README.md

In zhibinghe/ChangePoint: Multiple Testing of Local Extrema for Detection of Structural Breaks

An R package for change point detection: dSTEM

Zhibing He June 20, 2023

dSTEM: differential Smoothing and TEsting of Maxima/Minima

A new generic and low-computational approach for multiple change points detection in linear models. The method is designed for the data sequence modeled as piecewise linear signal plus correlated random noise (a stationary Gaussian process). See the related papers: “Multiple testing of local extrema for detection of change points” and “Multiple testing of local extrema for detection of structural breaks in piecewise linear models”.

Toy Example of the Method

The core idea of our method is to transform the change points into local maxima/minima of the differential smoothed data. By performing multiple testing on the local maxima/minima, the significant ones are detected as change points.

For example, a continuous change point will be transformed into a local maximum/minimum in the second derivative of the smoothed data, while a noncontinuous change point will be transformed into a local maximum/minimum in the first derivative of the smoothed data. A toy example is illustrated as follows

Usage

The main function is ‘dstem()’, which detect the change points in piecewise constant and piecewise linear signals.

l = 1200
h = seq(150,by=150,length.out=6)
jump = rep(0,7)
beta1 = c(2,-1,2.5,-3,-0.2,2.5)/50
beta1 = c(beta1,-sum(beta1*(c(h[1],diff(h))))/(l-tail(h,1)))
signal = gen.signal(l,h,jump,beta1)
noise = rnorm(length(signal),0,1)
gamma = 25
unlist(dstem(signal + noise,"I",gamma=gamma,alpha=0.05))

## vall1 vall2 vall3 peak1 peak2 peak3 
##   154   446   896   303   601   742

## piecewise constant
l = 1200
h = seq(150,by=150,length.out=6)
jump = c(0,1.5,2,2.2,1.8,2,1.5)
beta1 = rep(0,length(h)+1)
signal = gen.signal(l,h,jump,beta1)
noise = rnorm(length(signal),0,1)
gamma = 25
unlist(dstem(signal + noise, "II-step",gamma,alpha=0.05))

## peak1 peak2 peak3 peak4 peak5 peak6 
##   159   296   449   600   755   899

## piecewise linear with jump
l = 1200
h = seq(150,by=150,length.out=6)
jump = c(0,1.5,2,2.2,1.8,2,1.5)*3
beta1 = c(2,-1,2.5,-3,-0.2,2.5,-0.5)/50
signal = gen.signal(l=l,h=h,jump=jump,b1=beta1)
noise = rnorm(length(signal),0,1)
gamma = 25
unlist(dstem(signal + noise, "II-linear",gamma,alpha=0.05))

## peak1 peak2 peak3 peak4 peak5 peak6 
##   141   308   440   607   755   894

zhibinghe/ChangePoint documentation built on Feb. 22, 2025, 12:34 p.m.