Jiayang Sun (Chair)

Abstract

Traditional analysis of a periodic time series assumes its pattern remains the same over the entire time range. However, using ad hoc methods some recent empirical studies in climatology and other fields find the amplitude may change along with time and that has important implications. We develop a formal procedure to detect and estimate change-points in the periodic pattern. Often there is also a smooth trend, and sometimes the period is unknown and there can be other covariate effects. Based on a new model that takes into account all these, a three-step estimation procedure is proposed to estimate accurately the unknown period, change-points and varying amplitude in the periodic component, the trend and the covariate effects. 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 estimate change-points in the periodic component. Finally, given the period and change-point estimates, we estimate the whole periodic component, trend and covariate effects using B-splines. Asymptotic results for the proposed estimators are derived, including consistency of the period and change-point estimators, and asymptotic normality of the estimated periodic sequence, trend and covariate effects. Simulation results demonstrate appealing performance of the new method, and empirical studies show its advantages.