Time-space scale analysis method based on time-scale local Hurst indexes

Abstract

The invention discloses a time-space scale analysis method based on time-scale local Hurst indexes. The method comprises the steps that a time sequence is established, and a fluctuation increment time sequence is generated; the local Hurst indexes are computed and constitute a Ht sequence; frequency number statistics is conducted to the Ht sequences under different spaces, and spatial probability density distribution is computed; Gaussian fitting is conduced to the spatial probability density distribution, spatial scale statistic characteristic values of original distribution and fitting distribution are determined, and changes of scale behaviors caused by spatial factors are investigated and quantified according to the statistic characteristic values; and interval division is conducted to the Ht sequence according to characteristic time, time probability density distribution of each interval Ht sequence is determined, the time scale statistic characteristic values are determined, and the changes of the scale behaviors caused by the time factors are investigated and quantified according to the statistic characteristic values. From the perspective of statistics, a fractal structure is established according to the time-scale local Hurst indexes; and conversion of the scale structure under different space and time are quantified by the statistic characteristic values.

Description

technical field [0001] The invention relates to a scale analysis method, in particular to a time-space scale analysis method based on the time-scale local Hurst exponent, and belongs to the technical field of data analysis. Background technique [0002] Natural processes or sequential processes generated by complex systems affected by multiple factors are usually characterized by disorder, instability, randomness, and nonlinearity. Traditional statistical methods have been unable to characterize such complex fluctuating processes. In recent years, studies have found that the oscillatory behavior of complex time structures is scale-free, and self-similarity is an inevitable property of this scale-free behavior. Hurst exponent is widely used to characterize scaling behavior with different correlations, as an index to judge whether time series follow random walk or score-biased random walk process. When 0<H<0.5, the fluctuation is an anti-continuous fluctuation, and when...

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Problems solved by technology

But as far as we know, the local Hurst index is estimated by local fluctuations, and a single local Hurst index does not reflect the scaling behavior characteristics in a significant sense

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