The distribution of p-variation of BridgeT(x) depends on n=length(x).
This fact is important for getting appropriate quantiles (or p-value).
These functions helps to deal with it.
PvarQuantile(n, prob = c(0.9, 0.95, 0.99), DF = PvarQuantileDF)PvarPvalue(n, stat, DF = PvarQuantileDF)
getMean(n, bMean = MeanCoef)
getSd(n, bSd = SdCoef)
NormalisePvar(x, n, bMean = MeanCoef, bSd = SdCoef)
Functions PvarQuantile and PvarPvalue returns a corresponding value quantile or the probability.
Functions getMean and getSd returns a corresponding value of mean and sd statistics.
Function NormalisePvar returns normalize values.
a positive integer indicating the length of data vector.
cumulative probabilities of p-variation distribution.
a data.frame that links prob and stat .
a vector of p-variation statistics.
a coefficient vector that defines a function of the mean of p-variation.
a coefficient vector that defines a function of the standard deviation of p-variation.
a numeric vector of data values.
The distribution of p-variance is form Monte-Carlo simulation based on 140 millions iterations.
The data frame PvarQuantileDF saves the results of Monte-Carlo simulation.
Meanwhile, MeanCoef and SdCoef defines the coefficients of functional
form (conditional on n) of mean and sd statistics.
A functional form of mean and sd statistics are the same, namely
$$
f(n) = b_1 + b_2 n^b_2 .
$$
The coefficients \((b_1, b_2, b_3)\) are saved in vectors MeanCoef and SdCoef.
Those vectors are estimated with nls function form Monte-Carlo simulation.
PvarBreakTest, PvarQuantileDF,
NormalisePvar, getMean, getSd