Layer histogram patterns in financial time series

This study aims to investigate whether the phenomena found by Shnoll et al. when applying histogram pattern analysis techniques to stochastic processes from chemistry and physics are also present in financial time series, particularly exchange rate and index data. The phenomena are related to fine structure of non-smoothed frequency distributions drawn from statistically insufficient samples of changes and their patterns in time. Shnoll et al. use the notion of macroscopic fluctuations (MF) to explain the behavior of sequences of histograms. Histogram patterns in time adhere to several laws that could not be detected when using time series analysis methods. In this study special emphasis is placed on the histogram pattern analysis of high frequency exchange rate data set. Following previous studies of the Shnoll phenomena from other fields, different steps of the histogram sequence analysis are carried out to determine whether the findings of Shnoll et al. could also be applied to financial market data. The findings presented here widen the understanding of time varying volatility and can aid in financial risk measurement and management. Outcomes of the study include an investigation of time series characteristics, more specifically the formation of discrete states.