Autoregressive models with piecewise constant volatility and regression parameters

We introduce herein a new class of autoregressive models in which the regression parameters and error variances may undergo changes at unknown time points while staying constant between adjacent change-points. Assuming conjugate priors, we derive closed-form recursive Bayes estimates of the regression parameters and error variances. Approximations to the Bayes estimates are developed that have much lower computational complexity and yet are comparable to the Bayes estimates in statistical efficiency. We also address the problem of unknown hyper-parameters and propose two practical methods for simultaneous estimation of the hyperparameters, regression parameters and error variances.