A Robust Goodness-of-Fit Test for Generalized Autoregressive Conditional Heteroscedastic Models

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, July 31, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yao Zheng* and Wai Keung Li and Guodong Li
• Companies: The University of Hong Kong and The University of Hong Kong and The University of Hong Kong
• Keywords: GARCH model ; Goodness-of-fit test ; Heavy tails ; Residual empirical process ; Robustness

Abstract

This paper proposes a robust goodness-of-fit test for GARCH models based on residual empirical processes. The test statistic is constructed from the sample autocorrelation function (ACF) of the absolute residuals transformed by their empirical distribution function; in effect, this sample ACF is simply the Spearman rank autocorrelation function of the absolute residuals. As a consequence of the bounded monotonic transformation, the proposed test performs superbly when the innovations are very heavy-tailed with even only a finite fractional moment, while maintaining desirable power for the light-tailed cases. The asymptotic null distribution of the test statistic is derived based on results for weighted residual empirical processes. Simulation experiments are conducted to assess its finite-sample performance and for comparison with existing methods, and a real data example is analyzed to further illustrate its usefulness.