A goodness-of-fit test of the errors in nonlinear autoregressive time series models with stationary $\alpha$-mixing error terms

TL;DR

This paper develops a goodness-of-fit test for the error density in nonlinear autoregressive time series models with stationary alpha-mixing errors, extending previous results from i.i.d. errors to dependent error structures.

Contribution

It introduces a new test statistic based on integrated squared error and proves its asymptotic normality for models with dependent errors, generalizing prior work.

Findings

Test statistic follows asymptotic normal distribution.

Extension of goodness-of-fit testing to alpha-mixing error processes.

Provides theoretical foundation for error density validation in complex models.

Abstract

In this work we deal with the problem of fitting an error density to the goodness-of-fit test of the errors in nonlinear autoregressive time series models with stationary $\alpha$-mixing error terms. The test statistic is based on the integrated squared error of the nonparametric error density estimate and the null error density. By deriving the asymptotic normality of test statistics in these models, we extend the result of Cheng and Sun (Statist. Probab. Lett. \textbf{78}, 1(2008), 50-59) in the model with i.i.d error terms to the more general case.