doc/simulation_and_estimation.R
In Sondre91/starmagarch: Estimation of spatio-temporal ARMA-GARCH models
## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
## ----parameters, eval=TRUE----------------------------------------------------
parameters <- list(
mu = 5,
phi = matrix(c(.8, .1), ncol = 1), #temporal order 1, spatial order 2
theta = matrix(c(-.42, -.2), ncol = 1), #temporal order 1, spatial order 2
omega = .9,
alpha = matrix(c(.09, .13,
.03, .07), ncol = 2), # temporal order 2, spatial order 2
beta = matrix(c(.5, .15), ncol = 1) #temporal order 1, spatial order 2
)
sum(parameters$alpha,parameters$beta)
## ----neighbourmatrix, eval = TRUE---------------------------------------------
# spatial dimension:
m <- c(25, 1)
library(starmagarch)
W <- create.neighbourhood.array(m = m, sp = 3, type = "rook", torus =TRUE)
## ----simulation, eval = TRUE, fig.width = 10----------------------------------
set.seed(1234)
y <- simSTARMAGARCH(parameters, n = 2500, m = m, W=W, burnin = 500) # 1
#y <- simSTARMAGARCH(parameters, n = 2500, m = m, burnin = 500, # 2
#type= "rook", torus = TRUE)
## ----plotting_data------------------------------------------------------------
library(ggplot2)
library(reshape2)
ggplot(data=melt(y), aes(Var2,Var1))+ geom_raster(aes(fill = value))+
scale_fill_gradient2(low="blue", mid="white", high = "red", midpoint = mean(y)) + xlab("Time") + ylab("Space") +
theme_bw()
## ----initial_parameters, eval = TRUE------------------------------------------
initial.parameters <- list(
mu = mean(y),
phi = matrix(c(.7, .01), ncol = 1),
theta = matrix(c(.01, .01), ncol = 1),
omega = 1,
alpha = matrix(c(.01, .01,
.01, .01), ncol = 2),
beta = matrix(c(.01, .01), ncol = 1)
)
## ----creatingLikelihood, eval = TRUE------------------------------------------
# Create likelihood object:
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters=initial.parameters)
# To save time, we use the true parameters as initial values:
f <- CreateLikelihood(y, W=W,
init = apply(y,1,var), parameters=parameters)
## ----fitting_model, eval = TRUE-----------------------------------------------
fit <- fitSTARMAGARCH(f, data = y, print = FALSE)
summary(fit)
## ----plotting_fit,eval = TRUE, fig.show='hold', fig.height = 5----------------
plot(fit)
plot_garch(fit)
## ----comparing_results--------------------------------------------------------
round(rbind(unlist(parameters), round(coef(fit),4)), 4)
## ----STGARCH, eval = FALSE----------------------------------------------------
# parameters <- list(
# mu = 0,
# phi = matrix(0, ncol = 1), #temporal order 1, spatial order 2
# theta = matrix(0, ncol = 1), #temporal order 1, spatial order 2
# omega = .9,
# alpha = matrix(c(.09, .13,
# .03, .07), ncol = 2), # temporal order 2, spatial order 2
# beta = matrix(c(.5, .15), ncol = 1) #temporal order 1, spatial order 2
# )
# y <- simSTARMAGARCH(parameters, n = 2500, m = c(25,1), W = W)
#
# initial.parameters <- list(
# mu = mean(y),
# phi = matrix(c(.7, .01), ncol = 1),
# theta = matrix(c(.01, .01), ncol = 1),
# omega = 1,
# alpha = matrix(c(.01, .01,
# .01, .01), ncol = 2),
# beta = matrix(c(.01, .01), ncol = 1)
# )
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters)
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> mu 0.01272265 0.009833892 1.2937556 9.787493e-02
