Stationarity As a Path Property with Applications in Time Series Analysis
Posted: 9 Jul 2016
Date Written: June 25, 2016
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
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