R/Portmanteau_test.R

In BEKKs: Multivariate Conditional Volatility Modelling and Forecasting

#' Performing a Portmanteau test checking for remaining correlation in the empirical co-variances of the estimated BEKK residuals.
#'
#' @description Method for a Portmanteau test of the null hypothesis of no remaining correlation in the co-variances of the estimated BEKK residuals.
#'
#' @param x An object of class "bekkFit" from function \link{bekk_fit}.
#' @param lags An integer defining the lag length.
#' @return  Returns an Object of class "htest" containing the p-value and test statistic.
#'
#' @details Here, the multivariate Portmanteau test of Hosking (1980) is implemented.
#'
#' @references  J. R. M. Hosking (1980). The Multivariate Portmanteau Statistic, Journal of the American Statistical Association, 75:371, 602-608.


#' @import xts
#' @import stats
#' @import ks
#' @export
portmanteau.test <- function(x, lags = 5){
  if(!is.numeric(lags)){
    stop("Please provide a numeric object or vector for 'lags'.")
  }
  if(any(lags<3)){
    stop("Please provide 'lags' larger than 2.")
  }
  UseMethod("portmanteau.test")
}

#' @export
portmanteau.test.bekkFit <- function(x, lags = 5){
  e <- x$e_t
  n <- nrow(e)
  N <- ncol(e)
  e <- matrix(e,n,N)
  #e <- matrix(e, nrow = n, ncol = N)
  e2 <- matrix(NA,nrow = n, ncol = N*(N+1)/2)

  for(i in 1:n){
    e2[i,] <- ks::vech(crossprod(t(e[i,])))
  }
  e=e2

  c_hat <- function(j){
        c= t(e[(j+1):n,]) %*% e[1:(n-j),]
        return(c/n)
  }
  c_0 = c_hat(0)
  #c_0_inv = solve(c_0)
  c_0_inv = chol2inv(chol(c_0))
  Q <- function(lgs){
    q=0
   for(i in 1:lgs){
     c_temp = t(c_hat(i))
     q=q+sum(diag(c_temp%*%c_0_inv%*%c_temp%*%c_0_inv))
   }
    return(q)
  }
  p_val_q <- function(k, lgs){
    return(1-pchisq(k, df=(lgs-2)*(N^2)))
  }



  statistic = Q(lags)
  names(statistic) = "statistic"
  p.value = p_val_q(p_val_q(statistic,lags),lags)
  names(p.value) = "p.value"
  parameter = (lags-2)*(N^2)
  names(parameter) = "df"
  data = "Residuals of estimated BEKK process"



  rval <- list(statistic = statistic, parameter = parameter, p.value = p.value, data.name

               = data, method = paste("Portmanteau Test (Lags = ", as.character(lags), ")", sep = "" ))
  class(rval) <- "htest"
  return(rval)
}