Testing second order dynamics for autoregressive processes in presence of time-varying variance

TL;DR

This paper develops testing procedures for ARCH effects in autoregressive processes with time-varying variance, highlighting limitations of standard tests under non-stationarity and demonstrating their performance through simulations and real data.

Contribution

It introduces adaptive testing methods for second order dynamics that account for non-constant variance, improving upon standard tests assuming stationarity.

Findings

Standard tests fail under time-varying variance.

Adaptive tests perform better in non-stationary conditions.

Simulations and real data validate the proposed methods.

Abstract

The volatility modeling for autoregressive univariate time series is considered. A benchmark approach is the stationary ARCH model of Engle (1982). Motivated by real data evidence, processes with non constant unconditional variance and ARCH effects have been recently introduced. We take into account such possible non stationarity and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li's portmanteau and ARCH-LM tests for checking for second order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional variance. We prove the failure of these standard tests with time-varying unconditional variance. The theoretical results are illustrated by mean of simulated and real data.