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

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