Dynamic adaptive partitioning for nonlinear time series

• 成果类型: Article
• 署名作者: Bühlmann, P
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/86.3.555
• 发表日期: 1999
• 页码: 555571
• 关键词: regression splines; MULTIVARIATE

摘要

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 R-d. We discuss estimation, explore asymptotic properties of the new method and give some numerical results which reflect the finite sample behaviour.