Testing the Order of Integration in a VAR

We propose a test for the order of integration of the univariate components of a vector process integrated of order two, i.e. an I(2) process, generated by a vector autoregressive (VAR) model. The null hypothesis of the test is that the particular univariate time series is an I(1) process. The hypotheses are formulated as linear restrictions on the directions orthogonal to the I(1) cointegration space. The statistic considered is the Wald test, which asymptotically follows a chi-squared distribution, such that standard inference can be applied. The theoretical results are illustrated by a Monte Carlo experiment. ∗This work is part of my Ph.D. thesis under the patient guidance of Søren Johansen. Thanks are also due to N. Haldrup, D. O’Brien and A. Soro Bonmati and seminar participants of the European University Institute, the Universidad de Alicante, the ASSET 2000 Euroconference at Lisbon and The Spring Meeting of Young Economists 2001 at Copenhagen who commented on earlier drafts of the paper. Any remaining errors are mine. †Address for correspondence: Department of Economics, European University Institute, Via dei Roccettini, 9 I-50016 San Domenico di Fiesole (FI), Italy. E-mail: [email protected]