Nothing
R/sim-functions.R
In fEGarch: SM/LM EGARCH & GARCH, VaR/ES Backtesting & Dual LM Extensions
Defines functions
garch_sim
tgarch_sim
gjrgarch_sim
aparch_sim
figarch_sim
fitgarch_sim
figjrgarch_sim
fiaparch_sim
fEGarch_sim
Documented in
aparch_sim
fEGarch_sim
fiaparch_sim
figarch_sim
figjrgarch_sim
fitgarch_sim
garch_sim
gjrgarch_sim
tgarch_sim
#'Simulate From Models of the Broader EGARCH Family
#'
#'A streamlined simulation function to simulate from models
#'that are part of the broader EGARCH family specifiable
#'through \code{\link{fEGarch_spec}}.
#'
#'@param spec an object of class \code{"egarch_type_spec"} or
#'\code{"loggarch_type_spec"} returned by \code{\link{fEGarch_spec}}
#'or related wrapper functions; note that the model orders in the
#'conditional mean and in the
#'conditional variance as well as the long-memory settings are not
#'controlled through the element
#'\code{orders} and \code{long_memo} of \code{spec} but
#'solely through the parameter settings in \code{pars}.
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{fEGarch_spec}} for information
#'on the models of the broader EGARCH family. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'spec <- megarch_spec()
#'sim <- fEGarch_sim(spec = spec)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
fEGarch_sim <- function(spec = egarch_spec(),
pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega_sig = -9,
phi = 0.8,
psi = numeric(0),
kappa = -0.2,
gamma = 0.3,
d = 0,
df = 10,
shape = 2,
P = 3,
skew = 1
), n = 1000, nstart = 5e3, trunc = "none") {
nn <- n + nstart # pre-sample plus sample number of observations
N <- n
trunc_vol <- trunc
trunc_mean <- trunc
# Parameter defaults (relevant if a truncated parameter list is provided)
pars_default <- lookup_table$sim_pars_default
names_pars <- names(pars)
for (nam in names_pars) {
pars_default[[nam]] <- pars[[nam]]
}
# Extract parameter settings
mu <- pars_default$mu
omega_sig <- pars_default$omega_sig
phi <- pars_default$phi
psi <- pars_default$psi
kappa <- pars_default$kappa
gamma <- pars_default$gamma
d <- pars_default$d
df <- pars_default$df
shape <- pars_default$shape
P <- pars_default$P
skew <- pars_default$skew
cond_dist <- spec@cond_dist
lm <- d != 0
# ARMA / FARIMA parameters
ar <- pars_default$ar
ma <- pars_default$ma
D <- pars_default$D
lm_arma <- D != 0
# Simulate even more observations if ARMA / FARIMA required
check <- length(ar) + length(ma) > 0 || lm_arma
nn <- if (check) {
N <- N + nstart
nn + nstart
} else {
nn
}
if ((lm || lm_arma) && ((is.character(trunc) && trunc == "none") || (is.numeric(trunc) && trunc >= nn))) {
trunc_vol <- nn - 1
trunc_mean <- N - 1
}
if (cond_dist %in% c("std", "sstd")) {
shape <- df # all functions are defined with "shape" argument (even if not used then within the function; for t-distr. types, we need to make shape our df)
} else if (cond_dist %in% c("ald", "sald")) {
shape <- P
}
# Simulate innovations following selected distribution
sim_fun <- simfun_selector(cond_dist)
innov <- sim_fun(nn, shape = shape, skew = skew)
PDF <- fun1_selector(cond_dist)
model_type <- c("logGARCH", "eGARCH")[[inherits(spec, "egarch_type_spec") + 1]]
if (model_type == "eGARCH") {
modulus <- spec@modulus
powers <- spec@powers
mod_a <- modulus[[1]]
mod_m <- modulus[[2]]
pow_a <- powers[[1]]
pow_m <- powers[[2]]
log_a <- (pow_a > 0) + 1
log_m <- (pow_m > 0) + 1
# Obtain the various functions to integrate over for the expectations
# in the magnitude and asymmetry terms
Func_a <- exp_funs[["asy"]][[mod_a + 1]][[log_a]]
Func_m <- exp_funs[["mag"]][[mod_m + 1]][[log_m]]
# Then we can integrate numerically over those function and thus
# follow the definition of an expectation
E_asy <- stats::integrate(
f = Func_a, lower = -Inf, upper = Inf,
subdivisions = 1000L, rel.tol = 1e-6, abs.tol = 1e-6,
stop.on.error = FALSE, pow = pow_a, dfun = PDF, shape = shape,
skew = skew
)[[1]]
E_mag <- stats::integrate(
f = Func_m, lower = -Inf, upper = Inf,
subdivisions = 1000L, rel.tol = 1e-6, abs.tol = 1e-6,
stop.on.error = FALSE, pow = pow_m, dfun = PDF, shape = shape,
skew = skew
)[[1]]
mode <- mode_mat[log_a, log_m]
if (lm) {
# we need coefficients for the 1 pre-pre-sample time points, for the pre-sample,
# and for the sample with the exception of the very last sample time point
coef_inf <- c(0, ma_infty(ar = phi, ma = psi, d = d,
max_i = trunc_vol - 1))
