Change Point Detection in R

What is the differnce between change point and outlier?

To answer this question, we should really understand what is a change point for a time series.

Changepoints are also known as:

• breakpoints
• segmentation
• structural breaks
• regime switching
• detecting disorder

and can be found in a wide range of literature including

• quality control
• economics
• medicine
• environment
• linguistics
• $\cdots$

For data $y_1,\dots ,y_n$, if a changepoint exists at $\tau$, then $y_1,\dots ,y_{\tau }$ differ from $y_{\tau +1},\dots ,y_n$ in some way.

There are many different types of change.

Thus a changepoint model for a change in mean has the following formulation:

$$y_t=\{\begin{array}{lcl}{\mu }_1& \text{if}& 1\le t\le {\tau }_1\\ {\mu }_2& \text{if}& {\tau }_1<t\le {\tau }_2\\ ⋮& & ⋮\\ {\mu }_{m+1}& \text{if}& {\tau }_m<t\le {\tau }_{m+1}=n\end{array}$$

What is the goal?

• Has a change occurred?
• If yes, where is the change?
• What is the difference between the pre and post change data?
  • Maybe this is the type of change
  • Maybe it is the parameter values before and after the change
• What is the probability that a change has occured?
• How certain are we of the changepoint location?
• How many changes have occurred (+ all the above for each change)?
• Why has there been a change?

Online vs Offline

• Online
  • Processes data as it arrives or in batches
  • Goal is quickest detection of a change
  • Often used in processing control, intrusion detection
• Offline
  • Processes all the data in one go
  • Goal is accurate detection of a change
  • Often used in genome analysis, audiology

change point detection function using ecp package

library(zeta.forecast)
zetaEDA::enable_zeta_ggplot_theme()

plot_ts_change_point(eg_diamond_ts)

## # A tibble: 2 × 3
##   time        value cpt  
##   <date>      <dbl> <fct>
## 1 2013-12-01 652769 yes  
## 2 2019-09-01 305745 yes