# #> phi1 -0.37973220 0.282238217 -1.3454315 8.924296e-02
# #> phi2 0.37536087 0.783248661 0.4792359 3.158854e-01
# #> theta1 0.37367411 0.283705318 1.3171206 9.389911e-02
# #> theta2 -0.36493089 0.791497331 -0.4610639 3.223764e-01
# #> omega 0.98304477 0.066042385 14.8850586 2.060627e-50
# #> alpha1 0.08262752 0.006244003 13.2331007 2.825359e-40
# #> alpha2 0.14105291 0.011764199 11.9900142 2.004181e-33
# #> alpha3 0.03092677 0.007764663 3.9830156 3.402315e-05
# #> alpha4 0.06686734 0.014844508 4.5045170 3.326203e-06
# #> beta1 0.51746041 0.033736850 15.3381362 2.126149e-53
# #> beta2 0.10477532 0.048024420 2.1817093 1.456550e-02
# #>
# #>
# #> Standardized residual standard error: 1 .
## ----STGARCH_with_map, eval = FALSE-------------------------------------------
# # Use "map"" to fix parameters to zero:
# initial.parameters$mu <- 0
# initial.parameters$phi <- matrix(0, ncol=1)
# initial.parameters$theta <- matrix(0, ncol=1)
# map <- list()
# map$mu <- as.factor(NA)
# map$phi <- as.factor(NA)
# map$theta <- as.factor(NA)
# dim(map$theta) <- dim(map$phi) <- c(1,1)
# map
# #> $mu
# #> [1] <NA>
# #> Levels:
# #>
# #> $phi
# #> [,1]
# #> [1,] <NA>
# #> Levels:
# #>
# #> $theta
# #> [,1]
# #> [1,] <NA>
# #> Levels:
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters, map = map)
#
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> omega 0.98281266 0.066025733 14.885297 2.053285e-50
# #> alpha1 0.08264733 0.006242327 13.239826 2.583416e-40
# #> alpha2 0.14108928 0.011764874 11.992417 1.946865e-33
# #> alpha3 0.03103404 0.007765063 3.996624 3.212613e-05
# #> alpha4 0.06653875 0.014844846 4.482279 3.692497e-06
# #> beta1 0.51727367 0.033725151 15.337920 2.133229e-53
# #> beta2 0.10519927 0.048014155 2.191005 1.422570e-02
# #>
# #>
# #> Standardized residual standard error: 1 .
# #> AIC: 148332.7 BIC: 148396
#
# round(rbind(unlist(parameters)[-(1:3)], fit$coefficients),4)
# #> omega alpha1 alpha2 alpha3 alpha4 beta1 beta2
# #> [1,] 0.9000 0.0900 0.1300 0.030 0.0700 0.5000 0.1500
# #> [2,] 0.9828 0.0826 0.1411 0.031 0.0665 0.5173 0.1052
## ----STARMA_with_map, eval = FALSE--------------------------------------------
# parameters <- list(
# mu = 5,
# phi = matrix(c(.8, .1), ncol = 1), #temporal order 1, spatial order 2
# theta = matrix(c(-.42, -.2), ncol = 1), #temporal order 1, spatial order 2
# omega = 30,
# alpha = matrix(0, ncol = 1), # temporal order 2, spatial order 2
# beta = matrix(0, ncol = 1) #temporal order 1, spatial order 2
# )
# y <- simSTARMAGARCH(parameters, n = 2500, m = c(25,1), W = W)
# initial.parameters <- list(
# mu = mean(y),
# phi = matrix(c(.7, .01), ncol = 1),
# theta = matrix(c(.01, .01), ncol = 1),
# omega = 1,
# alpha = matrix(c(.01, .01,
# .01, .01), ncol = 2),
# beta = matrix(c(.01, .01), ncol = 1)
# )
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters)
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> mu 5.0714676601 0.076651590 6.616259e+01 0.000000e+00
