MdVarianceRatio.R

#' @title Compute the Md statistic.
#' 
#' @description Compute the Md statistic. The Md statistic is the difference 
#' between two estimate values for Sigma computed using the calibrateSigma 
#' function for sampling intervals 1 and the estimate value for Sima computed 
#' using the CalibrateSigmaOverlapping function for sampling inveral q. 
#' This statistic should converge to zero.
#' 
#' @inheritParams calibrateSigma
#' @return Md double :: The Md statistic defined by Lo and MacKinlay.
#' 
mDifferences <- function(X, q, annualize = FALSE, unbiased = TRUE) {
  # Estimate the value of sigma at sampling intervals 1 and q.
  sigmaA <- calibrateSigma(X, q = 1, annualize, unbiased)
  sigmaB <- calibrateSigmaOverlapping(X, q = q, annualize, unbiased)
  Md <- sigmaB - sigmaA
  return(Md)
}