Academic

Traditional analysis of a periodic time series assumes its pattern remains the same. However, some recent empirical studies in climatology and other fields find that the amplitude may change over time, which has important implications. We develop a formal procedure to detect and estimate change-points in the periodic pattern with an unknown period.  Moreover, there is also a smooth trend and potentially other covariate effects. Based on a new model that takes all of these factors into account, we propose a three-step procedure to estimate them all accurately. First, we adopt penalized segmented least squares estimation for the unknown period, with the trend and covariate effects approximated by B-splines. Then, given the period estimate, we construct a novel test statistic and use it in binary segmentation to detect change-points in the periodic component. Finally, given the period and change-point estimates, we estimate the entire periodic component, trend, and covariate effects. Asymptotic results for the proposed estimators are derived, including consistency of the period and change-point estimators, and the asymptotic normality of the estimated periodic sequence, trend and covariate effects. Simulation results and empirical studies demonstrate the appealing performance of the new method.