Specification testing in nonparametric AR-ARCH models

TL;DR

This paper introduces a new nonparametric test for independence in AR-ARCH models, using empirical characteristic functions, with proven asymptotic properties and validated through simulations.

Contribution

It proposes a novel independence test for nonparametric AR-ARCH models based on weighted L2-distance of empirical characteristic functions, including bootstrap validation.

Findings

Test has correct asymptotic distribution under null hypothesis.

Test is consistent against fixed alternatives.

Simulation results demonstrate good performance.

Abstract

In this paper an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. A test for the model assumption of independence of innovations from past time series values is suggested. The test is based on an weighted $L^2$-distance of empirical characteristic functions. The asymptotic distribution under the null hypothesis of independence is derived and consistency against fixed alternatives is shown. A smooth autoregressive residual bootstrap procedure is suggested and its performance is shown in a simulation study.