np2 <- nextpow2(2 * nn - 1)
# Compute the function g for the simulated innovations
sim <- egarch_longmemo_type_sim(
innov = innov, omega_sig = omega_sig, coef_inf = coef_inf,
kappa = kappa, gamma = gamma, n_out = N, mu = mu,
E_mag = E_mag, E_asy = E_asy, powers = powers,
modulus = modulus, mode = mode, np2)
} else {
sim <- egarch_shortmemo_type_sim(
innov = innov, omega_sig = omega_sig, ar_coef = phi,
ma_coef = c(1, psi),
kappa = kappa, gamma = gamma, n_out = N, mu = mu,
E_mag = E_mag, E_asy = E_asy, powers = powers,
modulus = modulus, mode = mode)
}
} else if (model_type == "logGARCH") {
Func <- function(x, shape, skew, dfun) {
log(x^2) * dfun(x, shape = shape, skew = skew)
}
E_const <- stats::integrate(
f = Func, lower = -Inf, upper = Inf,
subdivisions = 1000L, rel.tol = 1e-6, abs.tol = 1e-6,
stop.on.error = FALSE, dfun = PDF, shape = shape,
skew = skew
)[[1]]
if (lm) {
np2 <- nextpow2(2 * nn - 1)
coef_inf <- ma_infty(
ar = phi, ma = psi, d = d, max_i = trunc_vol
)
coef_inf[[1]] <- 0
sim <- loggarch_longmemo_type_sim(
innov, omega_sig,
coef_inf = coef_inf,
n_out = N,
mu = mu,
Econst = E_const, np2 = np2)
} else {
n_ar <- length(phi)
n_ma <- length(psi)
if (n_ma > n_ar) {
phi <- c(phi, rep(0, n_ma - n_ar))
} else if (n_ar > n_ma) {
psi <- c(psi, rep(0, n_ar - n_ma))
}
sim <- loggarch_shortmemo_type_sim(
innov, omega_sig,
ar_coef = phi, ma_coef = psi + phi,
n_out = N,
mu = mu,
Econst = E_const)
}
}
out <- list(
"rt" = stats::ts(c(sim[["rt"]])),
"sigt" = stats::ts(c(sim[["sigt"]])),
"etat" = stats::ts(c(sim[["etat"]])),
"cmeans" = stats::ts(rep(mu, n))
)
if (check) {
rt <- out$rt - mu # subtract mean again and then feed these as
# the errors into an ARMA / FARIMA model
if (!lm_arma) {
yt_data <- arma_sim_Cpp(innov = rt, ar = ar, ma = ma, nout = n, mu = mu)
} else {
coef_inf <- ar_infty(ar = ar, ma = ma, d = D, max_i = trunc_mean)[-1]
yt_data <- farima_sim_Cpp(innov = rt, coef_inf = coef_inf, nout = n, mu = mu)
}
out[["rt"]] <- stats::ts(c(yt_data[["rt"]]))
out[["cmeans"]] <- stats::ts(c(yt_data[["cmeans"]]))
out[["etat"]] <- stats::ts(utils::tail(out[["etat"]], n))
out[["sigt"]] <- stats::ts(utils::tail(out[["sigt"]], n))
}
out
}
#'Simulate From FIAPARCH Models
#'
#'A streamlined simulation function to simulate from
#'fractionally integrated asymmetric power autoregressive
#'conditional heteroskedasticity (FIAPARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{fiaparch}} for information
#'on the FIAPARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- fiaparch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
fiaparch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
gamma = 0.1,
delta = 2,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
cond_dist <- match.arg(cond_dist)
nn <- n + nstart # pre-sample plus sample number of observations
N <- n
trunc_vol <- trunc
trunc_mean <- trunc
# Parameter defaults (relevant if a truncated parameter list is provided)
pars_default <- lookup_table$sim_pars_default_fiaparch
names_pars <- names(pars)
for (nam in names_pars) {
pars_default[[nam]] <- pars[[nam]]
}
# Extract parameter settings
mu <- pars_default$mu
omega <- pars_default$omega
phi <- pars_default$phi
beta <- -pars_default$beta # "-" required to create a polynomial with positive signs
gamma <- pars_default$gamma
delta <- pars_default$delta
d <- pars_default$d
df <- pars_default$df
P <- pars_default$P
shape <- pars_default$shape
skew <- pars_default$skew
# ARMA / FARIMA parameters
ar <- pars_default$ar
ma <- pars_default$ma
D <- pars_default$D
lm_arma <- D != 0
# Simulate even more observations if ARMA / FARIMA required
check <- length(ar) + length(ma) > 0 || lm_arma
nn <- if (check) {
N <- N + nstart
nn + nstart
} else {
nn
}
lm <- TRUE
if ((lm || lm_arma) && ((is.character(trunc) && trunc == "none") || (is.numeric(trunc) && trunc >= nn))) {
trunc_vol <- nn - 1
trunc_mean <- N - 1
}
if (cond_dist %in% c("std", "sstd")) {
shape <- df # all functions are defined with "shape" argument (even if not used then within the function; for t-distr. types, we need to make shape our df)
} else if (cond_dist %in% c("ald", "sald")) {
shape <- P
}
# Simulate innovations following selected distribution
sim_fun <- simfun_selector(cond_dist)
innov <- sim_fun(nn, shape = shape, skew = skew)
# we need coefficients for the 1 pre-pre-sample time points, for the pre-sample,
# and for the sample with the exception of the very last sample time point
coef_inf <- ar_infty(ar = phi, ma = beta, d = d,
