Practical powerful wavelet packet tests for second-order stationarity. 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.
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References in zbMATH (referenced in 7 articles , 1 standard article )
Showing results 1 to 7 of 7.
- Killick, Rebecca; Knight, Marina I.; Nason, Guy P.; Eckley, Idris A.: The local partial autocorrelation function and some applications (2020)
- Bücher, Axel; Fermanian, Jean-David; Kojadinovic, Ivan: Combining cumulative sum change-point detection tests for assessing the stationarity of univariate time series (2019)
- Cardinali, Alessandro; Nason, Guy P.: Practical powerful wavelet packet tests for second-order stationarity (2018)
- Nelson, J. D. B.; Gibberd, A. J.; Nafornita, C.; Kingsbury, N.: The locally stationary dual-tree complex wavelet model (2018)
- Richard, Alexandre; Orio, Patricio; Tanré, Etienne: An integrate-and-fire model to generate spike trains with long-range dependence (2018)
- Cardinali, Alessandro; Nason, Guy P.: Locally stationary wavelet packet processes: basis selection and model fitting (2017)
- Michis, Antonis A.; Nason, Guy P.: Case study: shipping trend estimation and prediction via multiscale variance stabilisation (2017)