Robust tests for parameter change in conditionally heteroscedastic time series models

TL;DR

This paper develops robust statistical tests for detecting parameter changes in heteroscedastic time series, effectively handling outliers through a two-step estimation and residual truncation approach, with proven theoretical properties and practical Bitcoin data analysis.

Contribution

It introduces a novel robust testing procedure for heteroscedastic models that remains effective in the presence of outliers, with proven asymptotic properties.

Findings

Tests are robust against outliers in simulations.

The proposed methods have well-defined limiting null distributions.

Application to Bitcoin data demonstrates practical utility.

Abstract

Structural changes and outliers often coexist, complicating statistical inference. This paper addresses the problem of testing for parameter changes in conditionally heteroscedastic time series models, particularly in the presence of outliers. To mitigate the impact of outliers, we introduce a two-step procedure comprising robust estimation and residual truncation. Based on this procedure, we propose a residual-based robust CUSUM test and its self-normalized counterpart. We derive the limiting null distributions of the proposed robust tests and establish their consistency. Simulation results demonstrate the strong robustness of the tests against outliers. To illustrate the practical application, we analyze Bitcoin data.