# #> phi1 0.7977517884 0.005226702 1.526301e+02 0.000000e+00
# #> phi2 0.1119027906 0.010694371 1.046371e+01 6.339603e-26
# #> theta1 -0.4178454614 0.007787193 -5.365803e+01 0.000000e+00
# #> theta2 -0.2233686304 0.016775178 -1.331543e+01 9.414894e-41
# #> omega 29.8237638244 15.355764525 1.942187e+00 2.605724e-02
# #> alpha1 0.0000000100 0.002948183 3.391920e-06 4.999986e-01
# #> alpha2 0.0005736162 NaN NaN NaN
# #> alpha3 0.0001235004 0.002756660 4.480074e-02 4.821331e-01
# #> alpha4 0.0001525837 0.009304228 1.639939e-02 4.934579e-01
# #> beta1 0.0000000100 NaN NaN NaN
# #> beta2 0.0000000100 NaN NaN NaN
# #>
# #>
# #> Standardized residual standard error: 1 .
# #> AIC: 194676 BIC: 194784.5
#
# # Use "map"" to fix parameters to zero:
# initial.parameters$alpha <- matrix(0, ncol=1)
# initial.parameters$beta <- matrix(0, ncol=1)
# map <- list()
# map$alpha <- as.factor(NA)
# map$beta <- as.factor(NA)
# dim(map$alpha) <- dim(map$beta) <- c(1,1)
# map
# #> $alpha
# #> [,1]
# #> [1,] <NA>
# #> Levels:
# #>
# #> $beta
# #> [,1]
# #> [1,] <NA>
# #> Levels:
#
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters, map = map)
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> mu 5.0714315 0.076639614 66.17246 0.000000e+00
# #> phi1 0.7977492 0.005225273 152.67130 0.000000e+00
# #> phi2 0.1118951 0.010696428 10.46098 6.525081e-26
# #> theta1 -0.4178449 0.007784903 -53.67374 0.000000e+00
# #> theta2 -0.2233527 0.016775596 -13.31414 9.577871e-41
# #> omega 29.8436922 0.168888961 176.70600 0.000000e+00
# #>
# #>
# #> Standardized residual standard error: 1 .
# #> AIC: 194664 BIC: 194718.2
#
# round(rbind(unlist(parameters)[1:6],coef(fit)), 4)
# #> mu phi1 phi2 theta1 theta2 omega
# #> [1,] 5.0000 0.8000 0.1000 -0.4200 -0.2000 30.0000
# #> [2,] 5.0714 0.7977 0.1119 -0.4178 -0.2234 29.8437
Sondre91/starmagarch documentation built on July 16, 2025, 4:53 p.m.
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## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
## ----parameters, eval=TRUE----------------------------------------------------
parameters <- list(
mu = 5,
phi = matrix(c(.8, .1), ncol = 1), #temporal order 1, spatial order 2
theta = matrix(c(-.42, -.2), ncol = 1), #temporal order 1, spatial order 2
omega = .9,
alpha = matrix(c(.09, .13,
.03, .07), ncol = 2), # temporal order 2, spatial order 2
beta = matrix(c(.5, .15), ncol = 1) #temporal order 1, spatial order 2
)
sum(parameters$alpha,parameters$beta)
## ----neighbourmatrix, eval = TRUE---------------------------------------------
# spatial dimension:
m <- c(25, 1)
library(starmagarch)
W <- create.neighbourhood.array(m = m, sp = 3, type = "rook", torus =TRUE)
## ----simulation, eval = TRUE, fig.width = 10----------------------------------
set.seed(1234)
y <- simSTARMAGARCH(parameters, n = 2500, m = m, W=W, burnin = 500) # 1
#y <- simSTARMAGARCH(parameters, n = 2500, m = m, burnin = 500, # 2
#type= "rook", torus = TRUE)
## ----plotting_data------------------------------------------------------------
library(ggplot2)
library(reshape2)
ggplot(data=melt(y), aes(Var2,Var1))+ geom_raster(aes(fill = value))+
scale_fill_gradient2(low="blue", mid="white", high = "red", midpoint = mean(y)) + xlab("Time") + ylab("Space") +
theme_bw()
