Dimensions of Synthesized Time Series Data

概要

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For the construction of standard scales in the determination of fractal dimensions of chaotic systems, we determine empirically dimensions of artificial time series data that are constructed of functions with different periods and some amount of Gaussian noise. Various trajectories of the data in multi-dimensional phase space are investigated in order to study the effect on the determined dimensions of several parameters, i.e. phase-space dimension, time delay, number of data, and inclusion of noise in the data, etc.. The results of the analysis show among others that the proper position of correlation distance to estimate the fractal dimension is about a half of the amplitude of valuation in the data. The fractal dimension D of a chaotic system should better be determined at the position such that the estimated dimension becomes first satulated with increasing the embedding phase-space dimension. At that position, the embedding dimension amounts about 2D + 1. Noise have considerable effect on the determination of the correlation dimension so that the latter dimension is difficult to predict if noise is mixed more than 0.12 of the rms dispersion of the system variation. Smoothing out of data to minimize the noise effect is neccesary prior to the analysis.
近畿大学の論文
1993-01-30