On Determining Stationary Periods within Time Series

Abstract

AbstractA novel approach is constructed for determining both the occurrence and the duration of stationary periods within time series. After reviewing four statistical techniques that provide stationarity measures invariant to applying a constant offset to the variable of interest, the reverse arrangement test is selected as the basic statistical operation to construct the approach. The probability distributions of the starting and ending points of stationary intervals are used to determine the nonstationary location at which a period should be split into two subperiods and nonstationary samples that should be discarded from analysis of time-averaged statistics. The approach provides efficient analysis of long-term datasets and is capable of relating data sampled at multiple locations. Applying the approach to data obtained within a walnut orchard canopy during the defoliated phase of the Canopy Horizontal Array Turbulence Study (CHATS) yields periods with stationary within-canopy velocities required by analysis of the bulk drag–wind relationship. The uncertainties in empirical estimates of the bulk drag–wind relationship associated with nonstationarity and finite duration of time series are evaluated. An integral view of various stationarity measures is presented, with a highlight of their links to physical processes.