## ----initial_parameters, eval = TRUE------------------------------------------
initial.parameters <- list(
mu = mean(y),
phi = matrix(c(.7, .01), ncol = 1),
theta = matrix(c(.01, .01), ncol = 1),
omega = 1,
alpha = matrix(c(.01, .01,
.01, .01), ncol = 2),
beta = matrix(c(.01, .01), ncol = 1)
)
## ----creatingLikelihood, eval = TRUE------------------------------------------
# Create likelihood object:
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters=initial.parameters)
# To save time, we use the true parameters as initial values:
f <- CreateLikelihood(y, W=W,
init = apply(y,1,var), parameters=parameters)
## ----fitting_model, eval = TRUE-----------------------------------------------
fit <- fitSTARMAGARCH(f, data = y, print = FALSE)
summary(fit)
## ----plotting_fit,eval = TRUE, fig.show='hold', fig.height = 5----------------
plot(fit)
plot_garch(fit)
## ----comparing_results--------------------------------------------------------
round(rbind(unlist(parameters), round(coef(fit),4)), 4)
## ----STGARCH, eval = FALSE----------------------------------------------------
# parameters <- list(
# mu = 0,
# phi = matrix(0, ncol = 1), #temporal order 1, spatial order 2
# theta = matrix(0, ncol = 1), #temporal order 1, spatial order 2
# omega = .9,
# alpha = matrix(c(.09, .13,
# .03, .07), ncol = 2), # temporal order 2, spatial order 2
# beta = matrix(c(.5, .15), ncol = 1) #temporal order 1, spatial order 2
# )
# y <- simSTARMAGARCH(parameters, n = 2500, m = c(25,1), W = W)
#
# initial.parameters <- list(
# mu = mean(y),
# phi = matrix(c(.7, .01), ncol = 1),
# theta = matrix(c(.01, .01), ncol = 1),
# omega = 1,
# alpha = matrix(c(.01, .01,
# .01, .01), ncol = 2),
# beta = matrix(c(.01, .01), ncol = 1)
# )
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters)
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> mu 0.01272265 0.009833892 1.2937556 9.787493e-02
# #> phi1 -0.37973220 0.282238217 -1.3454315 8.924296e-02
# #> phi2 0.37536087 0.783248661 0.4792359 3.158854e-01
# #> theta1 0.37367411 0.283705318 1.3171206 9.389911e-02
# #> theta2 -0.36493089 0.791497331 -0.4610639 3.223764e-01
# #> omega 0.98304477 0.066042385 14.8850586 2.060627e-50
# #> alpha1 0.08262752 0.006244003 13.2331007 2.825359e-40
# #> alpha2 0.14105291 0.011764199 11.9900142 2.004181e-33
# #> alpha3 0.03092677 0.007764663 3.9830156 3.402315e-05
# #> alpha4 0.06686734 0.014844508 4.5045170 3.326203e-06
# #> beta1 0.51746041 0.033736850 15.3381362 2.126149e-53
# #> beta2 0.10477532 0.048024420 2.1817093 1.456550e-02
# #>
# #>
# #> Standardized residual standard error: 1 .
## ----STGARCH_with_map, eval = FALSE-------------------------------------------
# # Use "map"" to fix parameters to zero:
# initial.parameters$mu <- 0
# initial.parameters$phi <- matrix(0, ncol=1)
# initial.parameters$theta <- matrix(0, ncol=1)
# map <- list()
# map$mu <- as.factor(NA)
# map$phi <- as.factor(NA)
# map$theta <- as.factor(NA)
# dim(map$theta) <- dim(map$phi) <- c(1,1)
# map
# #> $mu
# #> [1] <NA>
# #> Levels:
# #>
# #> $phi
# #> [,1]
# #> [1,] <NA>
# #> Levels:
# #>
# #> $theta
# #> [,1]
# #> [1,] <NA>
# #> Levels:
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters, map = map)
#
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> omega 0.98281266 0.066025733 14.885297 2.053285e-50
