A0679
Title: Inference for changing periodicity, smooth trend and covariate effects in nonstationary time series
Authors: Lucy Xia - The Hong Kong University of Science and Technology (Hong Kong) [presenting]
Ming-Yen Cheng - Hong Kong Baptist University (Hong Kong)
David Siegmund - Stanford University (United States)
Shouxia Wang - Peking University (China)
Abstract: Traditional analysis of a periodic time series assumes its pattern remains the same over the entire time range. However, some recent empirical studies in climatology and other fields find that the amplitude may change over time, and this has important implications. A formal procedure is developed to detect and estimate change points in the periodic pattern. Often, there is also a smooth trend, and sometimes, the period is unknown, with potential other covariate effects. Based on a new model that takes all of these factors into account, a three-step estimation procedure is proposed to accurately estimate the unknown period, change- points, and varying amplitude in the periodic component, as well as the trend and the covariate effects. First, penalized segmented least squares estimation is adopted for the unknown period, with the trend and covariate effects approximated by B-splines. Then, given the period estimate, a novel SupF statistic is constructed, and it is used in binary segmentation to estimate change points in the periodic component. Finally, given the period and change-point estimates, the entire periodic component, trend, and covariate are estimated effects using B-splines. 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 demonstrate the appealing performance of the new method.
