VarianceRatio.R

#' @title Given a log price process, X, compute the Z-score which can be used 
#' to accept or reject the hypothesis that the process evolved according to a 
#' Brownian Motion model with drift and stochastic volatility.
#' 
#' @description Given a log price process, X, and a sampling interval, q, this 
#' method returns a Z score indicating the confidence we have that X evolved 
#' according to a Brownian Motion mode with drift and stochastic volatility. This
#' heteroskedasticity-consistent variance ratio test essentially checks to see 
#' whether or not the observed Mr statistic for the number of observations, is 
#' within or out of the limiting distribution defined by the Asymptotic Variance.
#' 
#' @param X vector :: A log price process.
#' @param q int :: The sampling interval for the estimator.
#' 
VRTestZScore <- function(X, q) {
  n <- floor(length(X)/q)
  z <- sqrt(n * q) * mRatio(X, q)
  z <- z / sqrt(calibrateAsymptoticVariance(X, q))
  return(z)
}