Testing Statistical Hypotheses About Ergodic Processes

We propose a method for statistical analysis of time series, that allows us to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, we consider three problems: goodness-of-fit (or identity) testing, process classification, 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. The tests are based on empirical estimates of distributional distance.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Daniil Ryabko, Boris Ryabko
• Keywords: Change Point Problem, CORR 2008, Education, Problems, Statistical Analysis