  This paper describes and compares several prominent single and multiple
changepoint techniques for time series data. Due to their importance in
inferential matters, changepoint research on correlated data has accelerated
recently. Unfortunately, small perturbations in model assumptions can
drastically alter changepoint conclusions; for example, heavy positive
correlation in a time series can be misattributed to a mean shift should
correlation be ignored. This paper considers both single and multiple
changepoint techniques. The paper begins by examining cumulative sum (CUSUM)
and likelihood ratio tests and their variants for the single changepoint
problem; here, various statistics, boundary cropping scenarios, and scaling
methods (e.g., scaling to an extreme value or Brownian Bridge limit) are
compared. A recently developed test based on summing squared CUSUM statistics
over all times is shown to have realistic Type I errors and superior detection
power. The paper then turns to the multiple changepoint setting. Here,
penalized likelihoods drive the discourse, with AIC, BIC, mBIC, and MDL
penalties being considered. Binary and wild binary segmentation techniques are
also compared. We introduce a new distance metric specifically designed to
compare two multiple changepoint segmentations. Algorithmic and computational
concerns are discussed and simulations are provided to support all conclusions.
In the end, the multiple changepoint setting admits no clear methodological
winner, performance depending on the particular scenario. Nonetheless, some
practical guidance will emerge.
