Measuring the degree of non-stationarity of a time series

Sourav Das, Guy P Nason

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)
660 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)295-305
Number of pages11
Issue number1
Early online date13 Nov 2016
Publication statusPublished - Feb 2017


  • time series
  • non-parametric regression
  • bootstrap assessment


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