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Multidimensional fractal scaling analysis using higher order moving average polynomials and its fast algorithm
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DOI：10.1016/j.sigpro.2023.108997.png)
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Abstract
En 中文
The detrending moving average (DMA) analysis demonstrates excellent performance for the character-ization of long-range correlations and fractal scaling and is performed in various research fields. The conventional DMA with a simple moving average can remove linear trends embedded in the observed time series. To improve the detrending ability of the DMA, higher-order DMA including a higher order polynomial detrending was also introduced using the Savitzky-Golay filter and its fast implementation algorithm was developed. However, the higher-order DMA applicable to higher dimensional data is yet to be well established. As the data dimension increases, an increase in the computational cost becomes a problem that needs to be resolved. Further, the implementation of the higher order DMA is a time-consuming procedure. To resolve this problem, we here proposed a fast algorithm for multidimensional DMA with higher order polynomial detrending. In the proposed algorithm, to reduce the computational complexity, parallel translation and recurrence techniques are introduced. Monte Carlo experiments for two-dimensional data show that the computational time of the proposed algorithm is approximately proportional to the cubic of the data length, whereas the computational time of the conventional im-plementation is approximately proportional to the quartic of the data length. Moreover, we evaluate the estimation accuracy of the Hurst exponent of the proposed method. Finally, we demonstrate the possible application of the proposed method by estimating the Hurst exponent of images.(c) 2023 The Author(s). Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Keywords:
Time-series analysis
High-dimensional fractal
Higher order DMA
Hurst exponent
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