Generalized theory for detrending moving-average cross-correlation analysis: A practical guide. (September 2019)

• Record Type: Journal Article
• Authors: Nakata, Akio; Kaneko, Miki; Shigematsu, Taiki; Nakae, Satoshi; Evans, Naoko; Taki, Chinami; Kimura, Tetsuya; Kiyono, Ken
• Is Part Of: Chaos, solitons & fractals. Volume 3(2019)
• Publication Date: 2019-09
• Subjects: Long memory process -- Complex system interaction -- Cross-spectral analysis; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Solitons; Fractals; Chaotic behavior in systems; Periodicals; Electronic journals; 003.7
• DOI: 10.1016/j.csfx.2020.100022
• Languages: English
• ISSNs: 2590-0544

Abstract

Abstract : A generalized theory for detrending moving-average cross-correlation analysis (DMCA) is developed. Based on the mathematical validity, we provide a practical guide for long-range cross-correlation analysis. To overcome disadvantages of the previous approaches assessing the cross-correlation, a new method is introduced. Abstract: To evaluate the long-range cross-correlation in non-stationary bi-variate time-series, detrending-operation-based analysis methods such as the detrending moving-average cross-correlation analysis (DMCA), are widely used. However, its mathematical foundation has not been well established. In this paper, we propose a generalized theory to form the foundation of DMCA-type methods and introduce the higher-order DMCA in which Savitzky-Golay filters are employed as the detrending operator. Using this theory, we can understand the mathematical basis of DMCA-type methods. Our theory establishes a rigorous relationship between the DMCA-type analysis, the cross-correlation function analysis, and the cross-power spectral analysis. Based on the mathematical validity, we provide a practical guide for the use of higher-order DMCA. Additionally, we present illustrative results of a numerical and real-world analysis. To achieve reliable and accurate detection of the long-range cross-correlation, we emphasize the importance of time-lag estimation and time scale correction in DMCA, which has not been pointed out in the previous studies.