Nothing
R/initialization.R
In tsgarch: Univariate GARCH Models
Defines functions
.parameters_ewma
.parameters_igarch
.parameters_cgarch
.parameters_fgarch
.parameters_gjrgarch
.parameters_aparch
.parameters_egarch
.parameters_garch
initialize_parameters
initialize_parameters <- function(model = "garch", y, constant = 0.0,
order = c(1,1), variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
switch(model,
"garch" = .parameters_garch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"egarch" = .parameters_egarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"aparch" = .parameters_aparch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"gjrgarch" = .parameters_gjrgarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"fgarch" = .parameters_fgarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"cgarch" = .parameters_cgarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"igarch" = .parameters_igarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"ewma" = .parameters_ewma(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution))
}
.parameters_garch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
} else {
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2)) * 0.01]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_egarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = log(var_y) * 0.01,
lower = -10, upper = 10, estimate = 1,
scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = -10, upper = 10, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -10, upper = 10, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = -10,
upper = 10, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.1/order[1], lower = -10, upper = 10,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = -1 + 1e-12, upper = 1 - 1e-12,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = -1 + 1e-12,
upper = 1 - 1e-12, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_aparch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
delta <- 2
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1 - 1e-3, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -1 + 1e-3, upper = 1 - 1e-3, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = 0,
upper = 1 - 1e-3, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.05/order[1], lower = -1 + 1e-3,
upper = 1 - 1e-3,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = 0, upper = 1 - 1e-3,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.8/order[2], lower = 0,
upper = 1 - 1e-3, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
parmatrix <- rbind(parmatrix, data.table("parameter" = "delta", value = delta,
lower = 0.01, upper = 3.5,
estimate = 1,
scale = 1, group = "delta",
equation = "[GARCH]",
symbol = "\\delta"))
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_gjrgarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -1 + 1e-12, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = 0,
upper = 1 - 1e-12, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.05/order[1], lower = -1 + 1e-12,
upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = 0, upper = 1 - 1e-12,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.8/order[2], lower = 0,
upper = 1 - 1e-12, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_fgarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
delta <- 2
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -1 + 1e-12, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "eta1", value = 0,
lower = -10, upper = 10, estimate = 0,
scale = 1, group = "eta",
equation = "[ARCH]", symbol = "\\eta_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = 0,
upper = 1 - 1e-12, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.05/order[1], lower = -1 + 1e-12,
upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("eta",1:order[1]),
value = 0.05/order[1], lower = -10,
upper = 10,
estimate = 1, scale = 1, group = "eta",
equation = "[ARCH]",
symbol = paste0("\\eta_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = 0, upper = 1 - 1e-12,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.8/order[2], lower = 0,
upper = 1 - 1e-12, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
parmatrix <- rbind(parmatrix, data.table("parameter" = "delta", value = delta,
lower = 0.01, upper = 3.5,
estimate = 1,
scale = 1, group = "delta",
equation = "[GARCH]",
symbol = "\\delta"))
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_cgarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
} else {
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2)) * 0.01]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
# permanent component parameters \\rho and \\phi
parmatrix <- rbind(parmatrix,
data.table("parameter" = "rho", value = 0.98,
lower = 0, upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "rho",
equation = "[V]", symbol = "\\rho"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "phi", value = 0.025/order[1],
lower = 0 + 1e-12, upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "phi",
equation = "[V]", symbol = "\\phi"))
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_igarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
} else {
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2)) * 0.01]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
# now check for summation to 1 and other conditions
if (order[2] == 0 &
length(parmatrix[group == "alpha" & estimate == 0]$value) == order[1] &
sum(parmatrix[group == "alpha" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(p=0) and GARCH(q) fixed but
not summing to 1")
}
if (order[1] == 0 &
length(parmatrix[group == "beta" & estimate == 0]$value) == order[2] &
sum(parmatrix[group == "beta" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(q=0) and GARCH(p) fixed but
not summing to 1")
}
sum_alpha <- sum(parmatrix[group == "alpha"]$value)
parmatrix[group == "beta", value := (1 - sum_alpha)/order[2]]
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_ewma <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := 0]
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
# now check for summation to 1 and other conditions
if (order[2] == 0 &
length(parmatrix[group == "alpha" & estimate == 0]$value) == order[1] &
sum(parmatrix[group == "alpha" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(p=0) and GARCH(q) fixed but
not summing to 1")
}
if (order[1] == 0 &
length(parmatrix[group == "beta" & estimate == 0]$value) == order[2] &
sum(parmatrix[group == "beta" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(q=0) and GARCH(p) fixed but
not summing to 1")
}
sum_alpha <- sum(parmatrix[group == "alpha"]$value)
parmatrix[group == "beta", value := (1 - sum_alpha)/order[2]]
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
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Defines functions .parameters_ewma .parameters_igarch .parameters_cgarch .parameters_fgarch .parameters_gjrgarch .parameters_aparch .parameters_egarch .parameters_garch initialize_parameters
