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 algorithm and give examples of its application to stationary time series data showing stochastic volatility. We observe that our nonparametric procedure often gives better estimates of the unobserved latent volatility process than parametric GARCH(1,1) modelling, particularly when asymmetries are present in the data. We show how the basic iterative idea may be extended to more complex time series models combining ARMA or GARCH features of possibly higher order.

Download:

Compressed Postscript (521 Kb)
PDF (797 Kb)

Go back to the Research Reports from Seminar für Statistik.