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#' Compute the extended Fisher's g test statistic
#'
#' @description
#' The extended Fisher's g te statistic is computed for testing for periodicity.
#'
#' @param y Vector containing the series.
#'
#' @return Vector of length 2 containing the modified Fisher's G test statistic
#' and the frequency for the maximum periodogram.
#'
#' @details Extend the Fisher's g test by enlarging the searching region
#' of the frequency from the fourier frequencies to be
#' \eqn{En = {j/101 | j=1,\dots,50 and j/101 \ge 1/n}}.
#'
#' @author Yuanhao Lai
#'
#' @references Fisher, R.A. (1929). Tests of significance in harmonic analysis.
#' Proc. Roy. Soc. A, 125, 54-59.
#'
#' @keywords internal
GetFitExtendedG <- function(y) {
#Compute the extended Fisher's G test statistic
n <- length(y)
# Mean removal
y <- y-mean(y)
t0 <- ceiling(101/n)
Dpgram <- pgram(y, fr=101)
Dpgram <- Dpgram[t0:50,]
maxL <- which.max(Dpgram[,2])
D <- sum(Dpgram[,2])
gm <- Dpgram[maxL,2]/D
ans <- c(gm,Dpgram[maxL,1]) #statistic and frequency
names(ans) <- c("gm","freq")
ans
}
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