same set of tables of critical values for all the cointegration cases considered in Stock and
Watson (1988) and Johansen (1988, 1991, 1994).
The plan of the paper is as follows: First, in section 2, we formulate our maintained
hypotheses. In section 3 we propose a class of pairs of random matrices for which the
generalized eigenvalues have similar properties as in the Johansen approach, based on
weighted means of the level variables zt and the first differences ∆zt. On the basis of these
eigenvalues, we propose in section 4 similar tests for the number of cointegrating vectors as
Johansen’s (1988, 1991) lambda-max test. In section 5 we discuss the choice of the weight
functions. In section 6 we propose tests for linear restrictions on cointegrating vectors, and a
procedure for consistently estimating a basis of the space of cointegrating vectors. Up to this
point we have maintained the assumption that the data-generating process is an integrated
vector time series process with drift, where the vector of drift parameters is orthogonal to the
cointegrating vectors. In section 7 we show how to make our approach invariant to
unconstrained drift, including seasonal drift. Finally, in section 8 we compare our approach
with Johansen’s ML approach, empirically using the logs of wages and GNP from the
extended Nelson-Plosser (1982) data set, as well as by a limited Monte Carlo simulation.
Proofs of all the lemmas are given in a separate appendix to this paper. Also,
additional Monte Carlo results regarding the limiting null distributions of the tests, unit root
test results for the extended Nelson-Plosser data, and further details of the cointegration test
results for ln(wages) and ln(GNP), can be found in this separate appendix, which is available
from the author on request. The empirical applications have been conducted using a computer
program package developed by the author.2
2 This package, called SIMPLREG, conducts our nonparametric cointegration analysis
together with Johansen’s tests, various unit root tests, VAR innovation response analysis, OLS,
IV, Probit and Logit, and much more. It runs "stand-alone" under DOS. This package is available
from the author on request, as long as it is not (yet) commercially available. Please include a
formatted 3.5" (1.44 MB) diskette with your request.