max_i = trunc_vol)
coef_inf[[1]] <- 0
sim <- fiaparch_sim_Cpp(
innov = innov, omega = omega, coef_inf = coef_inf,
gamma = gamma, delta = delta, n_out = N, mu = mu)
out <- list(
"rt" = stats::ts(c(sim[["rt"]])),
"sigt" = stats::ts(c(sim[["sigt"]])),
"etat" = stats::ts(c(sim[["etat"]])),
"cmeans" = stats::ts(rep(mu, n))
)
if (check) {
rt <- out$rt - mu # subtract mean again and then feed these as
# the errors into an ARMA / FARIMA model
if (!lm_arma) {
yt_data <- arma_sim_Cpp(innov = rt, ar = ar, ma = ma, nout = n, mu = mu)
} else {
coef_inf <- ar_infty(ar = ar, ma = ma, d = D, max_i = trunc_mean)[-1]
yt_data <- farima_sim_Cpp(innov = rt, coef_inf = coef_inf, nout = n, mu = mu)
}
out[["rt"]] <- stats::ts(c(yt_data[["rt"]]))
out[["cmeans"]] <- stats::ts(c(yt_data[["cmeans"]]))
out[["etat"]] <- stats::ts(utils::tail(out[["etat"]], n))
out[["sigt"]] <- stats::ts(utils::tail(out[["sigt"]], n))
}
out
}
#'Simulate From FIGJR-GARCH Models
#'
#'A streamlined simulation function to simulate from
#'FIGJR-GARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{figjrgarch}} for information
#'on the FIGJR-GARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- figjrgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
figjrgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
gamma = 0.1,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 2
fiaparch_sim(pars = pars, cond_dist = cond_dist, n = n, nstart = nstart, trunc = trunc)
}
#'Simulate From FITGARCH Models
#'
#'A streamlined simulation function to simulate from
#'FITGARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{fitgarch}} for information
#'on the FITGARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- fitgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
fitgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
gamma = 0.1,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 1
fiaparch_sim(pars = pars, cond_dist = cond_dist, n = n, nstart = nstart, trunc = trunc)
}
#'Simulate From FIGARCH Models
#'
#'A streamlined simulation function to simulate from
#'fractionally integrated generalized autoregressive conditional
#'heteroskedasticity (FIGARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{figarch}} for information
#'on the FIGARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- figarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
figarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 2
pars[["gamma"]] <- 0
fiaparch_sim(pars = pars, cond_dist = cond_dist, n = n, nstart = nstart, trunc = trunc)
}
#'Simulate From APARCH Models
#'
#'A streamlined simulation function to simulate from
#'asymmetric power autoregressive
#'conditional heteroskedasticity (APARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{aparch}} for information
#'on the APARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- aparch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
aparch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
gamma = 0.1,
delta = 2,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
cond_dist <- match.arg(cond_dist)
nn <- n + nstart # pre-sample plus sample number of observations
N <- n
trunc_mean <- trunc
# Parameter defaults (relevant if a truncated parameter list is provided)
pars_default <- lookup_table$sim_pars_default_aparch
names_pars <- names(pars)
for (nam in names_pars) {
pars_default[[nam]] <- pars[[nam]]
}
# Extract parameter settings
mu <- pars_default$mu
omega <- pars_default$omega
phi <- pars_default$phi
beta <- pars_default$beta
gamma <- pars_default$gamma
delta <- pars_default$delta
df <- pars_default$df
P <- pars_default$P
shape <- pars_default$shape
skew <- pars_default$skew
l_phi <- length(phi)
l_gamma <- length(gamma)
stopifnot("Input parameter vectors phi and gamma must be of the same length." = l_phi == l_gamma)
# ARMA / FARIMA parameters
ar <- pars_default$ar
ma <- pars_default$ma
D <- pars_default$D
lm_arma <- D != 0
# Simulate even more observations if ARMA / FARIMA required
check <- length(ar) + length(ma) > 0 || lm_arma
nn <- if (check) {
N <- N + nstart
nn + nstart
} else {
nn
}
if (lm_arma && ((is.character(trunc) && trunc == "none") || (is.numeric(trunc) && trunc >= nn))) {
trunc_mean <- N - 1
}
if (cond_dist %in% c("std", "sstd")) {
