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Thummadi NB, Charutha S, Pal M, Manimaran P. Multifractal and cross-correlation analysis on mitochondrial genome sequences using chaos game representation. Mitochondrion 2021; 60:121-128. [PMID: 34375735 DOI: 10.1016/j.mito.2021.08.006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Revised: 08/02/2021] [Accepted: 08/05/2021] [Indexed: 11/25/2022]
Abstract
We characterized the multifractality and power-law cross-correlation of mitochondrial genomes of various species through the recently developed method which combines the chaos game representation theory and 2D-multifractal detrended cross-correlation analysis. In the present paper, we analyzed 32 mitochondrial genomes of different species and the obtained results show that all the analyzed data exhibit multifractal nature and power-law cross-correlation behaviour. Further, we performed a cluster analysis from the calculated scaling exponents to identify the class affiliation and its outcome is represented as a dendrogram. We suggest that this integrative approach may help the researchers to understand the phylogeny of any kingdom with their varying genome lengths and also this approach may find applications in characterizing the protein sequences, mRNA sequences, next-generation sequencing, and drug development, etc.
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Affiliation(s)
- N B Thummadi
- Department of Animal Biology, School of Life Sciences, University of Hyderabad, Gachibowli, Hyderabad 500 046, India
| | - S Charutha
- School of Physics, University of Hyderabad, Gachibowli, Hyderabad 500 046, India
| | - Mayukha Pal
- ABB Ability Innovation Centre, Asea Brown Boveri Company, Hyderabad 500084, India
| | - P Manimaran
- School of Physics, University of Hyderabad, Gachibowli, Hyderabad 500 046, India.
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2
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A spatio-temporal analysis of dengue spread in a Brazilian dry climate region. Sci Rep 2021; 11:11892. [PMID: 34088931 PMCID: PMC8178350 DOI: 10.1038/s41598-021-91306-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Accepted: 05/24/2021] [Indexed: 11/13/2022] Open
Abstract
We investigated the relation between the spread, time scale, and spatial arrangement of dengue in Bahia, a Brazilian dry climate region, for the period 2000 to 2009. The degree of cross-correlation is calculated for 15 economic regions. We propose a multiscale statistical analysis to datasets of dengue cases in order to verify the effect of infection dispersal on the economic regions from the metropolitan region of Salvador. Our empirical results support a significant and persistent cross-correlation between most regions, reinforcing the idea that economic regions or climatic conditions are non-statistically significant in the spread of dengue in the State of Bahia. Our main contribution lies in the cross-correlation results revealing multiple aspects related to the propagation of dengue in dry climate regions.
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3
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Nonlinear relationship between money market rate and stock market liquidity in China: A multifractal analysis. PLoS One 2021; 16:e0249852. [PMID: 33861757 PMCID: PMC8051788 DOI: 10.1371/journal.pone.0249852] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 03/25/2021] [Indexed: 11/30/2022] Open
Abstract
This paper employs the multifractal detrended cross-correlation analysis (MF-DCCA) model to estimate the nonlinear relationship between the money market rate and stock market liquidity in China from a multifractal perspective, leading to a better understanding of the complexity in the relationship between the interest rate and stock market liquidity. The empirical results show that the cross-correlations between the money market rate and stock market liquidity present antipersistence in the long run and that they tend to be positively persistent in the short run. The negative cross-correlations between the interest rate and stock market liquidity are more significant than the positive cross-correlations. Furthermore, the cross-correlations between the money market rate and stock market liquidity display multifractal characteristics, explaining the variations in the relationship between the interest rate and stock market liquidity at different time scales. In addition, the lower degree of multifractality in the cross-correlations between the money market rate and stock market liquidity confirms that it is effective for the interest rate to control stock market liquidity. The Chinese stock market liquidity is more sensitive to fluctuations in the money market rate in the short term and is inelastic in response to the money market rate in the long term. In particular, the positive cross-correlations between the money market rate and stock market liquidity in the short run become strong in periods of crises and emergencies. All the evidence proves that the interest rate policy is an emergency response rather than an effective response to mounting concerns regarding the economic impact of unexpected exogenous emergencies and that the interest rate cut policy will not be as effective as expected.
