Bidirectional Estimation and Confidence Regions for TES Processes

TES (Transform-Expand-Sample) is a versatile class of stationary stochastic processes which can model arbitrary marginals, a wide variety of autocorrelation functions, and a broad range of sample path behaviors. The TES modeling methodology aims to simultaneously capture the empirical marginal distribution (histogram) and autocorrelation function of empirical time series, assuming only that they are from a stationary probability law. In this paper we utilize the known transition structure of TES processes to calculate bidirectional point estimates for these processes as conditional expectations of the process and its time-reversed version, given the current value. We also show how to construct symmetric confidence regions about these point estimates. We demonstrate our results with an example, using the software environment, TEStool, which supports TES modeling.