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. Copyright © 2017 Biometrika Trust.
CitationZheng, Y., Li, W. K., & Li, G. (2018). A robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models. Biometrika, 105(1), 73-89. doi: 10.1093/biomet/asx063
- Conditional heteroscedastic model
- Goodness-of-fit test
- Heavy tail
- Residual empirical process