Autocorrelation and Parameter Estimation in a Bayesian Change Point Model

Abstract

A piecewise function can sometimes provide the best fit to a time series. The breaks in this function are called change points, which represent the point at which the statistical properties of the model change. Often, the exact placement of the change points is unknown, so an efficient algorithm is required to combat the combinatorial explosion in the number of potential solutions to the multiple change point problem. Bayesian solutions to the multiple change point problem can provide uncertainty estimates on both the number and location of change points in a dataset, but there has not yet been a systematic study to determine how the choice of hyperparameters or the presence of autocorrelation affects the inference made by the model. Here, we propose Bayesian model averaging as a way to address the uncertainty in the choice of hyperparameters and show how this approach highlights the most probable solution to the problem. Autocorrelation is addressed through a pre-whitening technique, which is shown to eliminate spurious change points that emerge due to a red noise process. However, pre-whitening a dataset tends to make true change points harder to detect. After an extensive simulation study, the model is applied to two climate applications: the Pacific Decadal Oscillation and a global surface temperature anomalies dataset.