Functional semiparametric modeling for nonstationary and periodic time series data

原文摘要

Inspired by a real data example illustrating the periodicity in hog price data, this study aims to analyze time series that exhibit an unknown period alongside complex covariate effects. To address these complexities and effectively handle the data structures, we incorporate the partial functional varying-coefficient single-index model into the classical time series decomposition model. We propose a two-stage estimation procedure designed to accurately estimate the unknown periodic component and the associated covariate functions. In the first stage, the unknown period is estimated using a penalized least squares approach, where the covariate functions are approximated via B-splines rather than being ignored. In the second stage, given the estimated period, we employ B-splines to estimate key components, including the amplitude of the periodic component, the varying-coefficient functions, the single-index link function, and the functional slope function. Asymptotic results for the proposed estimators are derived, encompassing the consistency of the period estimator as well as the asymptotic properties of the estimated periodic sequence and covariate functions. Furthermore, we conduct simulations to validate the superior performance of the proposed method and demonstrate its practical applicability through the aforementioned empirical example.

摘要来源：RePEc · 出版社摘要