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

• 成果类型: Article
• 署名作者: Zheng, Yao; Li, Wai Keung; Li, Guodong
• 署名单位: University of Hong Kong
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx063
• 发表日期: 2018
• 页码: 7389
• 关键词: absolute deviation estimation; time-series models; sample autocorrelations; garch processes; limit theory; rank-tests; ARCH; stationarity; covariance; randomness

摘要

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.