shape <- df # all functions are defined with "shape" argument (even if not used then within the function; for t-distr. types, we need to make shape our df)
} else if (cond_dist %in% c("ald", "sald")) {
shape <- P
}
# Simulate innovations following selected distribution
sim_fun <- simfun_selector(cond_dist)
innov <- sim_fun(nn, shape = shape, skew = skew)
dfun <- fun1_selector(cond_dist)
int_fun <- function(x, shape, skew, gamma_i, delta, dfun) {
(abs(x) - gamma_i * x)^delta * dfun(x, shape = shape, skew = skew)
}
E_g <- rep(NA, length(gamma))
for (i in seq_along(gamma)) {
E_g <- stats::integrate(
f = int_fun, lower = -Inf, upper = Inf, subdivisions = 1000L,
rel.tol = 1e-6, abs.tol = 1e-6,
shape = shape, skew = skew, gamma_i = gamma[[i]], delta = delta,
dfun = dfun
)[[1]]
}
E_sigd <- omega / (1 - sum(phi * E_g) - sum(beta))
sim <- aparch_sim_Cpp(
innov = innov, omega = omega, phi = phi, beta = beta,
gamma = gamma, delta = delta, n_out = N, mu = mu,
E_sigd = E_sigd)
out <- list(
"rt" = stats::ts(c(sim[["rt"]])),
"sigt" = stats::ts(c(sim[["sigt"]])),
"etat" = stats::ts(c(sim[["etat"]])),
"cmeans" = stats::ts(rep(mu, n))
)
if (check) {
rt <- out$rt - mu # subtract mean again and then feed these as
# the errors into an ARMA / FARIMA model
if (!lm_arma) {
yt_data <- arma_sim_Cpp(innov = rt, ar = ar, ma = ma, nout = n, mu = mu)
} else {
coef_inf <- ar_infty(ar = ar, ma = ma, d = D, max_i = N)[-1]
yt_data <- farima_sim_Cpp(innov = rt, coef_inf = coef_inf, nout = n, mu = mu)
}
out[["rt"]] <- stats::ts(c(yt_data[["rt"]]))
out[["cmeans"]] <- stats::ts(c(yt_data[["cmeans"]]))
out[["etat"]] <- stats::ts(utils::tail(out[["etat"]], n))
out[["sigt"]] <- stats::ts(utils::tail(out[["sigt"]], n))
}
out
}
#'Simulate From GJR-GARCH Models
#'
#'A streamlined simulation function to simulate from
#'GJR-GARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{gjrgarch}} for information
#'on the GJR-GARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- gjrgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
gjrgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
gamma = 0.1,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 2 # Fix delta at 2 and use APARCH functions
aparch_sim(
pars = pars,
cond_dist = cond_dist,
n = n, nstart = nstart, trunc = trunc
)
}
#'Simulate From TGARCH Models
#'
#'A streamlined simulation function to simulate from
#'TGARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{tgarch}} for information
#'on the TGARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- tgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
tgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
gamma = 0.1,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 1 # Fix delta at 1 and use APARCH functions
aparch_sim(
pars = pars,
cond_dist = cond_dist,
n = n, nstart = nstart, trunc = trunc
)
}
#'Simulate From GARCH Models
#'
#'A streamlined simulation function to simulate from
#'generalized autoregressive conditional heteroskedasticity
#'(GARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{garch}} for information
#'on the GARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- garch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
garch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
p <- length(pars$phi)
pars[["delta"]] <- 2 # Fix delta at 1 and use APARCH functions
pars[["gamma"]] <- rep(0, p)
aparch_sim(
pars = pars,
cond_dist = cond_dist,
n = n, nstart = nstart, trunc = trunc
)
}
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Defines functions garch_sim tgarch_sim gjrgarch_sim aparch_sim figarch_sim fitgarch_sim figjrgarch_sim fiaparch_sim fEGarch_sim
Documented in aparch_sim fEGarch_sim fiaparch_sim figarch_sim figjrgarch_sim fitgarch_sim garch_sim gjrgarch_sim tgarch_sim
#'Simulate From Models of the Broader EGARCH Family
#'
#'A streamlined simulation function to simulate from models
#'that are part of the broader EGARCH family specifiable
#'through \code{\link{fEGarch_spec}}.
#'
#'@param spec an object of class \code{"egarch_type_spec"} or
#'\code{"loggarch_type_spec"} returned by \code{\link{fEGarch_spec}}
#'or related wrapper functions; note that the model orders in the
#'conditional mean and in the
#'conditional variance as well as the long-memory settings are not
#'controlled through the element
#'\code{orders} and \code{long_memo} of \code{spec} but
#'solely through the parameter settings in \code{pars}.
