Journal of Time Series Analysis

BAYESIAN INFERENCE OF THRESHOLD AUTOREGRESSIVE MODELS

Journal Article

Abstract. The study of non‐linear time series has attracted much attention in recent years. Among the models proposed, the threshold autoregressive (TAR) model and bilinear model are perhaps the most popular ones in the literature. However, the TAR model has not been widely used in practice due to the difficulty in identifying the threshold variable and in estimating the associated threshold value. The main focal point of this paper is a Bayesian analysis of the TAR model with two regimes. The desired marginal posterior densities of the threshold value and other parameters are obtained via the Gibbs sampler. This approach avoids sophisticated analytical and numerical multiple integration. It also provides an estimate of the threshold value directly without resorting to a subjective choice from various scatterplots. We illustrate the proposed methodology by using simulation experiments and analysis of a real data set.

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