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

10/23/2019
by   Taiane Schaedler Prass, et al.
0

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 derived without the assumption of non-overlapping boxes for the polynomial fits. We prove the stationarity of the DFA and DCCA, viewed as a 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.

READ FULL TEXT

Authors

page 14

page 20

08/17/2021

Modelling Time-Varying First and Second-Order Structure of Time Series via Wavelets and Differencing

Most time series observed in practice exhibit time-varying trend (first-...
12/18/2019

Method of moments estimators for the extremal index of a stationary time series

The extremal index θ, a number in the interval [0,1], is known to be a m...
06/07/2021

Modeling Nonstationary Time Series using Locally Stationary Basis Processes

Methods of estimation and forecasting for stationary models are well kno...
01/02/2020

Prediction in locally stationary time series

We develop an estimator for the high-dimensional covariance matrix of a ...
06/23/2021

Gaussian and Hermite Ornstein-Uhlenbeck processes

In the present paper we study the asymptotic behavior of the auto-covari...
05/13/2019

A Spatial Concordance Correlation Coefficient with an Application to Image Analysis

In this work we define a spatial concordance coefficient for second-orde...
12/28/2021

Block Bootstrapping the Empirical Distance Covariance

We prove the validity of a non-overlapping block bootstrap for the empir...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.