 'mcgf_rs' model( x, model = c("all", "base", "lagrangian"), old = FALSE, print_model = TRUE, ... )
x |
An mcgf object. |
model |
Which model to display. |
old |
Logical; TRUE if the old model needs to be printed. |
print_model |
Logical; TRUE if time lag and forecast horizon need to be printed. |
... |
Additional arguments. Not in use. |
For mcgf and mcgf_rs objects, model() displays the fitted models and
their parameters. When old = TRUE, the old model is printed as well. Note
that the old model is not used for parameter estimation or for kriging.
None (invisible NULL).
mcgf object.Print an mcgf object.
## S3 method for class 'mcgf' print(x, attr = ".Data", ...)## S3 method for class 'mcgf' print(x, attr = ".Data", ...)
x |
An |
attr |
Attribute to be printed. |
... |
Optional arguments to print methods. |
No return value, called for side effects.
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) print(sim1_mcgf, "dists")data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) print(sim1_mcgf, "dists")
Generate random distance matrices
rdists(N, names, scale = 100)rdists(N, names, scale = 100)
N |
Number of locations. |
names |
Names of locations. |
scale |
Scale of the distance matrices. Default is 100. |
This function generates random distance matrices using rnorm. scale
controls the scale of the distance matrices.
List of signed distances.
set.seed(123) rdists(3) rdists(3, scale = 1) rdists(3, names = LETTERS[1:3])set.seed(123) rdists(3) rdists(3, scale = 1) rdists(3, names = LETTERS[1:3])
Calculate standard deviation for each location under each regime.
sd_rs(x, label)sd_rs(x, label)
x |
A |
label |
A vector of regime labels. Its length must be the same as
the number rows in |
A list of standard deviations for each regime.
set.seed(123) x <- matrix(rnorm(200), nrow = 100) label <- sample(1:2, 100, replace = TRUE) sd_rs(x, label = factor(label))set.seed(123) x <- matrix(rnorm(200), nrow = 100) label <- sample(1:2, 100, replace = TRUE) sd_rs(x, label = factor(label))
Generic function for standard deviations for each column
sds(x, ...)sds(x, ...)
x |
An R object. |
... |
Additional parameters or attributes. |
Refer to sds.mcgf() and sds.mcgf_rs() for more details.
A vector of standard deviations for mcgf objects, or that plus
a list of regime-switching standard deviations for mcgf_rs objects.
mcgf or
mcgf_rs object.Extract, calculate, or assign standard deviations for an mcgf or
mcgf_rs object.
## S3 method for class 'mcgf' sds(x, ...) ## S3 method for class 'mcgf_rs' sds(x, replace = FALSE, ...) sds(x) <- value## S3 method for class 'mcgf' sds(x, ...) ## S3 method for class 'mcgf_rs' sds(x, replace = FALSE, ...) sds(x) <- value
x |
An |
... |
Additional parameters or attributes. Not in use. |
replace |
Logical; if TRUE, |
value |
A vector (or list of vectors) of standard deviations for all stations (under each regime and combined). |
For mcgf objects, sds() extracts or computes the empirical standard
deviations. The output is a vector of sds.
For mcgf_rs objects, sds() extracts or computes the regime-switching
empirical standard deviations. The output is a list of vectors of sds. Each
element in the list corresponds to the sds for a regime.
sds<- assigns sds to x. Use add_ccfs() to add both ccfs and
sds to x.
sds() returns empirical (regime-switching) standard deviations.
data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sds(sim1_mcgf) data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sds(sim2_mcgf) data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_sds <- sds(sim1_mcgf) sds(sim1_mcgf) <- sim1_sds data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_sds <- sds(sim2_mcgf) sds(sim2_mcgf) <- sim2_sdsdata(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sds(sim1_mcgf) data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sds(sim2_mcgf) data(sim1) sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists) sim1_sds <- sds(sim1_mcgf) sds(sim1_mcgf) <- sim1_sds data(sim2) sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label) sim2_sds <- sds(sim2_mcgf) sds(sim2_mcgf) <- sim2_sds
Simulated MCGF for 10 locations.
