A Segmented Autoregressive Model Based on the Horizontal and Vertical Axes

This paper aims to further discuss the segmentation and estimation issues of autoregressive (AR) models. The innovations in the AR model do not follow the default normal distribution but rather an arbitrary distribution or a mixture of several distributions. We use a mixture of normal distributions to fit the distribution of the innovations, and employ the Dirichlet process as the prior for the variance of the mixture normal distribution to obtain the posterior estimates of the parameters. By combining Gibbs sampling, we continuously update the parameter estimates of the model to achieve more accurate results.In this study, segmentation is performed along both the horizontal and vertical axes. For the horizontal axis, we use the Bayesian method to identify the threshold values and lag parameters. For the vertical axis, we employ the LASSO method to identify the locations of change points. Numerical simulations are conducted to demonstrate the feasibility of the two segmentation approaches. Moreover, the model estimation and analysis are carried out on real time series data