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4
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Li B, Han G, Jiang S, Yu Z. Composite Multiscale Partial Cross-Sample Entropy Analysis for Quantifying Intrinsic Similarity of Two Time Series Affected by Common External Factors. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1003. [PMID: 33286772 PMCID: PMC7597075 DOI: 10.3390/e22091003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 09/04/2020] [Accepted: 09/06/2020] [Indexed: 12/02/2022]
Abstract
In this paper, we propose a new cross-sample entropy, namely the composite multiscale partial cross-sample entropy (CMPCSE), for quantifying the intrinsic similarity of two time series affected by common external factors. First, in order to test the validity of CMPCSE, we apply it to three sets of artificial data. Experimental results show that CMPCSE can accurately measure the intrinsic cross-sample entropy of two simultaneously recorded time series by removing the effects from the third time series. Then CMPCSE is employed to investigate the partial cross-sample entropy of Shanghai securities composite index (SSEC) and Shenzhen Stock Exchange Component Index (SZSE) by eliminating the effect of Hang Seng Index (HSI). Compared with the composite multiscale cross-sample entropy, the results obtained by CMPCSE show that SSEC and SZSE have stronger similarity. We believe that CMPCSE is an effective tool to study intrinsic similarity of two time series.
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Affiliation(s)
- Baogen Li
- Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China; (B.L.); (G.H.); (S.J.)
| | - Guosheng Han
- Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China; (B.L.); (G.H.); (S.J.)
| | - Shan Jiang
- Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China; (B.L.); (G.H.); (S.J.)
| | - Zuguo Yu
- Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China; (B.L.); (G.H.); (S.J.)
- School of Electrical Engineering and Computer Science, Queensland University of Technology, GPO Box 2434, Brisbane QLD 4000, Australia
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5
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Jiang ZQ, Xie WJ, Zhou WX, Sornette D. Multifractal analysis of financial markets: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:125901. [PMID: 31505468 DOI: 10.1088/1361-6633/ab42fb] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.
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Affiliation(s)
- Zhi-Qiang Jiang
- Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, People's Republic of China. Department of Finance, School of Business, East China University of Science and Technology, Shanghai 200237, People's Republic of China
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6
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Comparative Analysis between Hydrous Ethanol and Gasoline C Pricing in Brazilian Retail Market. SUSTAINABILITY 2019. [DOI: 10.3390/su11174719] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The global energy landscape is rapidly changing, including the transition to a low carbon economy and the use of liquid biofuel. The production of liquid biofuel has emerged as an alternative to the use of fossil fuels for purposes of energy conservation, carbon emission mitigation and agricultural development. In this article we study the co-movements between hydrous ethanol and gasoline C in the Brazilian retail market. A multi-scale cross correlation analysis was applied to the Average Retail Margin time series of hydrous ethanol for fifteen relevant retail markets in Brazil to analyze the competitiveness of hydrous ethanol towards gasoline C. The empirical results showed a remarkable different behavior between hydrous ethanol and gasoline C, for any time scale, regardless of geographical distance or regional differences.
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7
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Ranganathan S, Kivelä M, Kanniainen J. Dynamics of investor spanning trees around dot-com bubble. PLoS One 2018; 13:e0198807. [PMID: 29897973 PMCID: PMC5999117 DOI: 10.1371/journal.pone.0198807] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Accepted: 05/27/2018] [Indexed: 12/01/2022] Open
Abstract
We identify temporal investor networks for Nokia stock by constructing networks from correlations between investor-specific net-volumes and analyze changes in the networks around dot-com bubble. The analysis is conducted separately for households, financial, and non-financial institutions. Our results indicate that spanning tree measures for households reflected the boom and crisis: the maximum spanning tree measures had a clear upward tendency in the bull markets when the bubble was building up, and, even more importantly, the minimum spanning tree measures pre-reacted the burst of the bubble. At the same time, we find less clear reactions in the minimal and maximal spanning trees of non-financial and financial institutions around the bubble, which suggests that household investors can have a greater herding tendency around bubbles.
