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1. Identity statement Reference Type Conference Paper (Conference Proceedings) Site mtc-m21b.sid.inpe.br Holder Code isadg {BR SPINPE} ibi 8JMKD3MGPCW/3DT298S Identifier 8JMKD3MGP3W34P/3LTDALB Repository sid.inpe.br/mtc-m21b/2016/06.20.17.48 Metadata Repository sid.inpe.br/mtc-m21b/2016/06.20.17.48.04 Metadata Last Update 2018:06.04.02.40.56 (UTC) administrator Secondary Key INPE--PRE/ Citation Key CampanharoRamo:2016:HuExEs Title Hurst exponent estimation of self-affine time series through a complex network approach Year 2016 Access Date 2024, Apr. 29 Secondary Type PRE CI 2. Context Author 1 Campanharo, Adriana Susana Lopes de Oliveira 2 Ramos, Fernando Manuel Resume Identifier 1 2 8JMKD3MGP5W/3C9JH4A Group 1 2 LAC-CTE-INPE-MCTI-GOV-BR Affiliation 1 Universidade Estadual Paulista (UNESP) 2 Instituto Nacional de Pesquisas Espaciais (INPE) Author e-Mail Address 1 andriana@ibb.unesp.br 2 fernando.ramos@inpe.br Conference Name International Conference on Nonlinear Science and Complexity, 6 Conference Location São José dos Campos, SP Date 16-20 May History (UTC) 2016-06-20 17:48:31 :: simone -> administrator :: 2016 2018-06-04 02:40:56 :: administrator -> simone :: 2016 3. Content and structure Is the master or a copy? is the master Content Stage completed Transferable 1 Content Type External Contribution Keywords nonlinear dynamics and complex systems time series analysis complex networks Hurst exponent quantile graphs Abstract Many natural signals present a fractal-like structure and are characterized by two parameters, β, the power-spectrum power-law exponent, and H, the Hurst exponent [1]. For time series with a self-affine structure, like fractional Gaussian noises (fGn) and fractional Brownian motions (fBm), the Hurst exponent H is one of the key parameters. Over time, researchers accumulated a large number of time series analysis techniques, ranging from time-frequency methods, such as Fourier and wavelet transforms [2, 3], to nonlinear methods, such as phase-space embeddings, Lyapunov exponents, correlation dimensions and entropies [4]. These techniques allow researchers to summarize the characteristics of a time series into compact metrics, which can then be used to understand the dynamics or predict how the system will evolve with time [5]. Obviously, these measures do not preserve all of the properties of a time series, so there is considerable research toward developing novel metrics that capture additional information or quantify time series in new ways [5, 6, 7]. One of the most interesting advances is mapping a time series into a network, based on the concept of transition probabilities [5]. This study has demonstrated that distinct features of a time series can be mapped onto networks (here called quantile graph or QG) with distinct topological properties. This finding suggests that network measures can be used to differentiate properties of fractal-like time series. In spite of the large number of applications of complex networks methods in the study time series, usually involving the classification of dynamical systems or the identification of dynamical transitions [8], establishing a link between a network measure and H remains an open question [1]. Recently, a linear relationship between the exponent of the power law degree distribution of visibility graphs and H has been established for noises and motions [9,10]. Here, we show an alternative approach for the computation of the Hurst exponent [1]. This new approach is based on a generalization of the method introduced in Ref. [5], in which time series quantiles are mapped into nodes of a graph. In this approach, a quantile graph is obtained as follows: The values of a given time series is coarse-grained into Q quantiles q1, q2,,qQ. A map M from a time series to a network assigns each quantile qi to a node ni in the corresponding network. Two nodes ni and nj are connected with a weighted arc ni, nj, wij k whenever two values x(t) and x(t + k) belong respectively to quantiles qi and qj, with t = 1, 2, . . . ,T and the time differences k = 1, . . . , kmax < T. Weights wij k are given by the number of times a value in quantile qi at time t is followed by a point in quantile qj at time t+k, normalized by the total number of transitions. Repeated transitions through the same arc increase the value of the corresponding weight. With proper normalization, the weighted adjacency matrix becomes a Markov transition matrix. The resulting network is weighted, directed and connected. Besides, the QG method is numerically simple and has only one free parameter, Q, the number of quantiles/nodes [1, 5]. The QG method for estimating the Hurst exponent was applied to fBm with different H values. Based on the QG method described above, H was 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 [1]. Results were compared to the exact H values used to generate the motions and showed a good agreement. For a given time series length, estimation error depends basically on the statistical framework used for determining the exponent of a power-law model [1]. Therefore, the QG method permits to quantify features such as long-range correlations or anticorrelations associated with the signals underlying dynamics, expanding the traditional tools of time series analysis in a new and useful way [1,5]. Area COMP Arrangement urlib.net > LABAC > Hurst exponent estimation... doc Directory Content there are no files source Directory Content there are no files agreement Directory Content agreement.html 20/06/2016 14:48 1.0 KiB  4. Conditions of access and use Language en User Group simone Reader Group administrator simone Visibility shown Read Permission allow from all Update Permission not transferred 5. Allied materials Mirror Repository urlib.net/www/2011/03.29.20.55 Next Higher Units 8JMKD3MGPCW/3ESGTTP Citing Item List Host Collection sid.inpe.br/mtc-m21b/2013/09.26.14.25.20 6. Notes Empty Fields archivingpolicy archivist booktitle callnumber copyholder copyright creatorhistory descriptionlevel dissemination doi e-mailaddress edition editor format isbn issn label lineage mark nextedition notes numberoffiles numberofvolumes orcid organization pages parameterlist parentrepositories previousedition previouslowerunit progress project publisher publisheraddress rightsholder schedulinginformation secondarydate secondarymark serieseditor session shorttitle size sponsor subject targetfile tertiarymark tertiarytype type url versiontype volume 7. Description control e-Mail (login) simone update

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