Practical powerful wavelet packet tests for second-order stationarity

Alessandro Cardinali, Guy P Nason

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

13 Citations (Scopus)
640 Downloads (Pure)


Methods designed for second-order stationary time series can be misleading when applied to nonstationary series, often resulting in inaccurate models and poor forecasts. Hence, testing time series stationarity is important especially with the advent of the `data revolution' and the recent explosion in the number of nonstationary time series analysis tools. Most existing stationarity tests rely on a single basis. We propose new tests that use nondecimated basis libraries which permit discovery of a wider range of nonstationary behaviours, with greater power whilst preserving acceptable statistical size. Our tests work with a wide range of time series including those whose marginal distributions possess heavy tails. We provide freeware R software that implements our tests and a range of graphical tools to identify the location and duration of nonstationarities. Theoretical and simulated power calculations show the superiority of our wavelet packet approach in a number of important situations and, hence, we suggest that the new tests are useful additions to the analyst's toolbox.
Original languageEnglish
Pages (from-to)558-583
Number of pages26
JournalApplied and Computational Harmonic Analysis
Issue number3
Early online date28 Jun 2016
Publication statusPublished - May 2018


  • stationarity test
  • local stationarity
  • bootstrap


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