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#'Fits an AR1 Autocorrelation Function Using Dichotomy
#'
#'This function fits the theoretical autocorrelation function of an AR1 to
#'the first guess of the estimated autocorrelation function estacf containing
#'any number of lags. The fitting relies on a dichotomial minimisation of the
#'mean square differences between both autocorrelation functions. It returns
#'the autocorrelation at lag 1 of the fitted AR1 process.
#'
#'@param estacf First guess for the autocorrelation function.
#'@param window Interval in which the autocorrelation at lag 1 should be found.
#'@param prec Precision to which the autocorrelation function at lag 1 is to be estimated.
#'
#'@return Best estimate of the autocorrelation at lag 1.
#'
#'@keywords datagen
#'@author History:\cr
#'0.1 - 2012-02 (V. Guemas) - Original code\cr
#'1.0 - 2013-09 (N. Manubens) - Formatting to CRAN
#'@examples
#'series <- GenSeries(1000, 0.35, 2, 1)
#'estacf <- acf(series[951:1000], plot = FALSE)$acf
#'alpha <- FitAutocor(estacf, c(-1, 1), 0.01)
#'print(alpha)
#'@export
FitAutocor <- function(estacf, window = c(-1, 1), prec = 0.01) {
nacf <- length(estacf)
alpha <- mean(window)
dist <- nacf * 4
for (jind in 1:nacf) {
estacf[jind] <- max(estacf[jind], 0)
}
for (jalph in seq(window[1], window[2], prec)) {
test <- sum(((estacf - (jalph ^ c(1:nacf - 1))) / c(1:nacf)) ^ 2)
if (test < dist) {
dist <- test
alpha <- jalph
}
}
alpha
}
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