Choosing between persistent and stationary volatility

TY - JOUR

T1 - Choosing between persistent and stationary volatility

AU - Chronopoulos, Ilias

AU - Giraitis, Liudas

AU - Kapetanios, George

N1 - Funding Information: The first author was supported by ESRC Grant ES/P000703/1. Publisher Copyright: © Institute of Mathematical Statistics, 2022.

PY - 2022/12/31

Y1 - 2022/12/31

N2 - 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.

AB - 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.

KW - ARCH effect

KW - nonparametric estimation

KW - persistence

KW - time-varying coefficient models

KW - volatility

UR - http://www.scopus.com/inward/record.url?scp=85146191344&partnerID=8YFLogxK

U2 - 10.1214/22-AOS2236

DO - 10.1214/22-AOS2236

M3 - Article

AN - SCOPUS:85146191344

SN - 0090-5364

VL - 50

SP - 3466

EP - 3483

JO - ANNALS OF STATISTICS

JF - ANNALS OF STATISTICS

IS - 6

ER -