Robust to noise and outliers estimator of correlation dimension

• Published in: Chaos, solitons and fractals Vol. 93; pp. 169 - 174
• Main Author: Dhifaoui, Zouhaier
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-12-2016
• Subjects: Correlation dimension; Gaussian kernel correlation integral; Modified Boltzmann sigmoidal function; Moving bloc bootstrap; Modified Boltzmann sigmoidal function; Gaussian kernel correlation integral; Correlation dimension; Moving bloc bootstrap
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2016.10.017

The estimation of correlation dimension of continuous and discreet deterministic chaotic processes corrupted by an additive noise and outliers observations is investigated. In this paper we propose a new estimator of correlation dimension based on similarity between the evolution of Gaussian kernel correlation sum (Gkcs) and that of modified Boltzmann sigmoidal function (mBsf), this estimator is given by the maximum value of the first derivative of logarithmic transform of Gkcs against logarithmic transform of bandwidth, so the proposed estimator is independent of the choice of regression region like other regression estimators of correlation dimension. Simulation study indicates the robustness of proposed estimator to the presence of different types of noise such us independent Gaussian noise, non independent Gaussian noise and uniform noise for high noise level, moreover, this estimator is also robust to presence of 60% of outliers observations. Application of this new estimator with determination of their confidence interval using the moving block bootstrap method to adjusted closed price of S&P500 index daily time series revels the stochastic behavior of such financial time series.