R/RcppExports.R

In tobiaskley/forecastSNSTS: Forecasting for Stationary and Non-Stationary Time Series

# Generated by using Rcpp::compileAttributes() -> do not edit by hand
# Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393

#' Mean Squared Prediction Errors, for a single \eqn{h}
#'
#' This function computes the estimated mean squared prediction errors from a
#' given time series and prediction coefficients
#'
#' The array of prediction coefficients \code{coef} is expected to be of
#' dimension \code{P x P x H x length(N) x length(t)} and in the format as
#' it is returned by the function \code{\link{predCoef}}. More precisely, for
#' \eqn{p=1,\ldots,P} and the \code{j.N}th element of \code{N} element of
#' \code{N} the coefficient of the
#' \code{h}-step ahead predictor for \eqn{X_{i+h}} which is computed from
#' the observations \eqn{X_i, \ldots, X_{i-p+1}} has to be available via
#' \code{coef[p, 1:p, h, j.N, t==i]}.
#'
#' Note that \code{t} have to be the indices corresponding to the coefficients.
#'
#' The resulting mean squared prediction error
#' \deqn{\frac{1}{|\mathcal{T}|} \sum_{t \in \mathcal{T}} (X_{t+h} - (X_t, \ldots, X_{t-p+1}) \hat v_{N[j.N],T}^{(p,h)}(t))^2}
#' is then stored in the resulting matrix at position \code{(p, j.N)}. 
#'
#' @name computeMSPEcpp
#'
#' @param X the data
#' @param coef the array of coefficients.
#' @param h which lead time to compute the MSPE for
#' @param t a vector of times from which backward the forecasts are computed
#' @param type indicating what type of measure of accuracy is to be computed;
#'            1: mspe, 2: msae
#' @param trimLo percentage of lower observations to be trimmed away
#' @param trimUp percentage of upper observations to be trimmed away
#'
#' @return Returns a \code{P x length(N)} matrix with the results.
NULL

computeMSPEcpp <- function(X, coef, h, t, type, trimLo, trimUp) {
    .Call('_forecastSNSTS_computeMSPEcpp', PACKAGE = 'forecastSNSTS', X, coef, h, t, type, trimLo, trimUp)
}