sim1sim1
sim1: a list containing a data.frame with 1000 rows and 10 columns
and a list of distances
sim1 contains a simulated MCGF for 10 locations. It is simulated with a
separable base model and a triangular Lagrangian model. The true parameters
for the base model are: , and those for the Lagrangian model are:
Other (simulated) datasets:
sim2,
sim3,
wind
# Code used to generate `sim1` library(mcgf) set.seed(123) x <- stats::rnorm(10, -110) y <- stats::rnorm(10, 50) locations <- cbind(x, y) h <- find_dists(locations, longlat = TRUE) N <- 1000 lag <- 5 par_base <- list( par_s = list(nugget = 0, c = 0.001, gamma = 0.5), par_t = list(a = 0.5, alpha = 0.8) ) par_lagr <- list(v1 = 200, v2 = 200, k = 2) sim1 <- mcgf_sim( N = N, base = "sep", lagrangian = "lagr_tri", par_base = par_base, par_lagr = par_lagr, lambda = 0.2, dists = h, lag = lag ) sim1 <- sim1[-c(1:(lag + 1)), ] rownames(sim1) <- 1:nrow(sim1) sim1 <- list(data = sim1, locations = locations, dists = h)# Code used to generate `sim1` library(mcgf) set.seed(123) x <- stats::rnorm(10, -110) y <- stats::rnorm(10, 50) locations <- cbind(x, y) h <- find_dists(locations, longlat = TRUE) N <- 1000 lag <- 5 par_base <- list( par_s = list(nugget = 0, c = 0.001, gamma = 0.5), par_t = list(a = 0.5, alpha = 0.8) ) par_lagr <- list(v1 = 200, v2 = 200, k = 2) sim1 <- mcgf_sim( N = N, base = "sep", lagrangian = "lagr_tri", par_base = par_base, par_lagr = par_lagr, lambda = 0.2, dists = h, lag = lag ) sim1 <- sim1[-c(1:(lag + 1)), ] rownames(sim1) <- 1:nrow(sim1) sim1 <- list(data = sim1, locations = locations, dists = h)
Simulated RS-MCGF for 10 locations.
sim2sim2
sim2: a list containing a data.frame with 1000 rows and 10 columns,
a list of distances, and a vector of regime labels.
sim2 contains a simulated RS-MCGF for 10 locations. It is simulated with
a regime-switching separable base model. The true parameters for the base
model are:
Other (simulated) datasets:
sim1,
sim3,
wind
# Code used to generate `sim2` library(mcgf) set.seed(123) x <- stats::rnorm(10, -110) y <- stats::rnorm(10, 50) locations <- cbind(x, y) h <- find_dists(locations, longlat = TRUE) # simulate regimes K <- 2 N <- 1000 lag <- 5 tran_mat <- matrix(rnorm(K^2, mean = 0.06 / (K - 1), sd = 0.01), nrow = K) diag(tran_mat) <- rnorm(K, mean = 0.94, sd = 0.1) tran_mat <- sweep(abs(tran_mat), 1, rowSums(tran_mat), `/`) tran_mat # [,1] [,2] # [1,] 0.94635675 0.05364325 # [2,] 0.06973429 0.93026571 regime <- rep(NA, N) regime[1] <- 