Dynamic Combination of Models for Nonlinear Time Series

Peter Bühlmann und Fiorenzo Ferrari

September 2002

Abstract: We propose a new method for stationary nonlinear time series analysis which dynamically combines models, either parametric or nonparametric, by using mixture probabilities from so-called variable length Markov chains. The approach is very general and flexible: it can be used for modelling conditional means, conditional variances or conditional densities given the previous lagged values, and the methodology can be applied to dynamically combine almost any kind of models. Parameter estimation (finite or infinite-dimensional) and model selection can be done in a fully data-driven way. We demonstrate the predictive power of the method on finite sample data and an asymptotic consistency result is presented.

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