Cattani, Carlo and Ciancio, Armando (2001) Wavelet Estimate of Time Series. Accademia Peloritana dei Pericolanti - Classe di Scienze FF.MM.NN., 78-79 (1). pp. 159-170.
In this paper a wavelet technique to study time series by discrete wavelet coefficients, is proposed. Since time series are mainly represented by histograms we will use the Haar waveletes and the Haar wavelet interpolation [1,2]. Moreover we propose an improvement (from computational point of view) of the discrete Haar wavelet transform, called reduced Haar wavelet transform [1,2], allowing a local windowing of the transform. Due to their localization property, the wavelet coefficients of the histogram, together with the wavelet coefficients of the generalized derivative of the histogram, allow to study, with high level of accuracy, the rate of change as well as other characteristics of the time series. Numerical experiments with two kind of (financial) time series show the effectiveness of this technique.
AMS Classification: 35A35, 47A58, 65N13, 65F10, 76W05. JEL Classification: C63, E43.
Key words and phrases: Wavelets, Haar function, interpolation, time series.
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