Hurst exponent estimation of self-affine time series using quantile graphs

Autor(es)

Campanharo, Andriana S. L. O. ^[1] ; Ramos, Fernando M. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Inst Biociencias, Dept Bioestat, Botucatu, SP - Brazil

^[2] Inst Nacl Pesquisas Espaciais, Lab Comp & Matemat Aplicada, BR-12201 Sao Jose Dos Campos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 444, p. 43-48, FEB 15 2016.
• Citações Web of Science: 7

Resumo

In the context of dynamical systems, time series analysis is frequently used to identify the underlying nature of a phenomenon of interest from a sequence of observations. For signals with a self-affine structure, like fractional Brownian motions (fBm), the Hurst exponent H is one of the key parameters. Here, the use of quantile graphs (QGs) for the estimation of H is proposed. A QG is generated by mapping the quantiles of a time series into nodes of a graph. H is then computed directly as the power-law scaling exponent of the mean jump length performed by a random walker on the QG, for different time differences between the time series data points. The QG method for estimating the Hurst exponent was applied to fBm with different H values. Comparison with the exact H values used to generate the motions showed an excellent agreement. For a given time series length, estimation error depends basically on the statistical framework used for determining the exponent of the power-law model. The QG method is numerically simple and has only one free parameter, Q, the number of quantiles/nodes. With a simple modification, it can be extended to the analysis of fractional Gaussian noises. (C) 2015 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 13/19905-3 - Caracterização e análise de séries temporais fisiológicas e de redes complexas biológicas
• Beneficiário: Andriana Susana Lopes de Oliveira Campanharo
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/05145-0 - NetSci 2014 International School and Conference on Network Science
• Beneficiário: Andriana Susana Lopes de Oliveira Campanharo
• Linha de fomento: Auxílio à Pesquisa - Reunião - Exterior