A Bayesian nonparametric Markovian model for non-stationary time series

作者：DeYoreo Maria^*; Kottas Athanasios

来源：Statistics and Computing, 2017, 27(6): 1525-1538.

DOI：10.1007/s11222-016-9702-x

• Autoregressive models
• Bayesian nonparametrics
• Dirichlet process mixtures
• Markov chain Monte Carlo
• Non-stationarity
• Time series

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture non-standard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This results in a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, non-stationary Markovian model for real-valued data indexed in discrete time. To obtain a computationally tractable algorithm for posterior inference, we utilize a square-root-free Cholesky decomposition of the mixture kernel covariance matrix. Results from simulated data suggest that the model is able to recover challenging transition densities and non-linear dynamic relationships. We also illustrate the model on time intervals between eruptions of the Old Faithful geyser. Extensions to accommodate higher order structure and to develop a state-space model are also discussed.

• 出版日期2017-11