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

原文摘要

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 10 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 15 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.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）