Long-range correlation properties of financial stochastic time series y have been investigated with the main aim to demonstrate the ability of a recently proposed method to extract the scaling parameters of a stochastic series. According to this technique, the Hurst coefficient H is calculated by means of the following function: EQUATION where y_n(i)is the moving average of y(i), defined as EQUATION the moving average window and N_max is the dimension of the stochastic series. The method is called Detrending Moving Average Analysis (DMA) on account of the several analogies with the well-known Detrended Fluctuation Analysis (DFA). The DMA technique has been widely tested on stochastic series with assigned H generated by suitable algorithms. It has been demonstrated that the ability of the proposed technique relies on very general grounds: the function EQUATION generates indeed a sequence of clusters with power-law distribution of amplitudes and lifetimes. In particular the exponent of the distribution of cluster lifetime varies as the fractal dimension 2 - H of the series, as expected on the basis of the box-counting method. In the present paper we will report on the scaling coefficients of real data series (the BOBL and DAX German future) calculated by the DMA technique.

Date Published: 7 May 2003
PDF: 9 pages
Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.497039

Published in SPIE Proceedings Vol. 5114:
Noise in Complex Systems and Stochastic Dynamics
Lutz Schimansky-Geier; Derek Abbott; Alexander Neiman; Christian Van den Broeck, Editor(s)