A NEW IRREGULARITY CRITERION FOR DISCRIMINATION OF STOCHASTIC AND DETERMINISTIC TIME SERIES

Abstract

In this paper, a new irregularity criterion based on fractal dimensions is introduced. In fact, this criterion (which is called ONH criterion) is the state space version of Higuchi fractal dimension, which can discriminate stochastic and deterministic time series from each other. To compute this criterion, we have exploited "the amount of state vectors fluctuations" in embedding space. By varying the reconstruction delay in embedding space, one can obtain a logarithmic diagram of overall changes corresponding to reconstructed state space versus delays. The slope of the linear region of this diagram could be considered as a new irregularity criterion. To discriminate random and deterministic time series, this criterion is adopted as a new statistic for hypothesis testing. Probability density function of this statistic under H0hypothesis is constructed and regarding to a certain confidence level, one can determine whether randomness is accepted or rejected.