Medium and Small Scale Analysis of Financial Data
Andreas P. Nawroth, Joachim Peinke
Abstract
A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays τ. The scale dependent behaviour of financial data can be divided into two regions. The first time-range, the small-timescale region (in the range of seconds) seems to be characterized by universal features. The second time-range, the medium-timescale range from several minutes upwards and can be characterized by a cascade process, which is given by a stochastic Markov process in the scale τ. A corresponding Fokker-Planck equation can be extracted from given data and provides a non equilibrium thermodynamical description of the complexity of financial data.
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