MrVarianceRatio.R

#' @title Compute the Mr statistic.
#' 
#' @description Compute the Mr statistic. The Md statistic is the ratio 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 minus 1. 
#' This statistic should converge to zero.
#' 
#' @inheritParams calibrateSigma
#' @return Mr double :: The Mr statistic defined by Lo and MacKinlay.
#' 
mRatio <- 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)
  Mr <- (sigmaB / sigmaA) - 1
  return(Mr)
}