Dynamic adaptive partitioning for nonlinear time series

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 diierent from the more common static schemes in the regression setup. 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 nite-valued variable length Markov chains to processes with values in IR d. We discuss estimation, explore asymptotic properties of the new method and give some numerical results which reeect the nite sample behaviour.