1 for (n in 2:(N)) { regime[n] <- sample(1:K, 1, prob = tran_mat[regime[n - 1], ]) } table(regime) # regime # 1 2 # 567 433 # simulate RS MCGF par_base1 <- list( par_s = list(nugget = 0, c = 0.001, gamma = 0.5), par_t = list(a = 0.5, alpha = 0.2) ) par_base2 <- list( par_s = list(nugget = 0, c = 0.004, gamma = 0.5), par_t = list(a = 0.3, alpha = 0.9) ) sim2 <- mcgf_rs_sim( N = N, label = regime, base_ls = list("sep"), lagrangian_ls = list("none"), par_base_ls = list(par_base1, par_base2), lambda_ls = list(0.1, 0.3), lag_ls = list(lag, lag), dists_ls = list(h, h) ) sim2 <- sim2[-c(1:(lag + 1)), ] rownames(sim2) <- 1:nrow(sim2) sim2 <- list( data = sim2[, -1], locations = locations, dists = h, label = sim2[, 1] )# Code used to generate `sim2` library(mcgf) set.seed(123) x <- stats::rnorm(10, -110) y <- stats::rnorm(10, 50) locations <- cbind(x, y) h <- find_dists(locations, longlat = TRUE) # simulate regimes K <- 2 N <- 1000 lag <- 5 tran_mat <- matrix(rnorm(K^2, mean = 0.06 / (K - 1), sd = 0.01), nrow = K) diag(tran_mat) <- rnorm(K, mean = 0.94, sd = 0.1) tran_mat <- sweep(abs(tran_mat), 1, rowSums(tran_mat), `/`) tran_mat # [,1] [,2] # [1,] 0.94635675 0.05364325 # [2,] 0.06973429 0.93026571 regime <- rep(NA, N) regime[1] <- 1 for (n in 2:(N)) { regime[n] <- sample(1:K, 1, prob = tran_mat[regime[n - 1], ]) } table(regime) # regime # 1 2 # 567 433 # simulate RS MCGF par_base1 <- list( par_s = list(nugget = 0, c = 0.001, gamma = 0.5), par_t = list(a = 0.5, alpha = 0.2) ) par_base2 <- list( par_s = list(nugget = 0, c = 0.004, gamma = 0.5), par_t = list(a = 0.3, alpha = 0.9) ) sim2 <- mcgf_rs_sim( N = N, label = regime, base_ls = list("sep"), lagrangian_ls = list("none"), par_base_ls = list(par_base1, par_base2), lambda_ls = list(0.1, 0.3), lag_ls = list(lag, lag), dists_ls = list(h, h) ) sim2 <- sim2[-c(1:(lag + 1)), ] rownames(sim2) <- 1:nrow(sim2) sim2 <- list( data = sim2[, -1], locations = locations, dists = h, label = sim2[, 1] )
Simulated RS-MCGF for 20 locations.
sim3sim3
sim3: a list containing a data.frame with 5000 rows and 20 columns
and a list of locations.
sim3 contains a simulated RS-MCGF for 20 locations. It is simulated with
the same base model and a regime-switching Lagrangian model. The true
parameters for the base model are: , and the true parameters for the
Lagrangian model are
For parameter estimation, the base model is assumed known and is used to estimate the regime-switching prevailing winds.
