Date of Award
Doctor of Philosophy (PhD)
School of Mathematical and Statistical Sciences
Changepoint analysis has played an important role in modern time series study. Detection of changepoints helps modelling and prediction of time series and is found in applications of many fields. This dissertation focuses on the detection of mean structure changes in correlated time series. It consists of the results of three research projects on changepoint problems: (1) the comparison of changepoint techniques; (2) autocovariance estimation of an AR(p) time series with changepoints; and (3) L1-regularization in changepoint analysis.
In chapter 2 the single changepoint techniques, or At-Most-One-Changepoint (AMOC) tests are reviewed. A new AMOC test, Sum of Squared CUSUMz is developed and is shown to be the most powerful AMOC test through simulation studies on the time series with various ARMA(p,q) structures. Multiple changepoint techniques that are applicable to correlated time series are discussed in chapter $3$, which includes an in-depth discussion on the wild binary segmentation. A new distance metric is also proposed in this chapter for comparing the multiple changepoint techniques. Next in the chapter 4 a Yule-Walk moment estimator based on the first order difference is proposed for autocovariance estimation of an AR(p) time series with a small number of changepoints. The last chapter simply reviews the L1- regularization and its application to changepoint analysis.
Shi, Xueheng, "A Survey of Changepoint Techniques for Time Series Data" (2020). All Dissertations. 2697.