BBT: Brownian Bridge transformation

Description

Transforms data according to empirical Brownian Bridge precess.

Usage

BBT(x)

Arguments

a numeric vector of data values. The length must be greater then 1 and variance greater then 0.

Value

A numeric vector.

Details

Let n denotes the length ox x. For each $m \in [1,n]$ transformations BBT difined as $$BBT(m, x) = \frac{1}{\sqrt{n var(x)}} \left{ \sum_{i=1}^m x_i - \frac{m}{n} \sum_{i=1}^n x_i \right} .$$

Examples

Run this code

x = c(rnorm(250,0),rnorm(250,0.3), rnorm(250,0), rnorm(250,0.3))
Y = BBT(x)
Pv = pvar(Y, p = 4)
plot(Pv)

PvarBreakTest(x, FullInfo = FALSE)