Measuring the degree of non‐stationarity of a time series. Issue 1 (13th November 2016) - Das, Sourav; Nason, Guy P.
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