Geometric fractal index as a tool of the time series analysis

Abstract

The problem of the fractal dimension estimation for the time series is considered. It is proposed to use special fractality indices based on the geometric characteristics of the observed discrete realization, namely on the analysis of its curvature. The relationship between proposed indices and the Hurst exponent is demonstrated and their properties are discussed. The effectiveness of the algorithms based on the geometric approach is demonstrated using known model fractals and real time series. The fractal analysis of the internet traffic, including detection of DDoS-attacks is discussed.