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

39 Pages Posted: 14 Nov 2015 Last revised: 15 Apr 2016

See all articles by Yao Zheng

Yao Zheng

The University of Hong Kong - Department of Statistics & Actuarial Science

Wai Keung Li

The University of Hong Kong

Guodong Li

The University of Hong Kong - Department of Statistics & Actuarial Science

Date Written: April 15, 2016

Abstract

The estimation for time series models with heavy-tailed innovations has been widely discussed in the literature, while the corresponding goodness-of-fit tests have attracted less attention. This is mainly because the commonly used autocorrelation function in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the innovations. In the light of the fact that a bounded random variable has finite moments of all orders, we address this problem by first transforming the residuals with a bounded and increasing function. Specifically, this paper considers the autocorrelation function of the transformed absolute residuals from a fitted GARCH model. With the corresponding residual empirical distribution function naturally employed as the transformation, a robust goodness-of-fit test is constructed. The asymptotic null distribution of the test statistic is derived, and simulation experiments are conducted to assess its finite-sample performance. A real data example is analyzed to further illustrate its usefulness.

Keywords: GARCH model, Goodness-of-fit test, Heavy tails, Residual empirical process, Robustness

JEL Classification: C22, C52

Suggested Citation

Zheng, Yao and Li, Wai Keung and Li, Guodong, A Robust Goodness-of-Fit Test for Generalized Autoregressive Conditional Heteroscedastic Models (April 15, 2016). Available at SSRN: https://ssrn.com/abstract=2690099 or http://dx.doi.org/10.2139/ssrn.2690099

Yao Zheng (Contact Author)

The University of Hong Kong - Department of Statistics & Actuarial Science ( email )

Pokfulam Road
Hong Kong

Wai Keung Li

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

Guodong Li

The University of Hong Kong - Department of Statistics & Actuarial Science ( email )

Hong Kong

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