Specification testing in nonlinear and nonstationary time series autoregression

TL;DR

This paper develops a nonparametric kernel test for nonstationary autoregressive models, providing asymptotic distribution results and a bootstrap scheme for bandwidth selection, with demonstrated finite-sample effectiveness.

Contribution

It introduces a novel nonparametric test for nonstationary autoregression and a bootstrap method for bandwidth and critical value selection, extending prior work beyond stationary models.

Findings

The test has good finite-sample performance in simulations.

The bootstrap scheme effectively selects bandwidth and critical values.

Application to real data demonstrates practical utility.

Abstract

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.