Wavelet clustering in time series analysis

In this paper we shortly summarize the many advantages of the discrete wavelet transform in the analysis of time series. The data are transformed into clusters of wavelet coefficients and rate of change of the wavelet coefficients, both belonging to a suitable finite dimensional domain. It is shown that the wavelet coefficients are strictly related to the scheme of finite differences, thus giving information on the first and second 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. The wavelet coefficients projected into the phase space give rise to characteristic cluster which are connected with the volativility of the time series. By their localization they represent a sufficiently good and new estimate of the risk.