# #> alpha1 0.08264733 0.006242327 13.239826 2.583416e-40
# #> alpha2 0.14108928 0.011764874 11.992417 1.946865e-33
# #> alpha3 0.03103404 0.007765063 3.996624 3.212613e-05
# #> alpha4 0.06653875 0.014844846 4.482279 3.692497e-06
# #> beta1 0.51727367 0.033725151 15.337920 2.133229e-53
# #> beta2 0.10519927 0.048014155 2.191005 1.422570e-02
# #>
# #>
# #> Standardized residual standard error: 1 .
# #> AIC: 148332.7 BIC: 148396
#
# round(rbind(unlist(parameters)[-(1:3)], fit$coefficients),4)
# #> omega alpha1 alpha2 alpha3 alpha4 beta1 beta2
# #> [1,] 0.9000 0.0900 0.1300 0.030 0.0700 0.5000 0.1500
# #> [2,] 0.9828 0.0826 0.1411 0.031 0.0665 0.5173 0.1052
## ----STARMA_with_map, eval = FALSE--------------------------------------------
# parameters <- list(
# mu = 5,
# phi = matrix(c(.8, .1), ncol = 1), #temporal order 1, spatial order 2
# theta = matrix(c(-.42, -.2), ncol = 1), #temporal order 1, spatial order 2
# omega = 30,
# alpha = matrix(0, ncol = 1), # temporal order 2, spatial order 2
# beta = matrix(0, ncol = 1) #temporal order 1, spatial order 2
# )
# y <- simSTARMAGARCH(parameters, n = 2500, m = c(25,1), W = W)
# initial.parameters <- list(
# mu = mean(y),
# phi = matrix(c(.7, .01), ncol = 1),
# theta = matrix(c(.01, .01), ncol = 1),
# omega = 1,
# alpha = matrix(c(.01, .01,
# .01, .01), ncol = 2),
# beta = matrix(c(.01, .01), ncol = 1)
# )
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters)
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> mu 5.0714676601 0.076651590 6.616259e+01 0.000000e+00
# #> phi1 0.7977517884 0.005226702 1.526301e+02 0.000000e+00
# #> phi2 0.1119027906 0.010694371 1.046371e+01 6.339603e-26
# #> theta1 -0.4178454614 0.007787193 -5.365803e+01 0.000000e+00
# #> theta2 -0.2233686304 0.016775178 -1.331543e+01 9.414894e-41
# #> omega 29.8237638244 15.355764525 1.942187e+00 2.605724e-02
# #> alpha1 0.0000000100 0.002948183 3.391920e-06 4.999986e-01
# #> alpha2 0.0005736162 NaN NaN NaN
# #> alpha3 0.0001235004 0.002756660 4.480074e-02 4.821331e-01
# #> alpha4 0.0001525837 0.009304228 1.639939e-02 4.934579e-01
# #> beta1 0.0000000100 NaN NaN NaN
# #> beta2 0.0000000100 NaN NaN NaN
# #>
# #>
# #> Standardized residual standard error: 1 .
# #> AIC: 194676 BIC: 194784.5
#
# # Use "map"" to fix parameters to zero:
# initial.parameters$alpha <- matrix(0, ncol=1)
# initial.parameters$beta <- matrix(0, ncol=1)
# map <- list()
# map$alpha <- as.factor(NA)
# map$beta <- as.factor(NA)
# dim(map$alpha) <- dim(map$beta) <- c(1,1)
# map
# #> $alpha
# #> [,1]
# #> [1,] <NA>
# #> Levels:
# #>
# #> $beta
# #> [,1]
# #> [1,] <NA>
# #> Levels:
#
# f <- CreateLikelihood(y, W=W,
# init = apply(y,1,var), parameters = initial.parameters, map = map)
# fit <- fitSTARMAGARCH(f, data= y, print = FALSE)
# summary(fit)
# #> Estimates SD Zscore Pvalue
# #> mu 5.0714315 0.076639614 66.17246 0.000000e+00
# #> phi1 0.7977492 0.005225273 152.67130 0.000000e+00
# #> phi2 0.1118951 0.010696428 10.46098 6.525081e-26
# #> theta1 -0.4178449 0.007784903 -53.67374 0.000000e+00
# #> theta2 -0.2233527 0.016775596 -13.31414 9.577871e-41
# #> omega 29.8436922 0.168888961 176.70600 0.000000e+00
# #>
# #>
# #> Standardized residual standard error: 1 .
# #> AIC: 194664 BIC: 194718.2
#
# round(rbind(unlist(parameters)[1:6],coef(fit)), 4)
# #> mu phi1 phi2 theta1 theta2 omega
# #> [1,] 5.0000 0.8000 0.1000 -0.4200 -0.2000 30.0000
# #> [2,] 5.0714 0.7977 0.1119 -0.4178 -0.2234 29.8437
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