Limit theory for moderate deviation from Integrated GARCH processes

• Main Author: TAO, Yubo
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2019
• Subjects: Central limit theorem; Limiting process; Localization; Explosive GARCH; Volatility process; Econometrics; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2456; https://ink.library.smu.edu.sg/context/soe_research/article/3455/viewcontent/LimitTheory_MildlyIntegated_GARCH_Processes_sv.pdf
• Institution: Singapore Management University

This paper develops the limit theory of the GARCH(1,1) process that moderately deviates from IGARCH process towards both stationary and explosive regimes. The asymptotic theory extends Berkes et al. (2005) by allowing the parameters to have a slower rate of convergence. The results can be applied to unit root test for processes with mildly-integrated GARCH innovations (e.g. Boswijk (2001), Cavaliere and Taylor (2007, 2009)) and deriving limit theory of estimators for models involving mildly-integrated GARCH processes (e.g. Jensen and Rahbek (2004), Francq and Zakoïan (2012, 2013).