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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:182

Article

Prass, Taiane Schaedler¹  Pumi, Guilherme¹ 

[1] Univ Fed Rio Grande Do Sul, Programa Posgrad Estat, Inst Matemat & Estat, Av Bento Goncalves 9500, Porto Alegre, RS, Brazil

关键词: Cross-correlation;    DCCA;    Trend-stationary time series;   

DOI  :  10.1016/j.jmva.2020.104703

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free