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#' @title Probability integral transform.
#' @description Method returning the probability integral
#' transform (PIT).
#' @param object Model specification of class \code{MSGARCH_SPEC}
#' created with \code{\link{CreateSpec}} or fit object of type \code{MSGARCH_ML_FIT}
#' created with \code{\link{FitML}} or \code{MSGARCH_MCMC_FIT} created with \code{\link{FitMCMC}}.
#' @param x Vector (of size n). Used when \code{do.its = FALSE}.
#' @param par Vector (of size d) or matrix (of size \code{nmcmc} x d) of
#' parameter estimates where d must have
#' the same length as the default parameters of the specification.
#' @param data Vector (of size T) of observations.
#' @param newdata Vector (of size T*) of new observations. (Default: \code{newdata = NULL})
#' @param do.norm Logical indicating if the PIT values are transformed
#' into standard Normal variate. (Default: \code{do.norm = FALSE})
#' @param do.its Logical indicating if the in-sample PIT is returned. (Default: \code{do.its = FALSE})
#' @param nahead Scalar indicating the number of step-ahead evaluation.
#' Valid only when \code{do.its = FALSE}. (Default: \code{nahead = 1L})
#' @param do.cumulative Logical indicating if the PIT is computed on the cumulative simulations (typically log-returns, as they can be aggregated).
#' Only available for \code{do.its = FALSE}. (Default: \code{do.cumulative = FALSE})
#' @param ctr A list of control parameters:
#' \itemize{
#' \item \code{nsim} (integer >= 0):
#' Number indicating the number of simulation done for the
#' evaluation of the PIT at \code{nahead > 1}. (Default: \code{nsim = 10000L})
#' }
#' @param ... Not used. Other arguments to \code{PIT}.
#' @return A vector or matrix of class \code{MSGARCH_PIT}. \cr
#' If \code{do.its = FALSE}: Probability integral transform of the
#' points \code{x} at \cr \code{t = T + T* + 1, ... ,t = T + T* + nahead} or Normal variate derived from the probability
#' integral transform of \code{x} (matrix of size \code{nahead} x n).\cr
#' If \code{do.its = TRUE}: In-sample probability integral transform or Normal variate
#' derived from the probability integral transform of \code{data} if \code{x = NULL} (vector of
#' size T + T*) or in-sample probability integral transform or Normal variate
#' derived from the probability integral transform of \code{x} (matrix of size (T + T*) x n).
#' @details If a matrix of MCMC posterior draws is given, the
#' Bayesian probability integral transform is calculated.
#' Two or more step-ahead probability integral
#' transform are estimated via simulation of \code{nsim} paths up to \code{t = T + T* + nahead}.
#' The empirical probability integral transforms is then inferred from these simulations.\cr
#' If \code{do.its = FALSE}, the vector \code{x} are evaluated as \code{t = T + T* + 1, ... ,t = T + T* + nahead}
#' realizations.\cr
#' If \code{do.its = TRUE}, \code{x} is evaluated
#' at each time \code{t} up to time \code{t = T + T*}.\cr
#' Finally if \code{x = NULL} the vector \code{data} is evaluated for sample evaluation of the PIT.\cr
#' The \code{do.norm} argument transforms the PIT value into Normal variates so that normality test can be done.
#' @examples
#' # create model specification
#' spec <- CreateSpec()
#'
#' # load data
#' data("SMI", package = "MSGARCH")
#'
#' # fit the model on the data by ML
#' fit <- FitML(spec = spec, data = SMI)
#'
#' # run PIT method in-sample
#' pit.its <- PIT(object = fit, do.norm = TRUE, do.its = TRUE)
#'
#' # diagnostic of PIT with qqnorm
#' qqnorm(pit.its)
#' qqline(pit.its)
#'
#' # simulate a serie from the model
#' set.seed(123)
#' sim.series <- simulate(object = spec, par = fit$par, nahead= 1000L, nsim = 1L)
#' sim.series <- as.vector(sim.series$draw)
#'
#' # run PIT method on the simualed serie with the true par
#' pit.x <- PIT(object = spec, par = fit$par, data = sim.series, do.norm = TRUE, do.its = TRUE)
#' qqnorm(pit.x)
#' qqline(pit.x)
#' @importFrom stats qnorm
#' @export
PIT <- function(object, ...) {
UseMethod(generic = "PIT", object)
}
#' @rdname PIT
#' @export
PIT.MSGARCH_SPEC <- function(object, x = NULL, par = NULL, data = NULL,
