Measuring the degree of non‐stationarity of a time series

Abstract

In time series analysis, there is an extensive literature on hypothesis tests that attempt to distinguish a stationary time series from a non‐stationary one. However, the binary distinction provided by a hypothesis test can be somewhat blunt when trying to determine the degree of non‐stationarity of a time series. This article creates an index that estimates a degree of non‐stationarity. This index might be used, for example, to classify or discriminate between series. Our index is based on measuring the roughness of a statistic estimated from the time series, which is calculated from the roughness penalty associated with a spline smoothing/penalized least‐squares method. We further use a resampling technique to obtain a likely range of index values obtained from a single realization of a time series. We apply our method to ascertain and compare the non‐stationarity index of the well‐known earthquake and explosion data. © 2016 The Authors. Stat Published by John Wiley & Sons Ltd

Near Real-Time Characterization of Spatio-Temporal Precursory Evolution of a Rockslide from Radar Data: Integrating Statistical and Machine Learning with Dynamics of Granular Failure

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