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{fEGarch_spec}} for information
#'on the models of the broader EGARCH family. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'spec <- megarch_spec()
#'sim <- fEGarch_sim(spec = spec)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
fEGarch_sim <- function(spec = egarch_spec(),
pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega_sig = -9,
phi = 0.8,
psi = numeric(0),
kappa = -0.2,
gamma = 0.3,
d = 0,
df = 10,
shape = 2,
P = 3,
skew = 1
), n = 1000, nstart = 5e3, trunc = "none") {
nn <- n + nstart # pre-sample plus sample number of observations
N <- n
trunc_vol <- trunc
trunc_mean <- trunc
# Parameter defaults (relevant if a truncated parameter list is provided)
pars_default <- lookup_table$sim_pars_default
names_pars <- names(pars)
for (nam in names_pars) {
pars_default[[nam]] <- pars[[nam]]
}
# Extract parameter settings
mu <- pars_default$mu
omega_sig <- pars_default$omega_sig
phi <- pars_default$phi
psi <- pars_default$psi
kappa <- pars_default$kappa
gamma <- pars_default$gamma
d <- pars_default$d
df <- pars_default$df
shape <- pars_default$shape
P <- pars_default$P
skew <- pars_default$skew
cond_dist <- spec@cond_dist
lm <- d != 0
# ARMA / FARIMA parameters
ar <- pars_default$ar
ma <- pars_default$ma
D <- pars_default$D
lm_arma <- D != 0
# Simulate even more observations if ARMA / FARIMA required
check <- length(ar) + length(ma) > 0 || lm_arma
nn <- if (check) {
N <- N + nstart
nn + nstart
} else {
nn
}
if ((lm || lm_arma) && ((is.character(trunc) && trunc == "none") || (is.numeric(trunc) && trunc >= nn))) {
trunc_vol <- nn - 1
trunc_mean <- N - 1
}
if (cond_dist %in% c("std", "sstd")) {
shape <- df # all functions are defined with "shape" argument (even if not used then within the function; for t-distr. types, we need to make shape our df)
} else if (cond_dist %in% c("ald", "sald")) {
shape <- P
}
# Simulate innovations following selected distribution
sim_fun <- simfun_selector(cond_dist)
innov <- sim_fun(nn, shape = shape, skew = skew)
PDF <- fun1_selector(cond_dist)
model_type <- c("logGARCH", "eGARCH")[[inherits(spec, "egarch_type_spec") + 1]]
if (model_type == "eGARCH") {
modulus <- spec@modulus
powers <- spec@powers
mod_a <- modulus[[1]]
mod_m <- modulus[[2]]
pow_a <- powers[[1]]
pow_m <- powers[[2]]
log_a <- (pow_a > 0) + 1
log_m <- (pow_m > 0) + 1
# Obtain the various functions to integrate over for the expectations
# in the magnitude and asymmetry terms
Func_a <- exp_funs[["asy"]][[mod_a + 1]][[log_a]]
Func_m <- exp_funs[["mag"]][[mod_m + 1]][[log_m]]
# Then we can integrate numerically over those function and thus
# follow the definition of an expectation
E_asy <- stats::integrate(
f = Func_a, lower = -Inf, upper = Inf,
subdivisions = 1000L, rel.tol = 1e-6, abs.tol = 1e-6,
stop.on.error = FALSE, pow = pow_a, dfun = PDF, shape = shape,
skew = skew
)[[1]]
E_mag <- stats::integrate(
f = Func_m, lower = -Inf, upper = Inf,
subdivisions = 1000L, rel.tol = 1e-6, abs.tol = 1e-6,
stop.on.error = FALSE, pow = pow_m, dfun = PDF, shape = shape,
skew = skew
)[[1]]
mode <- mode_mat[log_a, log_m]
if (lm) {
# we need coefficients for the 1 pre-pre-sample time points, for the pre-sample,
# and for the sample with the exception of the very last sample time point
coef_inf <- c(0, ma_infty(ar = phi, ma = psi, d = d,
max_i = trunc_vol - 1))
np2 <- nextpow2(2 * nn - 1)
# Compute the function g for the simulated innovations
sim <- egarch_longmemo_type_sim(
innov = innov, omega_sig = omega_sig, coef_inf = coef_inf,
kappa = kappa, gamma = gamma, n_out = N, mu = mu,
E_mag = E_mag, E_asy = E_asy, powers = powers,
modulus = modulus, mode = mode, np2)
} else {
sim <- egarch_shortmemo_type_sim(
innov = innov, omega_sig = omega_sig, ar_coef = phi,
ma_coef = c(1, psi),
kappa = kappa, gamma = gamma, n_out = N, mu = mu,
E_mag = E_mag, E_asy = E_asy, powers = powers,
modulus = modulus, mode = mode)
}
} else if (model_type == "logGARCH") {
Func <- function(x, shape, skew, dfun) {
log(x^2) * dfun(x, shape = shape, skew = skew)
}
E_const <- stats::integrate(
f = Func, lower = -Inf, upper = Inf,
subdivisions = 1000L, rel.tol = 1e-6, abs.tol = 1e-6,
stop.on.error = FALSE, dfun = PDF, shape = shape,
skew = skew
)[[1]]
if (lm) {
np2 <- nextpow2(2 * nn - 1)
coef_inf <- ma_infty(
ar = phi, ma = psi, d = d, max_i = trunc_vol
)
coef_inf[[1]] <- 0
