Optimal Change-Point Sequential Detection in Autoregressive Time Series

In this study, we consider a sequential detection problem in Bayesian setting for autoregressive times series based on a bounded number of observations under the condition that the post-change parameters are unknown. To this end we propose a new truncated sequential detection method through the theory developed in [5] for the statistical model with known post-change distributions. Based on the developed method, the quickest detection algorithm is proposed, that is, optimal in terms of the minimum mean time delay with the probability of a false alarm limited by some fixed known threshold.