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Fractal analyses for ‘short’ time series: A re-assessment of classical methods. (English) Zbl 1105.62085
Summary: The aim of this study was to evaluate the performances of some classical methods of fractal analysis with short time series. We simulated exact fractal series to test how well methods estimate the Hurst exponent. We successively tested power spectral density analysis, detrended fluctuation analysis, rescaled range analysis, dispersional analysis, maximum likelihood estimation, and two versions of scaled windowed variance methods. All methods presented different advantages and disadvantages, in terms of biases and variability. We propose in conclusion a systematic step-by-step procedure of analysis, based on the performances of each method and their appropriateness regarding the scientific aims that could motivate fractal analysis.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
28A80 Fractals
37M10 Time series analysis of dynamical systems
65C60 Computational problems in statistics (MSC2010)
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