© 1999 by Biometrika Trust
Dynamic adaptive partitioning for nonlinear time series
Seminar für Statistik, ETH Zürich, CH-8092 Zürich, Switzerland E-mal: buhlmann@stat.math.ethz.ch
We propose a dynamic adaptive partitioning scheme for nonparametric analysis of stationary nonlinear time series. It yields estimates of the whole probability distribution of the underlying process. We use information from past values to construct adaptive partitioning in a dynamic fashion which is then different from the more common static schemes in the regression set-up. The idea of dynamic partitioning is new. We make it constructive by an approach based on quantisation of the data and adaptively modelling partition cells with a parsimonious Markov chain. The methodology is formulated in terms of a new model class, the so-called quantised variable length Markov chains. It is a new extension of finite-valued variable length Markov chains to processes with values in Rd. We discuss estimation, explore asymptotic properties of the new method and five some numerical results which reflect the finite sample behaviour.
Key Words: Conditional heteroscedasticity; Context algorithm; Markov chain; Multivariate time series; Phi-mixing; Prediction; Quantisation; Stationary process; Tree model.