Fractional Dickey-Fuller test with or without prehistorical influence

Ahmed Bensalma

MPRA Paper from University Library of Munich, Germany

Abstract: Recently the generalization of the standard Dickey-Fuller test to the fractional case has been proposed. The proposed test, called fractional Dickey-Fuller test can be applied to sample generated from a type I or a type II fractional process. Depending on whether the test is applied to sample generated from a type I or type II process, it is referred to as a test with or without prehistoric influence respectively. The main and the first objective of this paper is to study the impact induced by a pre-sample of the finite sample null distribution. In fact, the recently proposed test is built based on a composite null hypothesis rather than a sample one. The second objective is to highlight the theoretical justifications for the choice of the null composite hypothesis. All the theoretical results are illustrated with simulated and real data sets. Furthermore, to facilitate the reproducibility of our simulation data and figures we provide all the necessary supplementary material consisting of EViews programs.

Keywords: ARFIMA; fractional integration, Dickey-Fuller test; Fractional Dickey-Fuller test; type I and type II fractional Brownian motion. (search for similar items in EconPapers)
JEL-codes: C12 C15 C4 C5 (search for similar items in EconPapers)
Date: 2021-04-25
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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