• Cardinali, Alessandro
• Nason, Guy

Abstract

Methods designed for second-order stationary time series can bemisleading when applied to nonstationary series, often resulting in inaccurate models and poor forecasts. Hence, testing time series stationarity isimportant 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. Weprovide freeware R software that implements our tests and arange of graphical tools toidentify the location and duration of nonstationarities. Theoretical and simulated power calculationsshow the superiority of our wavelet packet approachin 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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