Quantiles and probabilities of p-variation

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Description

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.

Usage

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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)

Arguments

n

a positive integer indicating the length of data vector.

prob

cumulative probabilities of p-variation distribution.

DF

a data.frame that links prob and stat .

stat

a vector of p-variation statistics.

bMean

a coefficient vector that defines a function of the mean of p-variation.

bSd

a coefficient vector that defines a function of the standard deviation of p-variation.

x

a numeric vector of data values.

Details

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.

Value

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.

Note

Arguments n, stat and prob might be vectors, but they can't be vectors simultaneously (at least one of then must be a number).

See Also

PvarBreakTest, PvarQuantileDF, NormalisePvar, getMean, getSd