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On the behavior of the DFA and DCCA in trend-stationary processes

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  • Prass, Taiane Schaedler
  • Pumi, Guilherme

Abstract

In this work, we develop the asymptotic theory of the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) for trend-stationary stochastic processes without any assumption on the specific form of the underlying distribution. All results are presented and derived under the general framework of potentially overlapping boxes for the polynomial fit. We prove the stationarity of the DFA and DCCA, viewed as stochastic processes, obtain closed forms for moments up to second order, including the covariance structure for DFA and DCCA and a miscellany of law of large number related results. Our results generalize and improve several results presented in the literature. To verify the behavior of our theoretical results in small samples, we present a Monte Carlo simulation study and an empirical application to econometric time series.

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  • Prass, Taiane Schaedler & Pumi, Guilherme, 2021. "On the behavior of the DFA and DCCA in trend-stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:jmvana:v:182:y:2021:i:c:s0047259x20302840
    DOI: 10.1016/j.jmva.2020.104703
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    References listed on IDEAS

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    4. Zebende, G.F., 2011. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 614-618.
    5. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
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    Cited by:

    1. Anokye M. Adam & Kwabena Kyei & Simiso Moyo & Ryan Gill & Emmanuel N. Gyamfi, 2022. "Multifrequency network for SADC exchange rate markets using EEMD-based DCCA," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 46(1), pages 145-166, January.

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