Choosing between persistent and stationary volatility
Ilias Chronopoulos, Liudas Giraitis, George Kapetanios
The Annals of Statistics · 2022 · Volume 50 · Issue 6
Abstract
This paper suggests a multiplicative volatility model where volatility is decomposed into a stationary and a nonstationary persistent part. We provide a testing procedure to determine which type of volatility is prevalent in the data. The persistent part of volatility is associated with a nonstationary persistent process satisfying some smoothness and moment conditions. The stationary part is related to stationary conditional heteroskedasticity. We outline theory and conditions that allow the extraction of the persistent part from the data and enable standard conditional heteroskedasticity tests to detect stationary volatility after persistent volatility is taken into account. Monte Carlo results support the testing strategy in small samples. The empirical application of the theory supports the persistent volatility paradigm, suggesting that stationary conditional heteroskedasticity is considerably less pronounced than previously thought.
Keywords
62F05, 62G05, 62G08, 62M10, ARCH effect, nonparametric estimation, Persistence, time-varying coefficient models, Volatility
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