ON THE DETERMINATION OF INTEGRATION INDEXES IN I(2) SYSTEMS

This paper proposes estimators of the numbers of common components int egrated 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 tw o-stage analysis proposed in Johansen (1995), which involves only regr ession and reduced rank regression. The asymptotic distributions of th e test statistics belong to the Limiting Gaussian Functional family an d are tabulated by simulation, The proposed estimators select the corr ect integration indices with limiting probability equal to the complem ent to 1 of the size of each test in the sequence. The statistical ana lysis allows also to test for the presence of a linear trend; the comb ined procedure presents similar asymptotic properties. The finite-samp le behavior of the above statistics is studied through a small Monte C arlo experiment. An application to a UK money demand system illustrate s the proposed procedures.