Classification of Fractal Time Series Using Recurrence Plots

The article considers classification task of fractal time series by the random forest method. It is proposed to classify time series as features to use the quantitative characteristics of recurrent plots. Time series of fractal Brownian motion were selected as input time series. The comparative analysis of different time series classification was held. The difference between fractal Brownian motion and fractal Gaussian noise in probabilities determining class and significant features are quite large. For fractal Brownian motion, it is enough recurrence features, while for fractal Gaussian noise it is necessary to use the estimate of H (except persistent series). The average probabilities for fractal Brownian motion are higher than for fractal Gaussian noise. For fractal Brownian motion, the most important features are ones of laminarity and determinism. For fractal Gaussian noise the laminar measure is not important, but the measures of average recurrence time and white vertical lines are significant. The results show that the important for the classification of fractal series is what kind of series is persistent or antipersistent. The results indicate the advantage of the recurrent features over the statistical and fractal ones.