A Bayesian Nonparametric Markovian Model for Nonstationary Time Series

TL;DR

This paper introduces a flexible Bayesian nonparametric Markovian model for nonstationary time series that captures complex dynamics without stationarity assumptions, demonstrated through simulated data and geyser eruption intervals.

Contribution

It proposes a novel nonstationary, nonparametric autoregressive model using Bayesian mixtures, extending traditional stationary time series modeling capabilities.

Findings

Successfully recovers complex transition densities in simulations

Effectively models geyser eruption interval data

Provides a computationally efficient inference algorithm

Abstract

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 nonstandard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This implies a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, nonstationary, Markovian model for real-valued data indexed in discrete-time. To obtain a more 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 the model is able to recover challenging transition and predictive densities. 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.