Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
W K Li, Department of Statistics and Actuarial Science,University of Hong Kong
Inviter:
陈敏
Title:
A robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models
Time & Venue:
2017.10.24 10:00-11:00 N613
Abstract:
The estimation for time series models with heavy-tailed innovations has been widely discussed in the literature, while the corresponding goodness-of-?t tests have attracted less attention. This is mainly because the commonly used autocorrelation function in constructing goodness-of-?t tests necessarily imposes certain moment conditions on the innovations. In the light of the fact that a bounded random variable has ?nite moments of all orders, we address this problem by ?rst transforming the residuals with a bounded and increasing function. Speci?cally, this paper considers the autocorrelation function of the transformed absolute residuals from a ?tted GARCH model. With the corresponding residual empirical distribution function naturally employed as the transformation, a robust goodness-of-?t test is constructed. The asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived. Simulation experiments are conducted to assess the ?nite-sample performance, and the proposed test is demonstrated by a real example to be more powerful than the existing ones in the literature.