Stationarity as a Path Property

• Autorzy: Shen Yi , Wirjanto Tony S.

Identyfikatory

DOI

10.19195/0208-4147.39.2.9

• Języki publikacji: EN

Abstrakty

EN

Traditionally, stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths, denoted by A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions.

Słowa kluczowe

EN

stationarity; path property

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 403--422
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Shen Yi

• University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

autor

Wirjanto Tony S.

• University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

Bibliografia

• [1] P. Billingsley, Probability and Measure, Wiley, 1995.
• [2] F. Busetti and A. C. Harvey, Tests of strict stationarity based on quantile indicators, J. Time Series Analysis 31 (2010), pp. 435-450.
• [3] D. A. Dickey and W. A. Fuller, Distribution of the estimators for autoregressive time series with a unit root, J. Amer. Statist. Assoc. 74 (1979), pp. 427-431.
• [4] I. Domowitz and M. A. El-Gamal, A consistent nonparametric test of ergodicity for time series with applications, J. Econometrics 102 (2001), pp. 365-398.
• [5] H. Furstenberg, Stationary Processes and Prediction Theory, Princeton University Press, Princeton 1960.
• [6] S. Kanaya, A nonparametric test for stationarity in continuous-time Markov processes, Job Market Paper, University of Oxford, 2011.
• [7] D. Kwiatkowski, P. C. B. Phillips, P. Schmidt, and Y. Shin, Testing the null hypothesis of stationarity against the alternative of a unit root, J. Econometrics 54 (1992), pp. 159-178.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).