Variance fluctuations in nonstationary time series: a comparative study of music genres

Jennings, Heather D; Ivanov, Plamen Ch.; Martins, Allan de Medeiros; Silva, P.C da; Viswanathan, G. M.

doi:10.1016/j.physa.2003.12.049

Cited by 58 publications

(44 citation statements)

References 23 publications

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“…One of the most famous and well-known approach used in many studies is Multifractal Detrended Fluctuations Analysis (MF-DFA) [51,52]. This method has been applied to various areas, such as economical time series [53-55,?,56], river flow [13] and sunspot fluctuations [57,58], cosmic microwave background radiations [59], music [60,61], plasma fluctuations [62].…”

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

132

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We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, (12 − 24) ≤ s ≤ 130 months, is λ = 1.17 ± 0.04 which is almost similar for all underlying rivers at 1σconfidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ ∈ (0.76, 0.85) and γ× ∈ (0.30, 0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), λ ≈ (hsun + hriver)/2 is confirmed.

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Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

132

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“…Dagdug et al [31] investigated a specific piece of Mozart employing detrended fluctuation analysis (DFA) [32]. Applying DFA in a volatility-like series, Jennings et al [33] found quantitative differences in the Hurst exponent depending on the music genre.…”

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confidence: 99%

Universal patterns in sound amplitudes of songs and music genres

et al. 2011

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We report a statistical analysis over more than eight thousand songs. Specifically, we investigate the probability distribution of the normalized sound amplitudes. Our findings seems to suggest a universal form of distribution which presents a good agreement with a one-parameter stretched Gaussian. We also argue that this parameter can give information on music complexity, and consequently it goes towards classifying songs as well as music genres. Additionally, we present statistical evidences that correlation aspects of the songs are directly related with the non-Gaussian nature of their sound amplitude distributions. In recent years, studies of complex systems have become widespread among the scientific community, specially in the statistical physics one [1][2][3][4][5]. Many of these investigations deal with data records ordered in time or space (i.e., time series), trying to extract some features, patterns or laws that may be present in the systems studied. This approach has been successfully applied to a variety of fields, from physics and astronomy [6] Music is a well known worldwide social phenomenon linked to the human cognitive habits, modes of consciousness as well as historical developments [14]. In the direction of music's social role, some authors investigated collective listening habits. For instance, Lambiotte and Ausloos [15] analyzed data from people music library finding audience groups with the size distribution following a power law. They also investigated correlations among these music groups, reporting non-trivial relations [16]. In another work, Silva et al.[17] studied the network structure of the song writers and the singers of Brazilian popular music (mpb). There is also an interest in the behavior of music sales [18] as well as in the success of musicians [19][20][21].Despite these cultural aspects, songs form a highly organized system presenting very complex structures and long-range correlations. All these features have attracted the attention of statistical physicists. In a seminal paper, Voss and Clarke [22] analyzed the power spectrum of radio stations and observed a 1/f noise like pattern. They also showed that the correlation can extend to longer or shorter time scales, depending on the music genre. Hsü and Hsü[23] investigated the changes of acoustic frequency in Bach's and Mozart's compositions, finding self-similarity and fractals structures. In contrast, they report no resemblance to fractal geometry [24] for modern music. Fractal structures have also been reported in the study of sequences of music notes [25], where Su and Wu [26] suggest that the multifractal spectrum can be used to distinguish different styles of music. In this brief literature review, we see that special attention was paid to the fractal structures of music, correlations and power spectrum analysis. However, much less attention has been paid to the understanding of the amplitude distribution. This last point has been noted by Diodati and Piazza[34]. In their work, they investigated the distribution of t...

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“…Detrended fluctuation analysis is a standard method that was developed in the context of time-series analysis to study 1/f noise and long-range correlations [37] and has proven to be very reliable particularly in dealing with nonstationary time series and trends in the data [6,37,38,44,45]. It has also been used outside the time domain, e.g., to study the organization of DNA nucleotides [39].…”

Section: B Detrended Fluctuation Analysismentioning

confidence: 99%

Fractal dynamics in chaotic quantum transport

et al. 2013

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Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

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Variance fluctuations in nonstationary time series: a comparative study of music genres

Cited by 58 publications

References 23 publications

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Universal patterns in sound amplitudes of songs and music genres

Fractal dynamics in chaotic quantum transport

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