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The authors deal with forecasting nonstationary time series using wavelets and kernel smoothing. Starting from a basic forecasting procedure based on the regression of the process on the nondecimated Haar wavelet coefficients of the past, the procedure was extended in various directions, including the use of an arbitrary wavelet or polynomial fitting for extrapolating low-frequency components. The authors study a further generalization of the prediction procedure dealing with multistep forecasting and combining kernel smoothing and wavelets. They finally illustrate the proposed procedure on nonstationary simulated and real data and then compare it to well-known competitors. [ABSTRACT FROM AUTHOR]

This paper deals with wavelets in time series, focusing on statistical forecasting purposes. Recent approaches involve wavelet decompositions in order to handle non-stationary time series in such context. A method, proposed by Renaud et al.,11 estimates directly the prediction equation by direct regression of the process on the Haar non-decimated wavelet coefficients depending on its past values. In this paper, this method is studied and extended in various directions. The new variants are used first for stationary data and after for stationary data contaminated by a deterministic trend. [ABSTRACT FROM AUTHOR]

We present two strategies for detecting patterns and clusters in high-dimensional timedependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first strategy uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high-dimensional populations. The second strategy uses a similarity measure between the whole time-scale representations that is based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Practical performance is illustrated through simulations as well as daily profiles of the French electricity power demand [ABSTRACT FROM AUTHOR]