A robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models

Yao Zheng, Wai Keung Li and Guodong Li

Biometrika, 2018, vol. 105, issue 1, 73-89

Abstract: Summary The estimation of time series models with heavy-tailed innovations has been widely discussed, but corresponding goodness-of-fit tests have attracted less attention, primarily because the autocorrelation function commonly used in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the innovations. As a bounded random variable has finite moments of all orders, we address the problem by first transforming the residuals with a bounded function. More specifically, we consider the sample autocorrelation function of the transformed absolute residuals of a fitted generalized autoregressive conditional heteroscedastic model. With the corresponding residual empirical distribution function naturally employed as the transformation, a robust goodness-of-fit test is then constructed. The asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived, and Monte Carlo experiments are conducted to examine finite-sample properties. The proposed test is shown to be more powerful than existing tests when the innovations are heavy-tailed.

Keywords: Conditional heteroscedastic model; Goodness-of-fit test; Heavy tail; Residual empirical process; Robustness (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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