Title: A consistent test for unit root against fractional alternative

Authors: Ahmed Bensalma

Addresses: Department of Statistic, Ecole Nationale Supérieure de la Statistique et de l'Economie Appliquée (ENSSEA), 11, Chemin Doudou Mokhtar, Ben-Aknoun, Algiers, Algeria

Abstract: This paper deals with a fractionally integrated, FI(d), processes {y_t, t = 1,... , n}, where the fractional integrated parameter d is any real number greater than 1/2. We show, for these processes, that the suitable hypotheses test for unit root are H₀: d ≥ 1 against H₁: d < 1. These new hypotheses test can be considered as a test for unit root against fractional alternative. The asymptotic distributions under the null and alternative generalise those obtained by Sowell (1990). Monte-Carlo simulations show that the proposed test is robust for any missepecification of the order of integration parameter d and that it fares very well in terms of power and size. The paper ends with empirical applications by revisiting Nelson-Plosser Data.

Keywords: fractional unit root; Dickey-Fuller test; fractional integration; Nelson-Plosser data; Monte-Carlo simulation.

DOI: 10.1504/IJOR.2016.078467

International Journal of Operational Research, 2016 Vol.27 No.1/2, pp.252 - 274

Received: 12 Nov 2013
Accepted: 03 May 2014
Published online: 22 Aug 2016 *

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