Asymptotic inference for hidden process regression models

Hidden process regression (HPR) is a relatively new solution to fitting time series data that undergo a regime change. Current research in HPR has concentrated entirely on its prediction capacity, and modifications for time series classification and clustering, rather than inferential problems such as confidence interval construction. In this article, we investigate results under which maximum likelihood estimates for HPR are consistent and asymptotically normal. Proceeding from these results, confidence intervals of interesting quantities are derived. In the process, we give a monotonically converging modification to the currently used maximum likelihood estimation algorithm for HPR. As a demonstration of our approach, the algorithm and intervals are applied to a climate science example.