Modelling Share Volume Traded in Financial Markets

A simple analytically solvable model exhibiting a 1/f spectrum in an arbitrarily wide frequency range was recently proposed by Kaulakys and Meškauskas (KM). Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is Brownian fluctuations of the average intervent time between subsequent pulses of the pulse sequence. We generalize the KM model to reproduce the variety of self-affine time series exhibiting power spectral density S(f) scaled as power of their frequency f. Numerical calculations with the generalized discrete model (GDM) reproduce power spectral density S(f) scaled as power of frequency 1/f β for various values of β, including β = 1/2 for applications in financial markets. The particular applications of the model proposed are related with financial time series of share volume traded.