Truncated moments of perpetuities and a new central limit theorem for GARCH processes without Kesten’s regularity

Adam Jakubowski and Zbigniew S. Szewczak

Stochastic Processes and their Applications, 2021, vol. 131, issue C, 151-171

Abstract: We consider a class of perpetuities which admit direct characterization of asymptotics of the key truncated moment. The class contains perpetuities without polynomial decay of tail probabilities thus not satisfying Kesten’s theorem. We show how to apply this result in deriving a new weak law of large numbers for solutions to stochastic recurrence equations and a new central limit theorem for GARCH(1,1) processes in the critical case.

Keywords: Stochastic recurrence equation; Central limit theorem; Weak law of large numbers; GARCH processes; Perpetuities (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:131:y:2021:i:c:p:151-171

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DOI: 10.1016/j.spa.2020.09.003

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