The predictive power of power-laws: An empirical time-arrow based investigation

Abstract

The efficient market hypothesis forbids any predictability towards future, but there is no such restriction in the case of reversed-looking approaches. We analyze if this asymmetry in non-predictability is reflected in the statistical features of financial time series. Our study is based on the analysis of the length-distribution of periods with high variability, and introduces time-asymmetric modifications of the method which are capable of revealing differences of the time series in forward and reversed time. We show that the future and reversed-looking time-series possess very similar properties, with some features being distinguishable with our method. Our findings give also evidence of the differences in the dynamics of markets before and after crisis, this implying the possibility to predict a forthcoming crisis.