Intraday patterns and local predictability of high-frequency financial time series

The structure of high-frequency time series of financial data taking the DAX future as an example is investigated with respect to the existence of local order on a time horizon of a few minutes. We will show that there might be special local situations where local order exists and where the predictability is considerably higher than average. We discretize the time series and investigate the continuation frequency of definite words of length n first. Besides higher order Shannon entropies and conditional entropies (dynamic entropies) which yield mean values of the uncertainty/predictability, we study the local values of the uncertainty/predictability and the distribution of these quantities. The local order significance is treated by means of surrogate sequences with identical short memory as the original data.