Statistical inference for nonparametric GARCH models

Alexander Meister and Jens-Peter Kreiß

Stochastic Processes and their Applications, 2016, vol. 126, issue 10, 3009-3040

Abstract: We consider extensions of the famous GARCH(1,1) model where the recursive equation for the volatilities is not specified by a parametric link but by a smooth autoregression function. Our goal is to estimate this function under nonparametric constraints when the volatilities are observed with multiplicative innovation errors. We construct an estimation procedure whose risk attains nearly the usual convergence rates for bivariate nonparametric regression estimation. Furthermore, those rates are shown to be nearly optimal in the minimax sense. Numerical simulations are provided for a parametric submodel.

Keywords: Autoregression; Financial time series; Inference for stochastic processes; Minimax rates; Nonparametric regression (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:10:p:3009-3040

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DOI: 10.1016/j.spa.2016.03.010

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