Bayesian change-point modeling with segmented ARMA model

Abstract

Time series segmentation aims to identify segment boundary points in a time series, and to determine the dynamical properties corresponding to each segment. To segment time series data, this article presents a Bayesian change-point model in which the data within segments follows an autoregressive moving average (ARMA) model. A prior distribution is defined for the number of change-points, their positions, segment means and error terms. To quantify uncertainty about the location of change-points, the resulting posterior probability distributions are sampled using the Generalized Gibbs sampler Markov chain Monte Carlo technique. This methodology is illustrated by applying it to simulated data and to real data known as the well-log time series data. This well-log data records the measurements of nuclear magnetic response of underground rocks during the drilling of a well. Our approach has high sensitivity, and detects a larger number of change-points than have been identified by comparable methods in the existing literature.