Trend Locally Stationary Wavelet Processes

Euan T. McGonigle, Rebecca Killick, Matthew A. Nunes

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)


Most time series observed in practice exhibit first- as well as second-order non-stationarity. In this article we propose a novel framework for modelling series with simultaneous time-varying first- and second-order structure, removing the restrictive zero-mean assumption of locally stationary wavelet processes and extending the applicability of the locally stationary wavelet model to include trend components. We develop an associated estimation theory for both first- and second-order time series quantities and show that our estimators achieve good properties in isolation of each other by making appropriate assumptions on the series trend. We demonstrate the utility of the method by analysing the global mean sea temperature time series, highlighting the impact of the changing climate.
Original languageEnglish
Pages (from-to)895-917
Number of pages23
JournalJournal of Time Series Analysis
Issue number6
Early online date2 Mar 2022
Publication statusPublished - 30 Nov 2022


  • Climate data
  • locally stationary
  • non-stationary time series
  • trend estimation
  • wavelet spectrum

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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