dorsal/arxiv
View SchemaOn correlations and fractal characteristics of time series
| Authors | Nikolay K. Vitanov, kenschi Sakai, Elka D. Yankulova |
|---|---|
| Categories | |
| ArXiv ID | physics/0508083 |
| URL | https://arxiv.org/abs/physics/0508083 |
| Journal | Journal of Theoritical and Applied Mechanics, vol. 35. p.p. 73-90 (2005) |
Abstract
Correlation analysis is convenient and frequently used tool for investigation of time series from complex systems. Recently new methods such as the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maximum method (WTMM) have been developed. By means of these methods (i) we can investigate long-range correlations in time series and (ii) we can calculate fractal spectra of these time series. But opposite to the classical tool for correlation analysis - the autocorrelation function, the newly developed tools are not applicable to all kinds of time series. The unappropriate application of MFDFA or WTMM leads to wrong results and conclusions. In this article we discuss the opportunities and risks connected to the application of the MFDFA method to time series from a random number generator and to experimentally measured time series (i) for accelerations of an agricultural tractor and (ii) for the heartbeat activity of {\sl Drosophila melanogaster}. Our main goal is to emphasize on what can be done and what can not be done by the MFDFA as tool for investigation of time series.
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"abstract": "Correlation analysis is convenient and frequently used tool for investigation\nof time series from complex systems. Recently new methods such as the\nmultifractal detrended fluctuation analysis (MFDFA) and the wavelet transform\nmodulus maximum method (WTMM) have been developed. By means of these methods\n(i) we can investigate long-range correlations in time series and (ii) we can\ncalculate fractal spectra of these time series. But opposite to the classical\ntool for correlation analysis - the autocorrelation function, the newly\ndeveloped tools are not applicable to all kinds of time series. The\nunappropriate application of MFDFA or WTMM leads to wrong results and\nconclusions. In this article we discuss the opportunities and risks connected\nto the application of the MFDFA method to time series from a random number\ngenerator and to experimentally measured time series (i) for accelerations of\nan agricultural tractor and (ii) for the heartbeat activity of {\\sl Drosophila\nmelanogaster}. Our main goal is to emphasize on what can be done and what can\nnot be done by the MFDFA as tool for investigation of time series.",
"arxiv_id": "physics/0508083",
"authors": [
"Nikolay K. Vitanov",
"kenschi Sakai",
"Elka D. Yankulova"
],
"categories": [
"physics.data-an",
"physics.bio-ph"
],
"journal_ref": "Journal of Theoritical and Applied Mechanics, vol. 35. p.p. 73-90\n (2005)",
"title": "On correlations and fractal characteristics of time series",
"url": "https://arxiv.org/abs/physics/0508083"
},
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