archived R/DLalg.R

In jlivsey/countsFun:

#' #' Univariate Durbin-Levinson algoithm.
#' #' This implimentation takes a mean value and subtracts it during calculation
#' #' of one-step-ahead predictors and residuals
#' #'
#' #' @param x univariate time series
#' #' @param g ACVF function where g[1] = gamma(0)
#' #' @param lam mean
#' #'
#' #' @return list with lower triangular matrix of predicition coefficients, mses,
#' #' one-step-ahead predictions and residuals
#' #' @export
#' #'
#' #' @examples
#' DLalg <- function(x, g, mean.x){
#'   # parameters known from inputs
#'   n <- length(x)
#'
#'   # Iniitalize storage
#'   phi <- matrix(NA, n, n)
#'   v <- rep(NA, n)
#'
#'   # inital values
#'   phi[1, 1] <- g[2]/g[1]
#'   v[1] <- g[1]
#'
#'   # main loop
#'   for(m in 2:n){
#'     phi[m, m] <- (g[m+1] - sum(phi[m-1, 1:(m-1)] * g[(m-1+1):2])) / v[m-1]
#'     phi[m, 1:(m-1)] <- phi[m-1, 1:(m-1)] - phi[m, m] * phi[m-1, (m-1):1]
#'     v[m] <- v[m-1] * (1 - phi[m-1, m-1]^2)
#'   }
#'
#'   # Calculate xhat's
#'   xhat <- rep(NA, n+1) #storage
#'   xhat[1] <- 0
#'   for(m in 1:n){
#'     xhat[m+1] <- sum(phi[m, 1:m] * (x[m:1] - mean.x))
#'   }
#'
#'   # residuals
#'   e <- (x - mean.x) - xhat[1:n]
#'
#'   return(list(
#'     phi  = phi,
#'     v    = v,
#'     xhat = xhat,
#'     e    = e
#'   ))
#'
#' }