A. Gandelli (Italy), M.J. Hinich (USA), S. Marchi, and R.E. Zich (Italy)
Nonstationary, wavelets, shift-variant, coherence spectrum, forecasting.
A novel method, based on wavelet transform, for analyzing nonstationary time series is presented. The wavelet or time-scale approach is especially suitable for localizing in time the frequency content. Based on the signal coherence spectrum approach, introduced for quasi-stationary spectral analysis, for measuring the variability from period to period, the authors extend the approach to the wavelet domain. The signal coherence spectrum is used, among the others, to extract persistent components in forecasting, thereby discarding low coherence components. The wavelet approach allows to localize in time high and low-coherence coefficients. However, since the wavelet spectrum is not shift invariant, it happens that small shifts that occurs from period to period are not recognized as such, and the corresponding low-coherence wavelet coefficients are discarded. A shift recognition algorithm allows to select highly coherent components which would be otherwise discarded. This approach allows to implement robust forecast techniques, by suitably triggering the shift recognition parameter. A numerical example, applied to the Alberta Electrical Market, is provided to illustrate the proposed method.
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