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.
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 language | English |
|---|---|
| Pages (from-to) | 895-917 |
| Number of pages | 23 |
| Journal | Journal of Time Series Analysis |
| Volume | 43 |
| Issue number | 6 |
| Early online date | 8 Feb 2022 |
| DOIs | |
| Publication status | Published - 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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This is the final published version of the article (version of record). It first appeared online via Wiley at https://doi.org/10.1111/jtsa.12643 . Please refer to any applicable terms of use of the publisher.