sim <- loggarch_longmemo_type_sim(
innov, omega_sig,
coef_inf = coef_inf,
n_out = N,
mu = mu,
Econst = E_const, np2 = np2)
} else {
n_ar <- length(phi)
n_ma <- length(psi)
if (n_ma > n_ar) {
phi <- c(phi, rep(0, n_ma - n_ar))
} else if (n_ar > n_ma) {
psi <- c(psi, rep(0, n_ar - n_ma))
}
sim <- loggarch_shortmemo_type_sim(
innov, omega_sig,
ar_coef = phi, ma_coef = psi + phi,
n_out = N,
mu = mu,
Econst = E_const)
}
}
out <- list(
"rt" = stats::ts(c(sim[["rt"]])),
"sigt" = stats::ts(c(sim[["sigt"]])),
"etat" = stats::ts(c(sim[["etat"]])),
"cmeans" = stats::ts(rep(mu, n))
)
if (check) {
rt <- out$rt - mu # subtract mean again and then feed these as
# the errors into an ARMA / FARIMA model
if (!lm_arma) {
yt_data <- arma_sim_Cpp(innov = rt, ar = ar, ma = ma, nout = n, mu = mu)
} else {
coef_inf <- ar_infty(ar = ar, ma = ma, d = D, max_i = trunc_mean)[-1]
yt_data <- farima_sim_Cpp(innov = rt, coef_inf = coef_inf, nout = n, mu = mu)
}
out[["rt"]] <- stats::ts(c(yt_data[["rt"]]))
out[["cmeans"]] <- stats::ts(c(yt_data[["cmeans"]]))
out[["etat"]] <- stats::ts(utils::tail(out[["etat"]], n))
out[["sigt"]] <- stats::ts(utils::tail(out[["sigt"]], n))
}
out
}
#'Simulate From FIAPARCH Models
#'
#'A streamlined simulation function to simulate from
#'fractionally integrated asymmetric power autoregressive
#'conditional heteroskedasticity (FIAPARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{fiaparch}} for information
#'on the FIAPARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- fiaparch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
fiaparch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
gamma = 0.1,
delta = 2,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
cond_dist <- match.arg(cond_dist)
nn <- n + nstart # pre-sample plus sample number of observations
N <- n
trunc_vol <- trunc
trunc_mean <- trunc
# Parameter defaults (relevant if a truncated parameter list is provided)
pars_default <- lookup_table$sim_pars_default_fiaparch
names_pars <- names(pars)
for (nam in names_pars) {
pars_default[[nam]] <- pars[[nam]]
}
# Extract parameter settings
mu <- pars_default$mu
omega <- pars_default$omega
phi <- pars_default$phi
beta <- -pars_default$beta # "-" required to create a polynomial with positive signs
gamma <- pars_default$gamma
delta <- pars_default$delta
d <- pars_default$d
df <- pars_default$df
P <- pars_default$P
shape <- pars_default$shape
skew <- pars_default$skew
# ARMA / FARIMA parameters
ar <- pars_default$ar
ma <- pars_default$ma
D <- pars_default$D
lm_arma <- D != 0
# Simulate even more observations if ARMA / FARIMA required
check <- length(ar) + length(ma) > 0 || lm_arma
nn <- if (check) {
N <- N + nstart
nn + nstart
} else {
nn
}
lm <- TRUE
if ((lm || lm_arma) && ((is.character(trunc) && trunc == "none") || (is.numeric(trunc) && trunc >= nn))) {
trunc_vol <- nn - 1
trunc_mean <- N - 1
}
if (cond_dist %in% c("std", "sstd")) {
shape <- df # all functions are defined with "shape" argument (even if not used then within the function; for t-distr. types, we need to make shape our df)
} else if (cond_dist %in% c("ald", "sald")) {
shape <- P
}
# Simulate innovations following selected distribution
sim_fun <- simfun_selector(cond_dist)
innov <- sim_fun(nn, shape = shape, skew = skew)
# we need coefficients for the 1 pre-pre-sample time points, for the pre-sample,
# and for the sample with the exception of the very last sample time point
coef_inf <- ar_infty(ar = phi, ma = beta, d = d,
max_i = trunc_vol)
coef_inf[[1]] <- 0
sim <- fiaparch_sim_Cpp(
innov = innov, omega = omega, coef_inf = coef_inf,
gamma = gamma, delta = delta, n_out = N, mu = mu)
out <- list(
"rt" = stats::ts(c(sim[["rt"]])),
"sigt" = stats::ts(c(sim[["sigt"]])),
"etat" = stats::ts(c(sim[["etat"]])),
"cmeans" = stats::ts(rep(mu, n))
)
if (check) {
rt <- out$rt - mu # subtract mean again and then feed these as
# the errors into an ARMA / FARIMA model
if (!lm_arma) {
yt_data <- arma_sim_Cpp(innov = rt, ar = ar, ma = ma, nout = n, mu = mu)
} else {
coef_inf <- ar_infty(ar = ar, ma = ma, d = D, max_i = trunc_mean)[-1]
yt_data <- farima_sim_Cpp(innov = rt, coef_inf = coef_inf, nout = n, mu = mu)
}
out[["rt"]] <- stats::ts(c(yt_data[["rt"]]))
out[["cmeans"]] <- stats::ts(c(yt_data[["cmeans"]]))
out[["etat"]] <- stats::ts(utils::tail(out[["etat"]], n))
out[["sigt"]] <- stats::ts(utils::tail(out[["sigt"]], n))
}
out
}