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Affiliation(s)
- Sindhuja Ranganathan
- Laboratory of Industrial and Information Management/Tampere University of Technology, Tampere, Finland
- * E-mail:
| | - Mikko Kivelä
- Department of Computer Science, School of Science/Aalto University, Espoo, Finland
| | - Juho Kanniainen
- Laboratory of Industrial and Information Management/Tampere University of Technology, Tampere, Finland
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8
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A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities. Sci Rep 2018; 8:7475. [PMID: 29748597 PMCID: PMC5945840 DOI: 10.1038/s41598-018-25822-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2017] [Accepted: 04/30/2018] [Indexed: 11/08/2022] Open
Abstract
On the basis of detrended fluctuation analysis (DFA), we propose a new bivariate linear regression model. This new model provides estimators of multi-scale regression coefficients to measure the dependence between variables and corresponding variables of interest with multi-scales. Numerical tests are performed to illustrate that the proposed DFA-bsaed regression estimators are capable of accurately depicting the dependence between the variables of interest and can be used to identify different dependence at different time scales. We apply this model to analyze the PM2.5 series of three adjacent cities (Beijing, Tianjin, and Baoding) in Northern China. The estimated regression coefficients confirmed the dependence of PM2.5 among the three cities and illustrated that each city has different influence on the others at different seasons and at different time scales. Two statistics based on the scale-dependent t-statistic and the partial detrended cross-correlation coefficient are used to demonstrate the significance of the dependence. Three new scale-dependent evaluation indices show that the new DFA-based bivariate regression model can provide rich information on studied variables.
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9
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Ide JS, Li CSR. Time scale properties of task and resting-state functional connectivity: Detrended partial cross-correlation analysis. Neuroimage 2018; 173:240-248. [PMID: 29454934 DOI: 10.1016/j.neuroimage.2018.02.029] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Revised: 01/09/2018] [Accepted: 02/14/2018] [Indexed: 12/19/2022] Open
Abstract
Functional connectivity analysis is an essential tool for understanding brain function. Previous studies showed that brain regions are functionally connected through low-frequency signals both within the default mode network (DMN) and task networks. However, no studies have directly compared the time scale (frequency) properties of network connectivity during task versus rest, or examined how they relate to task performance. Here, using fMRI data collected from sixty-eight subjects at rest and during a stop signal task, we addressed this issue with a novel functional connectivity measure based on detrended partial cross-correlation analysis (DPCCA). DPCCA has the advantage of quantifying correlations between two variables in different time scales while controlling for the influence of other variables. The results showed that the time scales of within-network connectivity of the DMN and task networks are modulated in opposite directions across rest and task, with the time scale increased during rest vs. task in the DMN and vice versa in task networks. In regions of interest analysis, the within-network connectivity time scale of the pre-supplementary motor area - a medial prefrontal cortical structure of the task network and critical to proactive inhibitory control - correlated inversely with Barratt impulsivity and stop signal reaction time. Together, these findings demonstrate that time scale properties of brain networks may vary across mental states and provide evidence in support of a role of low frequency fluctuations of BOLD signals in behavioral control.
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Affiliation(s)
- Jaime S Ide
- Department of Psychiatry, Yale University School of Medicine, New Haven, CT, 06519, USA.
| | - Chiang-Shan R Li
- Department of Psychiatry, Yale University School of Medicine, New Haven, CT, 06519, USA; Department of Neuroscience, Yale University School of Medicine, New Haven, CT, 06520, USA; Interdepartmental Neuroscience Program, Yale University, New Haven, CT, 06520, USA
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10
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Xu HC, Gu GF, Zhou WX. Direct determination approach for the multifractal detrending moving average analysis. Phys Rev E 2017; 96:052201. [PMID: 29347787 DOI: 10.1103/physreve.96.052201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Indexed: 06/07/2023]
Abstract
In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent τ(q) is related to the partition function and the multifractal spectrum f(α) can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional p-model, the two-dimensional p-model, and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum f(α) can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.