#' \eqn{h}-step Prediction coefficients
#'
#' This function computes the localised and iterated Yule-Walker coefficients
#' for h-step ahead forecasting of \eqn{X_{t+h}} from \eqn{X_{t}, ..., X_{t-p+1}},
#' where \eqn{h = 1, \ldots,} \code{H} and \eqn{p = 1, \ldots,} \code{P}.
#' 
#' For every \eqn{t \in} \code{t} and every \eqn{N \in} \code{N} the (iterated) Yule-Walker
#' estimates \eqn{\hat v_{N,T}^{(p,h)}(t)} are computed. They are defined as
#' \deqn{\hat v_{N,T}^{(p,h)}(t) :=  e'_1 \big( e_1 \big( \hat a_{N,T}^{(p)}(t) \big)' + H \big)^h, \quad N \geq 1,}
#' and
#' \deqn{\hat v_{0,T}^{(p,h)}(t) :=  \hat v_{t,T}^{(p,h)}(t),}
#' with
#' \deqn{ e_1 := \left(\begin{array}{c} 1 \\ 0 \\ \vdots \\ 0 \end{array} \right), \quad H := \left( \begin{array}{ccccc} 0 & 0 & \cdots & 0 & 0 \\ 1 & 0 & \cdots & 0 & 0 \\ 0 & 1 & \cdots & 0 & 0 \\ \vdots & \ddots & \cdots & 0 & 0 \\ 0 & 0 & \cdots & 1 & 0 \end{array} \right)}
#' and
#' \deqn{ \hat a_{N,T}^{(p)}(t) := \big( \hat\Gamma_{N,T}^{(p)}(t) \big)^{-1} \hat\gamma_{N,T}^{(p)}(t),}
#' where
#' \deqn{\hat\Gamma_{N,T}^{(p)}(t) := \big[ \hat \gamma_{i-j;N,T}(t) \big]_{i,j = 1, \ldots, p}, \quad \hat \gamma_{N,T}^{(p)}(t) := \big( \hat \gamma_{1;N,T}(t), \ldots, \hat \gamma_{p;N,T}(t) \big)'}
#' and
#' \deqn{\hat \gamma_{k;N,T}(t) := \frac{1}{N} \sum_{\ell=t-N+|k|+1}^{t} X_{\ell-|k|,T} X_{\ell,T}}
#' is the usual lag-\eqn{k} autocovariance estimator (without mean adjustment),
#' computed from the observations \eqn{X_{t-N+1}, \ldots, X_{t}}.
#'
#' The Durbin-Levinson Algorithm is used to successively compute the solutions to the
#' Yule-Walker equations (cf. Brockwell/Davis (1991), Proposition 5.2.1).
#' To compute the \eqn{h}-step ahead coefficients we use the recursive relationship
#' \deqn{\hat v_{i,N,T}^{(p)}(t,h) = \hat a_{i,N,T}^{(p)}(t) \hat v_{1,N,T}^{(p,h-1)}(t) + \hat v_{i+1,N,T}^{(p,h-1)}(t) I\{i \leq p-1\},}
#' (cf. the proof of Lemma E.3 in Kley et al. (2017)).
#'
#' @name predCoef
#' @export
#'
#' @param X the data \eqn{X_1, \ldots, X_T}
#' @param P the maximum order of coefficients to be computed; has to be a positive integer
#' @param H the maximum lead time; has to be a positive integer
#' @param t a vector of values \eqn{t}; the elements have to satisfy
#'            \code{max(t) <= length(X)} and  \code{min(t) >= min(max(N[N != 0]),p)}.
#' @param N a vector of values \eqn{N}; the elements have to satisfy
#'            \code{max(N[N != 0]) <= min(t)} and \code{min(N[N != 0]) >= 1 + P}.
#'            \eqn{N = 0} corresponds to the case where all data is taken into account.
#'
#' @return Returns a named list with elements \code{coef}, \code{t}, and \code{N},
#'         where \code{coef} is an array of dimension
#'         \code{P} \eqn{\times} \code{P} \eqn{\times} \code{H} \eqn{\times}
#'         \code{length(t)} \eqn{\times} \code{length(N)}, and
#'         \code{t}, and \code{N} are the parameters provided on the call of the
#'         function. See the example on how to access the vector
#'         \eqn{\hat v_{N,T}^{(p,h)}(t)}.
#'
#' @references
#' Brockwell, P. J. & Davis, R. A. (1991).
#' Time Series: Theory and Methods. Springer, New York.
#'
#' @examples
#' T <- 100
#' X <- rnorm(T)
#'
#' P <- 5
#' H <- 1
#' m <- 20
#'
#' Nmin <- 25
#' pcoef <- predCoef(X, P, H, (T - m - H + 1):T, c(0, seq(Nmin, T - m - H, 1)))
#' 
#' ## Access the prediction vector for p = 2, h = 1, t = 95, N = 25
#' p <- 2
#' h <- 1
#' t <- 95
#' N <- 35
#' res <- pcoef$coef[p, 1:p, h, pcoef$t == t, pcoef$N == N]
NULL

predCoef <- function(X, P, H, t, N) {
    .Call('_forecastSNSTS_predCoef', PACKAGE = 'forecastSNSTS', X, P, H, t, N)
}

#' Workhorse function for tvARMA time series generation
#'
#' More explanation!
#'
#' @name tvARMAcpp
#'
#' @param z a ...
#' @param x_int a ...
#' @param A ...
#' @param B a ...
#' @param Sigma a ...
#'
#' @return Returns a ...
#'
NULL

tvARMAcpp <- function(z, x_init, A, B, Sigma) {
    .Call('_forecastSNSTS_tvARMAcpp', PACKAGE = 'forecastSNSTS', z, x_init, A, B, Sigma)
}