#'Simulate From FIGJR-GARCH Models
#'
#'A streamlined simulation function to simulate from
#'FIGJR-GARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{figjrgarch}} for information
#'on the FIGJR-GARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- figjrgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
figjrgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
gamma = 0.1,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 2
fiaparch_sim(pars = pars, cond_dist = cond_dist, n = n, nstart = nstart, trunc = trunc)
}
#'Simulate From FITGARCH Models
#'
#'A streamlined simulation function to simulate from
#'FITGARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{fitgarch}} for information
#'on the FITGARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- fitgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
fitgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
gamma = 0.1,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 1
fiaparch_sim(pars = pars, cond_dist = cond_dist, n = n, nstart = nstart, trunc = trunc)
}
#'Simulate From FIGARCH Models
#'
#'A streamlined simulation function to simulate from
#'fractionally integrated generalized autoregressive conditional
#'heteroskedasticity (FIGARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{figarch}} for information
#'on the FIGARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- figarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
figarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.2,
beta = 0.4,
d = 0.25,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 2
pars[["gamma"]] <- 0
fiaparch_sim(pars = pars, cond_dist = cond_dist, n = n, nstart = nstart, trunc = trunc)
}
#'Simulate From APARCH Models
#'
#'A streamlined simulation function to simulate from
#'asymmetric power autoregressive
#'conditional heteroskedasticity (APARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{aparch}} for information
#'on the APARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- aparch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
aparch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
gamma = 0.1,
delta = 2,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
cond_dist <- match.arg(cond_dist)
nn <- n + nstart # pre-sample plus sample number of observations
N <- n
trunc_mean <- trunc
# Parameter defaults (relevant if a truncated parameter list is provided)
pars_default <- lookup_table$sim_pars_default_aparch
names_pars <- names(pars)
for (nam in names_pars) {
pars_default[[nam]] <- pars[[nam]]
}
# Extract parameter settings
mu <- pars_default$mu
omega <- pars_default$omega
phi <- pars_default$phi
beta <- pars_default$beta
gamma <- pars_default$gamma
delta <- pars_default$delta
df <- pars_default$df
P <- pars_default$P
shape <- pars_default$shape
skew <- pars_default$skew
l_phi <- length(phi)
l_gamma <- length(gamma)
stopifnot("Input parameter vectors phi and gamma must be of the same length." = l_phi == l_gamma)
# ARMA / FARIMA parameters
ar <- pars_default$ar
ma <- pars_default$ma
D <- pars_default$D
lm_arma <- D != 0
# Simulate even more observations if ARMA / FARIMA required
check <- length(ar) + length(ma) > 0 || lm_arma
nn <- if (check) {
N <- N + nstart
nn + nstart
} else {
nn
}
if (lm_arma && ((is.character(trunc) && trunc == "none") || (is.numeric(trunc) && trunc >= nn))) {
trunc_mean <- N - 1
}
if (cond_dist %in% c("std", "sstd")) {
shape <- df # all functions are defined with "shape" argument (even if not used then within the function; for t-distr. types, we need to make shape our df)
} else if (cond_dist %in% c("ald", "sald")) {
shape <- P
}
# Simulate innovations following selected distribution
sim_fun <- simfun_selector(cond_dist)
innov <- sim_fun(nn, shape = shape, skew = skew)
dfun <- fun1_selector(cond_dist)
int_fun <- function(x, shape, skew, gamma_i, delta, dfun) {
(abs(x) - gamma_i * x)^delta * dfun(x, shape = shape, skew = skew)
}
E_g <- rep(NA, length(gamma))
for (i in seq_along(gamma)) {
E_g <- stats::integrate(
f = int_fun, lower = -Inf, upper = Inf, subdivisions = 1000L,
rel.tol = 1e-6, abs.tol = 1e-6,
shape = shape, skew = skew, gamma_i = gamma[[i]], delta = delta,
dfun = dfun
)[[1]]
}
E_sigd <- omega / (1 - sum(phi * E_g) - sum(beta))
sim <- aparch_sim_Cpp(
innov = innov, omega = omega, phi = phi, beta = beta,
gamma = gamma, delta = delta, n_out = N, mu = mu,
E_sigd = E_sigd)