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Affiliation(s)
- Hai-Chuan Xu
- Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China
- Department of Finance, East China University of Science and Technology, Shanghai 200237, China
| | - Gao-Feng Gu
- Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China
- Department of Finance, East China University of Science and Technology, Shanghai 200237, China
| | - Wei-Xing Zhou
- Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China
- Department of Finance, East China University of Science and Technology, Shanghai 200237, China
- School of Science, East China University of Science and Technology, Shanghai 200237, China
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11
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Wang F, Wang L, Chen Y. Detecting PM2.5's Correlations between Neighboring Cities Using a Time-Lagged Cross-Correlation Coefficient. Sci Rep 2017; 7:10109. [PMID: 28860644 PMCID: PMC5579243 DOI: 10.1038/s41598-017-10419-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 08/08/2017] [Indexed: 11/11/2022] Open
Abstract
In order to investigate the time-dependent cross-correlations of fine particulate (PM2.5) series among neighboring cities in Northern China, in this paper, we propose a new cross-correlation coefficient, the time-lagged q-L dependent height crosscorrelation coefficient (denoted by p q (τ, L)), which incorporates the time-lag factor and the fluctuation amplitude information into the analogous height cross-correlation analysis coefficient. Numerical tests are performed to illustrate that the newly proposed coefficient ρ q (τ, L) can be used to detect cross-correlations between two series with time lags and to identify different range of fluctuations at which two series possess cross-correlations. Applying the new coefficient to analyze the time-dependent cross-correlations of PM2.5 series between Beijing and the three neighboring cities of Tianjin, Zhangjiakou, and Baoding, we find that time lags between the PM2.5 series with larger fluctuations are longer than those between PM2.5 series withsmaller fluctuations. Our analysis also shows that cross-correlations between the PM2.5 series of two neighboring cities are significant and the time lags between two PM2.5 series of neighboring cities are significantly non-zero. These findings providenew scientific support on the view that air pollution in neighboring cities can affect one another not simultaneously but with a time lag.
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Affiliation(s)
- Fang Wang
- College of Science/Agricultural Mathematical Modeling and Data Processing Center, Hunan Agricultural University, Changsha, P. R. China.
- Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada.
| | - Lin Wang
- Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada
| | - Yuming Chen
- Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada
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12
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Zhao S, Tong Y, Wang Z, Tan S. Identifying Key Drivers of Return Reversal with Dynamical Bayesian Factor Graph. PLoS One 2016; 11:e0167050. [PMID: 27893780 PMCID: PMC5125680 DOI: 10.1371/journal.pone.0167050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2016] [Accepted: 11/08/2016] [Indexed: 11/21/2022] Open
Abstract
In the stock market, return reversal occurs when investors sell overbought stocks and buy oversold stocks, reversing the stocks’ price trends. In this paper, we develop a new method to identify key drivers of return reversal by incorporating a comprehensive set of factors derived from different economic theories into one unified dynamical Bayesian factor graph. We then use the model to depict factor relationships and their dynamics, from which we make some interesting discoveries about the mechanism behind return reversals. Through extensive experiments on the US stock market, we conclude that among the various factors, the liquidity factors consistently emerge as key drivers of return reversal, which is in support of the theory of liquidity effect. Specifically, we find that stocks with high turnover rates or high Amihud illiquidity measures have a greater probability of experiencing return reversals. Apart from the consistent drivers, we find other drivers of return reversal that generally change from year to year, and they serve as important characteristics for evaluating the trends of stock returns. Besides, we also identify some seldom discussed yet enlightening inter-factor relationships, one of which shows that stocks in Finance and Insurance industry are more likely to have high Amihud illiquidity measures in comparison with those in other industries. These conclusions are robust for return reversals under different thresholds.
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Affiliation(s)
- Shuai Zhao
- Key Laboratory of Machine Perception (Ministry of Education), School of Electronics Engineering and Computer Science, Peking University, Beijing, China
- * E-mail: (SZ); (YT)
| | - Yunhai Tong
- Key Laboratory of Machine Perception (Ministry of Education), School of Electronics Engineering and Computer Science, Peking University, Beijing, China
- * E-mail: (SZ); (YT)
| | - Zitian Wang
- Key Laboratory of Machine Perception (Ministry of Education), School of Electronics Engineering and Computer Science, Peking University, Beijing, China
| | - Shaohua Tan
- Key Laboratory of Machine Perception (Ministry of Education), School of Electronics Engineering and Computer Science, Peking University, Beijing, China
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13
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Jamali T, Jafari GR, Vasheghani Farahani S. Patterns for the waiting time in the context of discrete-time stochastic processes. Phys Rev E 2016; 94:032110. [PMID: 27739745 DOI: 10.1103/physreve.94.032110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2015] [Indexed: 11/07/2022]
Abstract
The aim of this study is to extend the scope and applicability of the level-crossing method to discrete-time stochastic processes and generalize it to enable us to study multiple discrete-time stochastic processes. In previous versions of the level-crossing method, problems with it correspond to the fact that this method had been developed for analyzing a continuous-time process or at most a multiple continuous-time process in an individual manner. However, since all empirical processes are discrete in time, the already-established level-crossing method may not prove adequate for studying empirical processes. Beyond this, due to the fact that most empirical processes are coupled; their individual study could lead to vague results. To achieve the objectives of this study, we first find an analytical expression for the average frequency of crossing a level in a discrete-time process, giving the measure of the time experienced for two consecutive crossings named as the "waiting time." We then introduce the generalized level-crossing method by which the consideration of coupling between the components of a multiple process becomes possible. Finally, we provide an analytic solution when the components of a multiple stochastic process are independent Gaussian white noises. The comparison of the results obtained for coupled and uncoupled processes measures the strength and efficiency of the coupling, justifying our model and analysis. The advantage of the proposed method is its sensitivity to the slightest coupling and shortest correlation length.
