On the determination of integration indices in I(2) systems

This paper proposes estimators of the numbers of common components integrated of a given order in a VAR system, possibly in the presence of a linear trend. The estimators are based on sequences of tests in a two-stage analysis proposed in Johansen (1995), which involves only regression and reduced rank regression. The asymptotic distributions of the test statistics belong to the Limiting Gaussian Functional family and are tabulated by simulation. The proposed estimators select the correct integration indices with limiting probability equal to the complement to 1 of the size of each test in the sequence. The statistical analysis allows also to test for the presence of a linear trend; the combined procedure presents similar asymptotic properties. The finite-sample behavior of the above statistics is studied through a small Monte Carlo experiment. An application to a UK money demand system illustrates the proposed procedures.