TY - JOUR
T1 - Robust Inference for Nonstationary Time Series with Possibly Multiple Changing Periodic Structures
AU - Wang, Shouxia
AU - Huang, Tao
AU - You, Jinhong
AU - Cheng, Ming Yen
N1 - Funding information:
The authors gratefully acknowledge support of the National Natural Science Foundation of China (grants nos. 11871323 and 11971291), the Hong Kong Baptist University (grant no. RC-ICRS-17-18), and the Research Grants Council GRF (grant no. HKBU12304120).
Publisher copyright:
© 2021 American Statistical Association
PY - 2022/10/2
Y1 - 2022/10/2
N2 - Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonparametric trending behavior and also additive covariate effects. Further, as the amplitude function may change at some known or unknown change-point(s), we extend our model to take this dynamical periodicity into account and introduce two change-point estimators. To the best of knowledge, this is the first work to study such complex periodic structure. A two-step estimation procedure is proposed to estimate accurately the periodicity, trend and covariate effects. First, we estimate the period with the trend and covariate effects being approximated by B-splines rather than being ignored. To achieve robustness we employ a penalized M-estimation method which uses post model selection inference ideas. Next, given the period estimate, we estimate the amplitude, trend and covariate effects. Asymptotic properties of our estimators are derived, including consistency of the period estimator and asymptotic normality and oracle property of the estimated periodic sequence, trend and covariate effects. Simulation studies confirm superiority of our method and illustrate good performance of our change-point estimators. Applications to the two motivating examples demonstrate utilities of our methods.
AB - Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonparametric trending behavior and also additive covariate effects. Further, as the amplitude function may change at some known or unknown change-point(s), we extend our model to take this dynamical periodicity into account and introduce two change-point estimators. To the best of knowledge, this is the first work to study such complex periodic structure. A two-step estimation procedure is proposed to estimate accurately the periodicity, trend and covariate effects. First, we estimate the period with the trend and covariate effects being approximated by B-splines rather than being ignored. To achieve robustness we employ a penalized M-estimation method which uses post model selection inference ideas. Next, given the period estimate, we estimate the amplitude, trend and covariate effects. Asymptotic properties of our estimators are derived, including consistency of the period estimator and asymptotic normality and oracle property of the estimated periodic sequence, trend and covariate effects. Simulation studies confirm superiority of our method and illustrate good performance of our change-point estimators. Applications to the two motivating examples demonstrate utilities of our methods.
KW - Additive model
KW - M-estimation
KW - Period estimation
KW - Semiparametric regression
KW - Smooth trend
UR - http://www.scopus.com/inward/record.url?scp=85115343022&partnerID=8YFLogxK
U2 - 10.1080/07350015.2021.1970574
DO - 10.1080/07350015.2021.1970574
M3 - Journal article
SN - 0735-0015
VL - 40
SP - 1718
EP - 1731
JO - Journal of Business and Economic Statistics
JF - Journal of Business and Economic Statistics
IS - 4
ER -