Testing Statistical Hypotheses About Ergodic Processes

Daniil Ryabko (1) , Boris Ryabko (2, 3)

1 SEQUEL - Sequential Learning
2 SIBSUTI - Siberian State University of Telecommunications and Informatics
3 ICT SBRAS - Institute of Computational Technologies [Novosibirsk]

We address three problems of statistical analysis of 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.

Mots clés: non-parametric; hypothesis testing; time series; ergodic processes; goodness-of-fit; process discrimination; change point

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]; Statistiques [math.ST]; Théorie [stat.TH]

Daniil Ryabko, Boris Ryabko. Testing Statistical Hypotheses About Ergodic Processes. IEEE Transactions on Information Theory, 2010, 56 (3), pp.1430-1435. ⟨inria-00269249v3⟩