Open Access
December 2009 Specification testing in nonlinear and nonstationary time series autoregression
Jiti Gao, Maxwell King, Zudi Lu, Dag Tjøstheim
Ann. Statist. 37(6B): 3893-3928 (December 2009). DOI: 10.1214/09-AOS698


This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting and the results differ from earlier work on nonparametric autoregression with stationarity. In addition, we develop a new bootstrap simulation scheme for the selection of a suitable bandwidth parameter involved in the kernel test as well as the choice of a simulated critical value. The finite-sample performance of the proposed test is assessed using one simulated example and one real data example.


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Jiti Gao. Maxwell King. Zudi Lu. Dag Tjøstheim. "Specification testing in nonlinear and nonstationary time series autoregression." Ann. Statist. 37 (6B) 3893 - 3928, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62148
MathSciNet: MR2572447
Digital Object Identifier: 10.1214/09-AOS698

Primary: 62G07 , 62M10
Secondary: 60F05

Keywords: cointegration , kernel test , Nonparametric regression , nonstationary time series , time series econometrics

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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