Other (simulated) datasets:
sim1,
sim2,
wind
# Code used to generate `sim3` library(mcgf) set.seed(123) x <- stats::rnorm(10, -110) y <- stats::rnorm(10, 50) locations <- cbind(x, y) h <- find_dists(locations, longlat = TRUE) # simulate regimes K <- 2 N <- 1000 lag <- 5 tran_mat <- matrix(rnorm(K^2, mean = 0.06 / (K - 1), sd = 0.01), nrow = K) diag(tran_mat) <- rnorm(K, mean = 0.94, sd = 0.1) tran_mat <- sweep(abs(tran_mat), 1, rowSums(tran_mat), `/`) tran_mat # [,1] [,2] # [1,] 0.94635675 0.05364325 # [2,] 0.06973429 0.93026571 regime <- rep(NA, N) regime[1] <- 1 for (n in 2:(N)) { regime[n] <- sample(1:K, 1, prob = tran_mat[regime[n - 1], ]) } table(regime) # regime # 1 2 # 567 433 # simulate RS MCGF par_base <- list( par_s = list(nugget = 0, c = 0.05, gamma = 0.5), par_t = list(a = 0.5, alpha = 0.2) ) par_lagr1 <- list(v1 = -100, v2 = 100, k = 2) par_lagr2 <- list(v1 = 200, v2 = 200, k = 2) sim3 <- mcgf_rs_sim( N = N, label = regime, base_ls = list("sep"), lagrangian_ls = list("lagr_tri"), par_base_ls = list(par_base), par_lagr_ls = list(par_lagr1, par_lagr2), lambda_ls = list(0.2, 0.2), lag_ls = list(lag, lag), dists_ls = list(h, h) ) sim3 <- sim3[-c(1:(lag + 1)), ] rownames(sim3) <- 1:nrow(sim3) sim3 <- list( data = sim3[, -1], locations = locations, dists = h, label = sim3[, 1] )# Code used to generate `sim3` library(mcgf) set.seed(123) x <- stats::rnorm(10, -110) y <- stats::rnorm(10, 50) locations <- cbind(x, y) h <- find_dists(locations, longlat = TRUE) # simulate regimes K <- 2 N <- 1000 lag <- 5 tran_mat <- matrix(rnorm(K^2, mean = 0.06 / (K - 1), sd = 0.01), nrow = K) diag(tran_mat) <- rnorm(K, mean = 0.94, sd = 0.1) tran_mat <- sweep(abs(tran_mat), 1, rowSums(tran_mat), `/`) tran_mat # [,1] [,2] # [1,] 0.94635675 0.05364325 # [2,] 0.06973429 0.93026571 regime <- rep(NA, N) regime[1] <- 1 for (n in 2:(N)) { regime[n] <- sample(1:K, 1, prob = tran_mat[regime[n - 1], ]) } table(regime) # regime # 1 2 # 567 433 # simulate RS MCGF par_base <- list( par_s = list(nugget = 0, c = 0.05, gamma = 0.5), par_t = list(a = 0.5, alpha = 0.2) ) par_lagr1 <- list(v1 = -100, v2 = 100, k = 2) par_lagr2 <- list(v1 = 200, v2 = 200, k = 2) sim3 <- mcgf_rs_sim( N = N, label = regime, base_ls = list("sep"), lagrangian_ls = list("lagr_tri"), par_base_ls = list(par_base), par_lagr_ls = list(par_lagr1, par_lagr2), lambda_ls = list(0.2, 0.2), lag_ls = list(lag, lag), dists_ls = list(h, h) ) sim3 <- sim3[-c(1:(lag + 1)), ] rownames(sim3) <- 1:nrow(sim3) sim3 <- list( data = sim3[, -1], locations = locations, dists = h, label = sim3[, 1] )
Daily average wind speeds for 1961-1978 at 11 synoptic meteorological stations in the Republic of Ireland (Haslett and raftery 1989). Wind speeds are in m/s. De-trended data sets are also provided.
windwind
wind: a list containing a data.frame with 6574 rows and 12 columns,
and a list of locations.
The data were obtained from the gstat package, and were modified so that
the first column is the time stamps. Locations of the 11 stations are given
in wind_loc. wind_train and wind_test contain de-trended and
square-root transformed train (1961-1970) and test (1971-1978) data sets.
See Gneiting et al. (2006) for de-trending details. wind_trend contains
the estimated annual trend and station-wise mean from the training dataset.
Haslett, J. and Raftery, A. E. (1989). Space-time Modelling with Long-memory Dependence: Assessing Ireland's Wind Power Resource (with Discussion). Applied Statistics 38, 1-50.
Gneiting, T., Genton, M., & Guttorp, P. (2006). Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry. In C&H/CRC Monographs on Statistics & Applied Probability (pp. 151–175). Chapman and Hall/CRC.
Other (simulated) datasets:
sim1,
sim2,
sim3