Specification testing in nonlinear and nonstationary time series autoregression

Details Specification testing in nonlinear and nonstationary time series autoregression Specification testing in nonlinear and nonstationary time series autoregression

2009-11-19

arxiv.org/abs/0911.3736v1

Annals of Statistics 2009, Vol. 37, No. 6B, 3893-3928

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS698 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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