Nonstationary Cointegration in the Fractionally Cointegrated VAR Model

27 Pages Posted: 29 May 2018

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Morten Ørregaard Nielsen

Queen's University - Department of Economics

Date Written: May 17, 2018

Abstract

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their consistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that when the parameter space is larger, stronger moment conditions are required. We show that these moment conditions can be relaxed, and for consistency we require just eight moments regardless of the parameter space. Second, Johansen and Nielsen (2012a) assumed that the cointegrating vectors are stationary, and we extend the analysis to include the possibility that the cointegrating vectors are nonstationary. Both contributions require new analysis and results for the asymptotic properties of the likelihood function of the fractional CVAR model, which we provide. Finally, our analysis follows recent research and applies a parameter space large enough that the usual (non-fractional) CVAR model constitutes an interior point and hence can be tested against the fractional model using a X2-test.

Keywords: Cointegration, fractional integration, likelihood inference, vector autoregressive model

JEL Classification: C32

Suggested Citation

Johansen, Soren and Nielsen, Morten Orregaard, Nonstationary Cointegration in the Fractionally Cointegrated VAR Model (May 17, 2018). Available at SSRN: https://ssrn.com/abstract=3180006 or http://dx.doi.org/10.2139/ssrn.3180006

Soren Johansen

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Morten Orregaard Nielsen (Contact Author)

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario
Canada

HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/

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