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Affiliation(s)
- Tayeb Jamali
- Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran
| | - G R Jafari
- Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran and Center for Network Science, Central European University, H-1051, Budapest, Hungary
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14
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Carbone A, Kiyono K. Detrending moving average algorithm: Frequency response and scaling performances. Phys Rev E 2016; 93:063309. [PMID: 27415389 DOI: 10.1103/physreve.93.063309] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2016] [Indexed: 06/06/2023]
Abstract
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) over either time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent, and finite scale range behavior will be discussed.
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Affiliation(s)
- Anna Carbone
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Ken Kiyono
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan
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15
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Influence of Sub-Daily Variation on Multi-Fractal Detrended Fluctuation Analysis of Wind Speed Time Series. PLoS One 2016; 11:e0146284. [PMID: 26741491 PMCID: PMC4711791 DOI: 10.1371/journal.pone.0146284] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2015] [Accepted: 12/14/2015] [Indexed: 11/19/2022] Open
Abstract
Using multi-fractal detrended fluctuation analysis (MF-DFA), the scaling features of wind speed time series (WSTS) could be explored. In this paper, we discuss the influence of sub-daily variation, which is a natural feature of wind, in MF-DFA of WSTS. First, the choice of the lower bound of the segment length, a significant parameter of MF-DFA, was studied. The results of expanding the lower bound into sub-daily scope shows that an abrupt declination and discrepancy of scaling exponents is caused by the inability to keep the whole diel process of wind in one single segment. Additionally, the specific value, which is effected by the sub-daily feature of local meteo-climatic, might be different. Second, the intra-day temporal order of wind was shuffled to determine the impact of diel variation on scaling exponents of MF-DFA. The results illustrate that disregarding diel variation leads to errors in scaling. We propose that during the MF-DFA of WSTS, the segment length should be longer than 1 day and the diel variation of wind should be maintained to avoid abnormal phenomena and discrepancy in scaling exponents.
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16
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Kwapień J, Oświęcimka P, Drożdż S. Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052815. [PMID: 26651752 DOI: 10.1103/physreve.92.052815] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Indexed: 06/05/2023]
Abstract
The detrended cross-correlation coefficient ρ(DCCA) has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, nonstationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analog of the Pearson coefficient in the case of the fluctuation analysis. The coefficient ρ(DCCA) works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations. In order to introduce some related flexibility, here we propose an extension of ρ(DCCA) that exploits the multifractal versions of DFA and DCCA: multifractal detrended fluctuation analysis and multifractal detrended cross-correlation analysis, respectively. The resulting new coefficient ρ(q) not only is able to quantify the strength of correlations but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. We show how the coefficient ρ(q) works in practical situations by applying it to stochastic time series representing processes with long memory: autoregressive and multiplicative ones. Such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence, so we are convinced that this new measure can successfully be applied in time-series analysis. In particular, we present an example of such application to highly complex empirical data from financial markets. The present formulation can straightforwardly be extended to multivariate data in terms of the q-dependent counterpart of the correlation matrices and then to the network representation.
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Affiliation(s)
- Jarosław Kwapień
- Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
| | - Paweł Oświęcimka
- Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
| | - Stanisław Drożdż
- Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland
- Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, Kraków, Poland
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