Modeling Financial Time Series: Multifractal Cascades and Rényi Entropy

Abstract

We show that a number of realistic financial time series can be well mimicked by multiplicative multifractal cascade processes. The key observation is that the multi-scale behavior in financial progressions fits well the multifractal cascade scaling paradigm. Connections with Kol- mogorov’s idea of multiplicative cascade of eddies in the well developed turbulence are briefly discussed. To put some flesh on a bare bones we compare volatility time series for S&P 500 stock index with a simulated multiplicative multifractal cascade processes. Qualitative agreement is surprisingly good. Salient issues, such as Codimension functions or Mul- tifractal Diffusion analysis and its role in scaling identification are also discussed.