Analysing multiple time series and extending significance testing in wavelet analysis

Type Article
Date 2008-04
Language English
Author(s) Rouyer Tristan1, 2, Fromentin Jean-Marc1, Stenseth N2, 3, Cazelles B4, 5
Affiliation(s) 1 : IFREMER, Ctr Rech Halieut Mediterraneenne & Trop, F-34203 Sete, France.
2 : Univ Oslo, Dept Biol, Ctr Ecol & Evolut Synth, N-0316 Oslo, Norway.
3 : Inst Marine Res, Dept Coastal Zone Studies, Flodevigen Res Stn, N-4817 His, Norway.
4 : Ecole Normale Super, CNRS, UMR 7625, F-75230 Paris 05, France.
5 : GEODES Ctr IRD Ile France, IRD, UR 079, F-93143 Bondy, France.
Source Marine Ecology Progress Series (0171-8630) (Inter-Research), 2008-04 , Vol. 359 , P. 11-23
DOI 10.3354/meps07330
WOS© Times Cited 61
Keyword(s) Maximum covariance analysis, Surrogates, Wavelet significance testing, Wavelet clustering, Multivariate time series, Non stationarity
Abstract In nature, non-stationarity is rather typical, but the number of statistical tools allowing for non-stationarity remains rather limited. Wavelet analysis is such a tool allowing for non-stationarity but the lack of an appropriate test for statistical inference as well as the difficulty to deal with multiple time series are 2 important shortcomings that limits its use in ecology. We present 2 approaches to deal with these shortcomings. First, we used 1/f beta models to test cycles in the wavelet spectrum against a null hypothesis that takes into account the highly autocorrelated nature of ecological time series. To illustrate the approach, we investigated the fluctuations in bluefin tuna trap catches with a set of different null models. The 1/f beta models approach proved to be the most consistent to discriminate significant cycles. Second, we used the maximum covariance analysis to compare, in a quantitative way, the time-frequency patterns (i.e. the wavelet spectra) of numerous time series. This approach built cluster trees that grouped the wavelet spectra according to their time-frequency patterns. Controlled signals and time series of sea surface temperature (SST) in the Mediterranean Sea were used to test the ability and power of this approach. The results were satisfactory and clusters on the SST time series displayed a hierarchical division of the Mediterranean into a few homogeneous areas that are known to display different hydrological and oceanic patterns. We discuss the limits and potentialities of these methods to study the associations between ecological and environmental fluctuations.
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