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Title: A CUSUM test for tail behavior of GARCH(1,1) models Authors:  Eunju Hwang - Gachon University (Korea, South) [presenting]
JunHyeong Kim - Hanyang University (Korea, South)
Abstract: A GARCH model has been a very popular time series model for the volatility of financial returns. A CUSUM test is proposed for detecting the tail behavior of a stationary GARCH(1,1) model, more particularly, for testing whether the tail index of the model is changed or not. The CUSUM test statistic is constructed using the empirical distribution function with sample extremes and its limiting distribution is shown to be a Brownian bridge. The proof is based on the weak dependence structure and on the existence of the phantom distribution function of the stationary GARCH model. This test can be used for general weakly-dependent time series models. A Monte-Carlo study is conducted to see the performance of power and size of the CUSUM test in GARCH(1,1) models with heavy-tailed noises, adopting tail index of the noises to be changed. Real data applications are given with financial data such as KOSPI.