Testing the equality of error distributions from k independent GARCH models

TL;DR

This paper develops and evaluates statistical tests to compare the error distributions of multiple GARCH models, demonstrating their effectiveness especially when errors deviate from Gaussian assumptions.

Contribution

It introduces a new class of residual-based tests for equality of error distributions in independent GARCH models, with flexible scoring functions and proven asymptotic validity.

Findings

Tests have reasonable size and high power.

Performance improves when errors are non-Gaussian.

Effective in real stock return data.

Abstract

In this paper we study the problem of testing the null hypothesis that errors from k independent parametrically specified generalized autoregressive conditional heteroskedasticity (GARCH) models have the same distribution versus a general alternative. First we establish the asymptotic validity of a class of linear test statistics derived from the k residual-based empirical distribution functions. A distinctive feature is that the asymptotic distribution of the test statistics involves terms depending on the distributions of errors and the parameters of the models, and weight functions providing the flexibility to choose scores for investigating power performance. A Monte Carlo study assesses the asymptotic performance in terms of empirical size and power of the three-sample test based on the Wilcoxon and Van der Waerden score generating functions in finite samples. The results demonstrate that the two proposed tests have overall reasonable size and their power is particularly high when the assumption of Gaussian errors is violated. As an illustrative example, the tests are applied to daily individual stock returns of the New York Stock Exchange data.