out <- list(
"rt" = stats::ts(c(sim[["rt"]])),
"sigt" = stats::ts(c(sim[["sigt"]])),
"etat" = stats::ts(c(sim[["etat"]])),
"cmeans" = stats::ts(rep(mu, n))
)
if (check) {
rt <- out$rt - mu # subtract mean again and then feed these as
# the errors into an ARMA / FARIMA model
if (!lm_arma) {
yt_data <- arma_sim_Cpp(innov = rt, ar = ar, ma = ma, nout = n, mu = mu)
} else {
coef_inf <- ar_infty(ar = ar, ma = ma, d = D, max_i = N)[-1]
yt_data <- farima_sim_Cpp(innov = rt, coef_inf = coef_inf, nout = n, mu = mu)
}
out[["rt"]] <- stats::ts(c(yt_data[["rt"]]))
out[["cmeans"]] <- stats::ts(c(yt_data[["cmeans"]]))
out[["etat"]] <- stats::ts(utils::tail(out[["etat"]], n))
out[["sigt"]] <- stats::ts(utils::tail(out[["sigt"]], n))
}
out
}
#'Simulate From GJR-GARCH Models
#'
#'A streamlined simulation function to simulate from
#'GJR-GARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{gjrgarch}} for information
#'on the GJR-GARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- gjrgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
gjrgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
gamma = 0.1,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 2 # Fix delta at 2 and use APARCH functions
aparch_sim(
pars = pars,
cond_dist = cond_dist,
n = n, nstart = nstart, trunc = trunc
)
}
#'Simulate From TGARCH Models
#'
#'A streamlined simulation function to simulate from
#'TGARCH models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{tgarch}} for information
#'on the TGARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- tgarch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
tgarch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
gamma = 0.1,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
pars[["delta"]] <- 1 # Fix delta at 1 and use APARCH functions
aparch_sim(
pars = pars,
cond_dist = cond_dist,
n = n, nstart = nstart, trunc = trunc
)
}
#'Simulate From GARCH Models
#'
#'A streamlined simulation function to simulate from
#'generalized autoregressive conditional heteroskedasticity
#'(GARCH) models.
#'
#'@param pars a named list with the parameter specifications; the user
#'can provide a named list with only the settings they would like to adjust
#'relative to the default settings.
#'@param cond_dist a one-element character vector specifying
#'the conditional distribution to consider.
#'@param n the number of observations to return.
#'@param nstart the number of burn-in observations to simulate before
#'the final \code{n} values to keep; the first \code{nstart} values
#'are not returned; if a dual model, i.e. with model in the conditional
#'mean and in the conditional variance, is considered, two times \code{nstart}
#'is considered in the first simulation step in the conditional variance,
#'so that \code{n + nstart} values can be fed into the second simulation
#'step for the conditional mean.
#'@param trunc a truncation for the finite-order coefficient series
#'in long-memory models; can either be the character \code{"none"} for truncation
#'back to the very first observation at each time point, or to any positive integer
#'for setting the corresponding truncation length of the infinite-order representation
#'polynomial.
#'
#'@details
#'See the documentation on \code{\link{garch}} for information
#'on the GARCH model. This function provides
#'an easy way to simulate from these models.
#'
#'@return
#'A list with four elements is returned: \code{rt} are the simulated
#'observations, \code{etat} are the underlying innovations,
#'\code{sigt} are the correspondingly simulated conditional
#'standard deviations, and \code{cmeans} are the simulated
#'conditional means. These four elements are formatted as
#'\code{"ts"} class time series objects.
#'
#'@export
#'
#'@examples
#'sim <- garch_sim(n = 1000)
#'mat <- do.call(cbind, sim)
#'plot(mat, main = "")
#'
garch_sim <- function(pars = list(
mu = 0,
ar = numeric(0),
ma = numeric(0),
D = 0,
omega = 0.0004,
phi = 0.05,
beta = 0.8,
df = 10,
shape = 2,
P = 3,
skew = 1
), cond_dist = c("norm", "std", "ged", "ald", "snorm", "sstd", "sged", "sald"),
n = 1000, nstart = 5e3, trunc = "none") {
p <- length(pars$phi)
pars[["delta"]] <- 2 # Fix delta at 1 and use APARCH functions
pars[["gamma"]] <- rep(0, p)
aparch_sim(
pars = pars,
cond_dist = cond_dist,
n = n, nstart = nstart, trunc = trunc
)
}
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