initialize_parameters <- function(model = "garch", y, constant = 0.0,
order = c(1,1), variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
switch(model,
"garch" = .parameters_garch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"egarch" = .parameters_egarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"aparch" = .parameters_aparch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"gjrgarch" = .parameters_gjrgarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"fgarch" = .parameters_fgarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"cgarch" = .parameters_cgarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"igarch" = .parameters_igarch(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution),
"ewma" = .parameters_ewma(y = y, constant = constant,
order = order,
variance_targeting = variance_targeting,
vreg = vreg,
multiplicative = multiplicative,
init = init,
backcast_lambda = backcast_lambda,
sample_n = sample_n,
distribution = distribution))
}
.parameters_garch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
} else {
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2)) * 0.01]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_egarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = log(var_y) * 0.01,
lower = -10, upper = 10, estimate = 1,
scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = -10, upper = 10, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -10, upper = 10, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = -10,
upper = 10, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.1/order[1], lower = -10, upper = 10,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = -1 + 1e-12, upper = 1 - 1e-12,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = -1 + 1e-12,
upper = 1 - 1e-12, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_aparch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
delta <- 2
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1 - 1e-3, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -1 + 1e-3, upper = 1 - 1e-3, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = 0,
upper = 1 - 1e-3, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.05/order[1], lower = -1 + 1e-3,
upper = 1 - 1e-3,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = 0, upper = 1 - 1e-3,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.8/order[2], lower = 0,
upper = 1 - 1e-3, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
parmatrix <- rbind(parmatrix, data.table("parameter" = "delta", value = delta,
lower = 0.01, upper = 3.5,
estimate = 1,
scale = 1, group = "delta",
equation = "[GARCH]",
symbol = "\\delta"))
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_gjrgarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -1 + 1e-12, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = 0,
upper = 1 - 1e-12, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.05/order[1], lower = -1 + 1e-12,
upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = 0, upper = 1 - 1e-12,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.8/order[2], lower = 0,
upper = 1 - 1e-12, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_fgarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
delta <- 2
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100, upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0), scale = 1,
group = "mu", equation = "[M]", symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "gamma1", value = 0,
lower = -1 + 1e-12, upper = 1 - 1e-12, estimate = 0,
scale = 1, group = "gamma",
equation = "[ARCH]", symbol = "\\gamma_1"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "eta1", value = 0,
lower = -10, upper = 10, estimate = 0,
scale = 1, group = "eta",
equation = "[ARCH]", symbol = "\\eta_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.1/order[1], lower = 0,
upper = 1 - 1e-12, estimate = 1, scale = 1,
group = "alpha", equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("gamma",1:order[1]),
value = 0.05/order[1], lower = -1 + 1e-12,
upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "gamma",
equation = "[ARCH]",
symbol = paste0("\\gamma_",1:order[1])))
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("eta",1:order[1]),
value = 0.05/order[1], lower = -10,
upper = 10,
estimate = 1, scale = 1, group = "eta",
equation = "[ARCH]",
symbol = paste0("\\eta_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0,
lower = 0, upper = 1 - 1e-12,
estimate = 0, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.8/order[2], lower = 0,
upper = 1 - 1e-12, estimate = 1,
scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
parmatrix <- rbind(parmatrix, data.table("parameter" = "delta", value = delta,
lower = 0.01, upper = 3.5,
estimate = 1,
scale = 1, group = "delta",
equation = "[GARCH]",
symbol = "\\delta"))
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = -1000, upper = 1000, estimate = 1,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0,
lower = -1000, upper = 1000, estimate = 0,
scale = 1, group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_cgarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
} else {
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2)) * 0.01]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
# permanent component parameters \\rho and \\phi
parmatrix <- rbind(parmatrix,
data.table("parameter" = "rho", value = 0.98,
lower = 0, upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "rho",
equation = "[V]", symbol = "\\rho"))
parmatrix <- rbind(parmatrix,
data.table("parameter" = "phi", value = 0.025/order[1],
lower = 0 + 1e-12, upper = 1 - 1e-12,
estimate = 1, scale = 1, group = "phi",
equation = "[V]", symbol = "\\phi"))
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_igarch <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
if (variance_targeting) {
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2))]
} else {
parmatrix[parameter == "omega", value := as.numeric(mean((y - mu)^2)) * 0.01]
}
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
# now check for summation to 1 and other conditions
if (order[2] == 0 &
length(parmatrix[group == "alpha" & estimate == 0]$value) == order[1] &
sum(parmatrix[group == "alpha" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(p=0) and GARCH(q) fixed but
not summing to 1")
}
if (order[1] == 0 &
length(parmatrix[group == "beta" & estimate == 0]$value) == order[2] &
sum(parmatrix[group == "beta" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(q=0) and GARCH(p) fixed but
not summing to 1")
}
sum_alpha <- sum(parmatrix[group == "alpha"]$value)
parmatrix[group == "beta", value := (1 - sum_alpha)/order[2]]
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
.parameters_ewma <- function(y, constant = FALSE, order = c(1,1),
variance_targeting = FALSE,
vreg = NULL, multiplicative = TRUE,
init = c("unconditional","sample","backcast"),
backcast_lambda = 0.7, sample_n = 10,
distribution = "norm", ...)
