Testing Statistical Hypotheses About Ergodic Processes

We address three problems of statistical analysis of real-valued time series: goodness-of-fit (or identity) testing, process discrimination, and the change point problem. For each of the problems we construct a test that is asymptotically accurate for the case when the data is generated by stationary ergodic processes. All problems are solved in a similar way by using empirical estimates of the distributional distance between the processes.