Local order, entropy and predictability of financial time series
Institute of Physics, Humboldt-University Berlin, Invalidenstrasse 110, 10115 Berlin, Germany
Published online: 15 June 2000
We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea is that in spite of the high stochasticity in average there might be special local situations where there local order exist and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the uncertainty/predictability and the distribution of these quantities.
PACS: 05.45.Tp – Time series analysis / 02.50.Ey – Stochastic processes / 65.50.+m – Thermodynamic properties and entropy
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000