Role of multifractal sources in the analysis of stock market time series

It has been repeatedly reported that time series of returns in stock markets are of multifractal (multiscaling) character. Recently, a direct geometrical framework, much more revealing about the underlying dynamics than usual statistical approaches, has been introduced. In this paper we use this geometrical method to undercover several aspects that concern the dynamics of stock market time series. We introduce and discuss a new, powerful processing tool, namely the computation of sources. With the aid of the source field, we will separate the fast, chaotic dynamics defined by the multifractal structure from a new, so-far unknown slow dynamics which concerns long cycles in the series. We discuss the results on the perspective of detection of sharp dynamic changes and forecasting.