Characterizing abrupt changes in the stock prices using a wavelet decomposition method

Abrupt changes in the stock prices, either upwards or downwards, are usually preceded by an oscillatory behavior with frequencies that tend to increase as the moment of transition becomes closer. The wavelet decomposition methods may be useful for analysis of this oscillations with varying frequencies, because they provide simultaneous information on the frequency (scale) and localization in time (translation). However, in order to use the wavelet decomposition, certain requirements have to be satisfied, so that the linear and cyclic trends are eliminated by standard least squares techniques. The coefficients obtained by the wavelet decomposition can be represented in a graphical form. A threshold can then be established to characterize the likelihood of a short-time abrupt change in the stock prices. Actual data from the São Paulo Stock Exchange (Bolsa de Valores de São Paulo) were used in this work to illustrate the proposed method.