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Nonparametric GARCH Models
Peter Bühlmann and Alexander J. McNeil
Dec 1999
Abstract: In this paper we describe a nonparametric GARCH model of first order and propose a simple iterative algorithm for its estimation from data. We provide a theoretical justification for this algorithmand give examples of its application to stationary time series data showingstochastic volatility. We observe that our nonparametric procedureoften gives better estimates of the unobserved latent volatilityprocess than parametric GARCH(1,1) modelling, particularly whenasymmetries are present in the data.We show how the basic iterative idea may be extended to more complextime series models combining ARMA or GARCH features of possibly higherorder.
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