R/estimateRho.R

In stanek-fi/ACV: Optimal Out-of-Sample Forecast Evaluation and Testing under Stationarity

#' Estimate `rho` coefficient
#'
#' Internal function for estimating the rho coefficient.
#'
#' @param Phi Matrix of computed contrasts generated by `tsACV()`.
#' @param rhoLimit Parameter `rhoLimit` limits to the absolute value of the estimated `rho` coefficient. This is useful as estimated values very close to 1 might cause instability.
#'
#' @return Estimated `rho` coefficient (numeric vector of length 1).
#'
#' @export
#' @keywords internal

estimateRho <- function(Phi, rhoLimit) {
  temp <- infoPhi(Phi)
  K <- temp$K
  mn <- temp$mn
  m <- temp$m
  v <- temp$v
  h <- temp$h
  mh <- temp$mh
  J <- temp$J

  Target <- 1 - 1 / (2 * stats::var(c(Phi), na.rm = T)) * sapply(1:K, function(k) {
    apply((Phi - Phi[, k])^2, 2, mean, na.rm = T)
  })
  Target <- sapply(1:K, function(k) mean(Target[cbind((k):K, 1:(K - k + 1))]))
  Weights <- pmax(mh - (0:(K - 1)) * v, 0) * (K:1)

  moments <- function(par) {
    return(ifelse(is.na(Target), 0, Target - par^(v * (0:(K - 1)))))
  }

  objective <- function(par) {
    return(sum(moments(par)^2 * Weights))
  }

  fit <- stats::optimize(objective, interval = c(-rhoLimit, rhoLimit))
  rho <- fit$minimum
  return(rho)
}