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TESTING FOR GENERAL FRACTIONAL INTEGRATION IN THE TIME DOMAIN

Published online by Cambridge University Press:  01 December 2009

Uwe Hassler ,
Paulo M.M. Rodrigues  and
Antonio Rubia
Uwe Hassler
Affiliation:
Goethe University Frankfurt
Paulo M.M. Rodrigues*
Affiliation:
Banco de Portugal, Universidade Nova de Lisboa, and CASEE
Antonio Rubia
Affiliation:
University of Alicante
*
*Address correspondence to Paulo M.M. Rodrigues, Banco de Portugal, Economic Research Department, Av. Almirante Reis, 71-6th floor, 1150-012 Lisbon, Portugal; e-mail: [email protected].
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Abstract

We propose a family of least-squares–based testing procedures that look to detect general forms of fractional integration at the long-run and/or the cyclical component of a time series, and that are asymptotically equivalent to Lagrange multiplier tests. Our setting extends Robinson’s (1994) results to allow for short memory in a regression framework and generalizes the procedures in Agiakloglou and Newbold (1994), Tanaka (1999), and Breitung and Hassler (2002) by allowing for single or multiple fractional unit roots at any frequency in [0, π]. Our testing procedure can be easily implemented in practical settings and is flexible enough to account for a broad family of long- and short-memory specifications, including ARMA and/or GARCH-type dynamics, among others. Furthermore, these tests have power against different types of alternative hypotheses and enable inference to be conducted under critical values drawn from a standard chi-square distribution, irrespective of the long-memory parameters.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009 , pp. 1793 - 1828
Copyright
Copyright © Cambridge University Press 2009

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