Archontakis Testing the Order of Integration in a VAR Model for I ( 2 ) Variables

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, given by an autoregressive 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.