ChangePointMean

Detect change point in the mean of a time series via randomization test of centered cumsum.

Installation

This package can be installed via its URL:

] add https://github.com/DaymondLing/ChangePointMean.jl

Purpose

If you are looking for general purpose change point detection, e.g., change in mean or variance or slope, this package is not it. Changepoints is probably what you are looking for.

This is a simple, useful, efficient package for detecting mean shift in a time series via cumsum randomization test. It is non-parametric in the sense that there are no distribution assumptions. References can be found here:

• https://variation.com/wp-content/uploads/change-point-analyzer/change-point-analysis-a-powerful-new-tool-for-detecting-changes.pdf

• https://support.sas.com/resources/papers/proceedings17/1489-2017.pdf

Single change

To find the most dominant change point in the mean of a time series, use mcpoint:

• mcpoint returns the index of a change point (beginning of change) if there is one, 0 otherwise.

You can specify the desired p-value threshold that's considered as significant, you can also specify the minimum length of a segment in order to avoid detection of short segments.

mcpoint uses two lower level functions:

• mcppv calculates the p-value of existence of a mean change point via cumsum randomization test of the centered series.

• mcptime estimates the location of the change point by looking for the point with minimum overall sum of squares.

You can use these two function to better understand how the algorithm reacts to various data patterns.

Note this package uses 1-based indexing of the time series vector.

Multiple changes

In general, there may be multiple change points, interest may be in the most recent change or all changes:

• mcplast returns the index of the most recent change point by repeatedly calling mcpoint on the more recent segment until no more change can be found. If there are no change points, 0 is returned.

• mcpall returns a vector of all change points via recursive partitioning, length of vector is the number of change points detected. This function recursively calls mcpoint on all segments until no more changes can be detected. If there are no changes, an empty vector is returned.

Plot

• mcplot plots the time series broken into segments to aid visualization.

For full documentation, see