{
parameter <- value <- group <- lower <- upper <- NULL
y <- as.numeric(y)
maxpq <- max(order)
n <- NROW(y)
if (constant) {
mu <- mean(y, na.rm = TRUE)
} else {
mu <- 0.0
}
var_y <- var(y, na.rm = T)
parmatrix <- data.table("parameter" = "mu", value = mu,
lower = -1.0 * abs(mu) * 100,
upper = abs(mu) * 100,
estimate = ifelse(constant, 1, 0),
scale = 1, group = "mu", equation = "[M]",
symbol = "\\mu")
parmatrix <- rbind(parmatrix,
data.table("parameter" = "omega", value = var_y * 0.01,
lower = 1e-12, upper = var_y/0.01,
estimate = 1, scale = 1, group = "omega",
equation = "[V]", symbol = "\\omega"))
parmatrix[parameter == "omega", estimate := 0]
parmatrix[parameter == "omega", value := 0]
if (!is.null(vreg)) {
if (multiplicative) {
parmatrix[parameter == "omega", lower := log(1e-12)]
parmatrix[parameter == "omega", upper := log(upper)]
parmatrix[parameter == "omega", value := log(value)]
}
}
if (order[1] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "alpha1", value = 0,
lower = 0, upper = 1, estimate = 0,
scale = 1, group = "alpha",
equation = "[ARCH]", symbol = "\\alpha_1"))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("alpha",1:order[1]),
value = 0.05/order[1], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "alpha",
equation = "[ARCH]",
symbol = paste0("\\alpha_",1:order[1])))
}
if (order[2] == 0) {
parmatrix <- rbind(parmatrix,
data.table("parameter" = "beta", value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1,
group = "beta", equation = "[GARCH]",
symbol = paste0("\\beta_",1)))
} else {
parmatrix <- rbind(parmatrix,
data.table("parameter" = paste0("beta",1:order[2]),
value = 0.9/order[2], lower = 0, upper = 1,
estimate = 1, scale = 1, group = "beta",
equation = "[GARCH]",
symbol = paste0("\\beta_",1:order[2])))
}
# now check for summation to 1 and other conditions
if (order[2] == 0 &
length(parmatrix[group == "alpha" & estimate == 0]$value) == order[1] &
sum(parmatrix[group == "alpha" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(p=0) and GARCH(q) fixed but
not summing to 1")
}
if (order[1] == 0 &
length(parmatrix[group == "beta" & estimate == 0]$value) == order[2] &
sum(parmatrix[group == "beta" & estimate == 0]$value) < 1) {
stop("\ncannot estimate an igarch model with GARCH(q=0) and GARCH(p) fixed but
not summing to 1")
}
sum_alpha <- sum(parmatrix[group == "alpha"]$value)
parmatrix[group == "beta", value := (1 - sum_alpha)/order[2]]
if (!is.null(vreg)) {
m <- NCOL(vreg)
vmatrix <- data.table("parameter" = paste0("xi",1:m), value = 1,
lower = 0, upper = 100, estimate = 1, scale = 1,
group = "xi", equation = "[V]",
symbol = paste0("\\xi_",1:m))
if (multiplicative) {
vmatrix$lower <- -1000
vmatrix$upper <- 1000
}
} else {
vmatrix <- data.table("parameter" = paste0("xi",1), value = 0, lower = 0,
upper = 1, estimate = 0, scale = 1, group = "xi",
equation = "[V]", symbol = paste0("\\xi_",1))
}
parmatrix <- rbind(parmatrix, vmatrix)
dmatrix <- distribution_parameters(distribution)
parmatrix <- rbind(parmatrix, dmatrix)
parmatrix[,estimate := as.integer(estimate)]
return(parmatrix)
}
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