Multidimensional Fractal Scaling Analysis Using Higher Order Moving Average Polynomials and Its Fast Algorithm

27 Pages Posted: 11 Dec 2022

See all articles by Hanqiu Ju

Hanqiu Ju

Kyoto University

Naoki Honda

Hiroshima University

Shige H. Yoshimura

Kyoto University

Miki Kaneko

The University of Osaka

Taiki Shigematsu

The University of Osaka

Ken Kiyono

The University of Osaka

Abstract

The detrending moving average (DMA) analysis demonstrates excellent performance for the characterization 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 SavitzkyGolay 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

Keywords: Time-series analysis, fractal, Hurst exponent

Suggested Citation

Ju, Hanqiu and Honda, Naoki and Yoshimura, Shige H. and Kaneko, Miki and Shigematsu, Taiki and Kiyono, Ken, Multidimensional Fractal Scaling Analysis Using Higher Order Moving Average Polynomials and Its Fast Algorithm. Available at SSRN: https://ssrn.com/abstract=4290825 or http://dx.doi.org/10.2139/ssrn.4290825

Hanqiu Ju

Kyoto University ( email )

Yoshida-Honmachi
Sakyo-ku
Kyoto, 606-8501
Japan

Naoki Honda

Hiroshima University ( email )

Higashihiroshima, 739-0046
Japan

Shige H. Yoshimura

Kyoto University ( email )

Yoshida-Honmachi
Sakyo-ku
Kyoto, 606-8501
Japan

Miki Kaneko

The University of Osaka ( email )

1-1 Yamadaoka
Suita
Osaka, 565-0871
Japan

Taiki Shigematsu

The University of Osaka ( email )

Ken Kiyono (Contact Author)

The University of Osaka ( email )

1-1 Yamadaoka
Suita
Osaka, 565-0871
Japan

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