Stationarity As a Path Property with Applications in Time Series Analysis

Posted: 9 Jul 2016

See all articles by Yi Shen

Yi Shen

Department of Statistics & Actuarial Science, University of Waterloo

Tony S. Wirjanto

University of Waterloo - School of Accounting and Finance; University of Waterloo, Department of Statistics & Actuarial Science

Date Written: June 25, 2016

Abstract

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 as 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. The results provide a united framework to understand and assess the existing time series tests for stationarity, and can potentially lead to new families of stationarity tests.

Keywords: stationary process; path property; time series

JEL Classification: C22

Suggested Citation

Shen, Yi and Wirjanto, Tony S., Stationarity As a Path Property with Applications in Time Series Analysis (June 25, 2016). Available at SSRN: https://ssrn.com/abstract=2806473

Yi Shen

Department of Statistics & Actuarial Science, University of Waterloo ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Croatia

HOME PAGE: http://https://uwaterloo.ca/statistics-and-actuarial-science/people-profiles/yi-shen

Tony S. Wirjanto (Contact Author)

University of Waterloo - School of Accounting and Finance ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)

HOME PAGE: http://https://uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

University of Waterloo, Department of Statistics & Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)
519-746-1875 (Fax)

HOME PAGE: http://math.uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

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