Energy wavelet analysis of time series

In this paperwe will approach the analysis of time series by the discrete Haar wavelet trasnform and by the energy distribution. it is shown that the wavelet coefficients are strictly related to the scheme of finite differences, thus giving information on the first order properties of the data. In particular, this method is tested on financial data, such as stock pricings, by characterizing the trends and the abrupt changes, by means of the Shannon's information function (entropy), which is defined on the local energy. AMS Classification: Primary 35A35, 42C40, 41A15, 47A58. Secondary 65T60. 65D07. Jel Classification: C63, E43. Key words and phrases: Wavelets, haar function, time series, entropy