Change-Point Analysis: Asymptotic Theory and Applications

The problem of undocumented change-points in data sets appears in many areas of science. Mathematical fundamentals of asymptotic methods used in change-point analysis are discussed, and several important maximally selected change-point statistics are introduced. First, the likelihood ratio method is applied to abstract data models within the setting of precipitation series. Basic inference as to the legitimacy and effectiveness of asymptotic methods at detecting undocumented change-points is provided. Next, maximally selected chi-square statistics are discussed in detail and applied to data on tropical cyclone behavior, where a widely available and widely analyzed data set on Atlantic basin cyclones is studied. Change-points in several indicators are found, and importantly a recent increase in cyclone frequency is verified. Next, several methods for detecting undocumented mean shifts in correlated data are introduced and analyzed. Here, we determine that LR-type tests are preferable to CUSUM tests. Finally, propositions regarding change-points in Markov chains and the full likelihood ratio test for ARMA process are discussed