Analysing multiple time series and extending significance testing in wavelet analysis
TLDR
This work used 1/ƒ β models to test cycles in the wavelet spectrum against a null hypothesis that takes into account the highly autocorrelated nature of ecological time series and used the maximum covariance analysis to compare the time-frequency patterns of numerous time series.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/ƒ β 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/ƒ β 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.read more
Citations
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Journal ArticleDOI
Wavelet analysis of ecological time series
Bernard Cazelles,Mario Chavez,Dominique Berteaux,Frédéric Ménard,Jon Olav Vik,Stéphanie Jenouvrier,Nils Chr. Stenseth +6 more
TL;DR: The basic properties of the wavelet approach for time-series analysis from an ecological perspective are reviewed, notably free from the assumption of stationarity that makes most methods unsuitable for many ecological time series.
Journal ArticleDOI
Linking climate change to lemming cycles
Kyrre Kausrud,Atle Mysterud,Harald Steen,Harald Steen,Jon Olav Vik,Eivind Østbye,Bernard Cazelles,Erik Framstad,Anne Maria Eikeset,Ivar Mysterud,Torstein Solhøy,Nils Chr. Stenseth +11 more
TL;DR: It is shown that winter weather and snow conditions, together with density dependence in the net population growth rate, account for the observed population dynamics of the rodent community dominated by lemmings in an alpine Norwegian core habitat between 1970 and 1997, and predict the observed absence of rodent peak years after 1994.
Wavelet-based representations for the 1/f family of fractal processes : Fractals in electrical engineering
TL;DR: In this paper, it was shown that 1/f processes are optimally represented in terms of orthonormal wavelet bases, and the wavelet expansion's role as a Karhunen-Loeve-type expansion was developed.
Journal ArticleDOI
Business Cycle Synchronization and the Euro: a Wavelet Analysis ∗
TL;DR: In this paper, the authors use wavelet analysis to study business cycle synchronization across the EU-15 and the Euro-12 countries and find that the French business cycle has been leading the German business cycle as well as the rest of Europe.
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Surrogate data for hypothesis testing of physical systems
Gemma Lancaster,Dmytro Iatsenko,Aleksandra Pidde,Aleksandra Pidde,Valentina Ticcinelli,Aneta Stefanovska +5 more
TL;DR: A detailed overview of a wide range of surrogate types is provided, which include Fourier transform based surrogates, which have since been developed to test increasingly varied null hypotheses while characterizing the dynamics of complex systems, including uncorrelated and correlated noise, coupling between systems, and synchronization.
References
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Wavelet-based representations for the 1/f family of fractal processes : Fractals in electrical engineering
TL;DR: In this paper, it was shown that 1/f processes are optimally represented in terms of orthonormal wavelet bases, and the wavelet expansion's role as a Karhunen-Loeve-type expansion was developed.
Journal ArticleDOI
A study of an intense density front in the eastern Alboran Sea: the Almeria-Oran front
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Journal ArticleDOI
Wavelet-based representations for the 1/f family of fractal processes
TL;DR: In this article, it is shown that 1/f fractal processes are optimally represented in terms of orthonormal wavelet bases, and the wavelet expansion's role as a Karhunen-Loeve-type expansion for 1 /f processes is developed.
Journal ArticleDOI
Adaptive covariance estimation of locally stationary processes
TL;DR: In this paper, the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions, and an adaptive covariance estimation is calculated by searching first for a "best" locally cosine basis which approximates the covariances by a band or a diagonal matrix.
Journal ArticleDOI
Characterizing canopy gap structure in forests using wavelet analysis
G. A. Bradshaw,Thomas A. Spies +1 more
TL;DR: The wavelet transform is introduced as a technique to identify spatial structure in transect data and its main advantages over other methods of spatial analysis are its ability to preserve and display hierarchical information while allowing for pattern decomposition.