Trend locally stationary wavelet processes

Euan T McGonigle*, Rebecca Killick, Matthew Nunes

*Corresponding author for this work

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

5 Citations (Scopus)
56 Downloads (Pure)

Abstract

Most time series observed in practice exhibit first as well as second-order nonstationarity. In this article we propose a novel framework for modelling series with simultaneous timevarying 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
Volume43
Issue number6
Early online date8 Feb 2022
DOIs
Publication statusPublished - 4 Oct 2022

Bibliographical note

Funding Information:
Euan T. McGonigle gratefully acknowledges financial support from EPSRC and Numerical Algorithms Group Ltd. via The Smith Institute i‐CASE award No. EP/R511997/1.

Publisher Copyright:
© 2022 The Authors. Journal of Time Series Analysis published by John Wiley & Sons Ltd.

Keywords

  • Climate Data
  • Locally stationary
  • Nonstationary time series
  • Trend estimation
  • Wavelet spectrum

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