do.norm = FALSE, do.its = FALSE, nahead = 1L, do.cumulative = FALSE, ctr = list(), ...) {
object <- f_check_spec(object)
data_ <- f_check_y(data)
if (is.vector(par)) {
par <- matrix(par, nrow = 1L)
}
if (nrow(par) == 1) {
ctr <- f_process_ctr(ctr)
nsim <- ctr$nsim
} else {
if(is.null(ctr$nsim)){
nsim = 1
} else {
nsim = ctr$nsim
}
}
ctr <- f_process_ctr(ctr)
x.is.null <- FALSE
if (is.null(x)) {
x.is.null <- TRUE
}
draw <- NULL
par_check <- f_check_par(object, par)
if (isTRUE(do.its)) {
if (is.null(x)) {
x <- matrix(data = data_, ncol = length(data_))
} else {
x <- matrix(x)
if (ncol(x) == 1L) {
x <- matrix(x, ncol = length(data_), nrow = nrow(x))
} else {
stop("x have more than 1 column: x must be a vector, NULL, or a matrix of size n x 1")
}
}
tmp <- matrix(data = 0, nrow = length(data_), ncol = nrow(x))
for (i in 1:nrow(par)) {
if (object$K == 1) {
tmp2 <- object$rcpp.func$cdf_Rcpp_its(par_check[i, ], data_, x, FALSE)
tmp <- tmp + tmp2[, , 1L]
} else {
Pstate <- State(object = object, par = par[i, ], data = data_)$PredProb
Pstate.tmp <- matrix(data = NA, nrow = dim(Pstate)[1L], ncol = dim(Pstate)[3L])
for (j in 1:dim(Pstate)[3L]) {
Pstate.tmp[, j] <- Pstate[, , j]
}
tmp2 <- object$rcpp.func$cdf_Rcpp_its(par_check[i, ], data_, x, FALSE)
for (k in 1:object$K) {
tmp <- tmp + tmp2[, , k] * matrix(Pstate.tmp[1:(nrow(Pstate.tmp) - 1L), k],
ncol = nrow(x), nrow = length(data))
}
}
}
tmp <- tmp/nrow(par)
rownames(tmp) = paste0("t=",1:length(data_))
if(zoo::is.zoo(data)){
tmp = zoo::zooreg(tmp, order.by = zoo::index(data))
}
if(is.ts(data)){
tmp = zoo::zooreg(tmp, order.by = zoo::index(data))
tmp = as.ts(tmp)
colnames(tmp) = rep("",ncol(tmp))
}
} else {
x <- matrix(x)
if (ncol(x) != 1L) {
stop("x must be a vector or a matrix of size N x 1")
}
tmp <- matrix(data = 0, nrow = nahead, ncol = nrow(x))
for (i in 1:nrow(par)) {
tmp[1,] <- tmp[1, ] + object$rcpp.func$cdf_Rcpp(x, par_check[i, ], data_, FALSE)
}
tmp <- tmp/nrow(par)
if (nahead > 1) {
draw <- Sim(object = object, data = data_, nahead = nahead, nsim = nsim, par = par)$draw
if(isTRUE(do.cumulative)){
draw = apply(draw, 2, cumsum)
}
for (j in 2:nahead) {
tmp[j, ] <- f_cdf_empirical(y = draw[j, ], x)
}
}
rownames(tmp) <- paste0("h=",1:nahead)
if(zoo::is.zoo(data)){
tmp = zoo::zooreg(tmp, order.by = zoo::index(data)[length(data)]+(1:nahead))
}
if(is.ts(data)){
tmp = zoo::zooreg(tmp, order.by = zoo::index(data)[length(data)]+(1:nahead))
tmp = as.ts(tmp)
colnames(tmp) = rep("",ncol(tmp))
}
}
if (!isTRUE(ctr$do.return.draw)) {
draw <- NULL
}
if (do.norm) {
tmp2 <- stats::qnorm(tmp, mean = 0, sd = 1)
colnames(tmp2) <- colnames(tmp)
rownames(tmp2) <- rownames(tmp)
tmp <- tmp2
}
if(isTRUE(x.is.null) && !is.ts(data)){
out <- tmp[,1]
} else {
out = tmp
}
class(out) <- c("MSGARCH_PIT", class(out))
return(out)
}
#' @rdname PIT
#' @export
PIT.MSGARCH_ML_FIT <- function(object, x = NULL, newdata = NULL,
do.norm = TRUE, do.its = FALSE, nahead = 1L, do.cumulative = FALSE, ctr = list(), ...) {
data = c(object$data, newdata)
if(is.ts(object$data)){
if(is.null(newdata)){
data = zoo::zooreg(data, order.by = c(zoo::index(data)))
} else {
data = zoo::zooreg(data, order.by = c(zoo::index(data),zoo::index(data)[length(data)]+(1:length(newdata))))
}
data = as.ts(data)
}
out <- PIT(object = object$spec, x = x, par = object$par, data = data,
do.norm = do.norm, do.its = do.its, nahead = nahead, do.cumulative = do.cumulative, ctr = ctr)
return(out)
}
#' @rdname PIT
#' @export
PIT.MSGARCH_MCMC_FIT <- function(object, x = NULL, newdata = NULL,
do.norm = TRUE, do.its = FALSE, nahead = 1L, do.cumulative = FALSE, ctr = list(), ...) {
data = c(object$data, newdata)
if(is.ts(object$data)){
if(is.null(newdata)){
data = zoo::zooreg(data, order.by = c(zoo::index(data)))
} else {
data = zoo::zooreg(data, order.by = c(zoo::index(data),zoo::index(data)[length(data)]+(1:length(newdata))))
}
data = as.ts(data)
}
out <- PIT(object = object$spec, x = x, par = object$par, data = data,
do.norm = do.norm, do.its = do.its, nahead = nahead, do.cumulative = do.cumulative, ctr = ctr)
return(out)
}
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