An algorithm for nonparametric GARCH modelling

Peter Bühlmann*, Alexander J. McNeil

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A simple iterative algorithm for nonparametric first-order GARCH modelling is proposed. This method offers an alternative to fitting one of the many different parametric GARCH specifications that have been proposed in the literature. A theoretical justification for the algorithm is provided and examples of its application to simulated data from various stationary processes showing stochastic volatility, as well as empirical financial return data, are given. The nonparametric procedure is found to often give better estimates of the unobserved latent volatility process than parametric modelling with the standard GARCH(1,1) model, particularly in the presence of asymmetry and other departures from the standard GARCH specification. Extensions of the basic iterative idea to more complex time series models combining ARMA or GARCH features of possibly higher order are suggested.

Original languageEnglish
Pages (from-to)665-683
Number of pages19
JournalComputational Statistics & Data Analysis
Issue number4
Publication statusPublished - 28 Oct 2002


  • GARCH modelling
  • Nonparametric methods
  • Volatility estimation

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