Entropy and Transfer Entropy: The Dow Jones and the Build Up to the 1997 Asian Crisis

Abstract

Entropy measures in their various incarnations play an important role in the study of stochastic time series providing important insights into both the correlative and the causative structure of the stochastic relationships between the individual components of a system. Recent applications of entropic techniques and their linear progenitors such as Pearson correlations and Granger causality have have included both normal as well as critical periods in a system's dynamical evolution. Here I measure the entropy, Pearson correlation and transfer entropy of the intra-day price changes of the Dow Jones Industrial Average in the period immediately leading up to and including the Asian financial crisis and subsequent mini-crash of the DJIA on the 27th October 1997. I use a novel variation of transfer entropy that dynamically adjusts to the arrival rate of individual prices and does not require the binning of data to show that quite different relationships emerge from those given by the conventional Pearson correlations between equities. These preliminary results illustrate how this modified form of the TE compares to results using Pearson correlation.