Tests for Volatility Shifts in GARCH Against Long-Range Dependence

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Tae Wook Lee* and Moosup Kim and Changryong Baek
• Companies: Hankuk University of Foreign Studies and Seoul National University and Sungkyunkwan University
• Keywords: Volatility shifts ; long-range dependence ; GARCH models ; change point analysis ; bootstrap

Abstract

Many empirical findings show that volatility in financial time series exhibits high persistence. Some researchers argue that such persistency is due to volatility shifts in the market, while others believe that this is a natural fluctuation explained by stationary long-range dependence models. In this article, therefore, we consider a statistical testing procedure to distinguish volatility shifts in generalized AR conditional heteroscedasticity (GARCH) model against long-range dependence. Our testing procedure is based on the residual-based cumulative sum test, which is designed to correct the size distortion observed for GARCH models. We examine the validity of our method by providing asymptotic distributions of test statistic. We also propose the bootstrap tests to avoid a size distortion. Monte Carlo simulations study shows that our proposed method achieves a good size while providing a reasonable power against long-range dependence.