Forecasting with Entropy

The paper describes an alternative approach to forecasting financial time series based on entropy (C. A. Zapart, On entropy, financial markets and minority games, Physica A: Statistical Mechanics and its Applications, 388 (7) 2009, pages 1157-1172). The research builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in (Molgedey, L and Ebeling, W, 2000, “Local order, entropy and predictability of financial time series”, European Physical Journal B Condensed Matter and Complex Systems). A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is applied to the prediction of Japanese Yen/US dollar intraday currency exchange time series. The study also reinterprets the Minority Game (Moro E, 2004, “The Minority Game: an introductory guide”, Advances in Condensed Matter and Statistical Physics) within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm. Subsequently the paper suggests using alternative entropy measures such as author’s NeuroEntropy or Approximate Entropy, introduced in (S Pincus, Approximate entropy as a measure of system complexity, Proceedings of National Academy of Sciences USA 1991 (88) pages 2297-2301) and (S Pincus, Irregularity, volatility, risk and financial market time series, Proceedings of National Academy of Sciences USA 2004 101 (38) pages 13709-13714). Exponentially-Weighted Smooth Approximate Entropy is proposed to make it more sensitive to recent data.