Bayesian Autoregressive Time Series Analysis

Two Bayesian autoregressive time series models for partially observable dynamic processes are presented. In the first model, a general inference procedure is developed for the situation in which k previous values of the time series plus a change error determine the next value. This general model is specialized to an example in which the observational and change errors follow a normal probability law; the results for k = 1 are given and discussed. The second general model adds the facility for simultaneously inferring an unknown and unchanging parameter of the time series. This model is specialized to the same normal example presented earlier, with the precision of the change error as the unknown process parameter.