The Annals of Statistics

Specification testing in nonlinear and nonstationary time series autoregression

Jiti Gao, Maxwell King, Zudi Lu, and Dag Tjøstheim

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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.

Article information

Ann. Statist., Volume 37, Number 6B (2009), 3893-3928.

First available in Project Euclid: 23 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G07: Density estimation
Secondary: 60F05: Central limit and other weak theorems

Cointegration kernel test nonparametric regression nonstationary time series time series econometrics


Gao, Jiti; King, Maxwell; Lu, Zudi; Tjøstheim, Dag. Specification testing in nonlinear and nonstationary time series autoregression. Ann. Statist. 37 (2009), no. 6B, 3893--3928. doi:10.1214/09-AOS698.

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