Oxford Bulletin of Economics and Statistics
Опубликовано на портале: 25-06-2004
Michael Osterwald-Lenum
Oxford Bulletin of Economics and Statistics.
1992.
Vol. 54.
No. 3.
P. 461-472.
The recent literature on maximum likelihood cointegration theory studies Gaussian
vector autoregression (VAR) models allowing for some deterministic components in
the form of polynomials in time. An examination is presented of such models for variables
integrated at most of order one, when tests for cointegration involve statistics
with non-standard asymptotic distributions. The asymptotic distributions of these
test statistics are known to be functions of the distribution of certain matrices
of stochastic variables involving integrals of Brownian motions. In fact, conditional
on which restrictions on the coefficients of the polynomial in time are valid, different
asymptotic distributions are obtained. The cases examined exhaust the hypotheses
relevant to the cointegration rank analysis of I(1) variables in models involving
up to linear trends and possibly seasonal dummies. The examination solves the numerical
problem in making most of the interesting quantiles of these asymptotic distributions
available to the applied econometrician.

Опубликовано на портале: 13-04-2004
Soren Johansen, Katarina Juselius
Oxford Bulletin of Economics and Statistics.
1970.
Vol. 52.
No. 2.
P. 169-210.
The estimation and testing of long-run relations in economic modeling are addressed.
Starting with a vector autoregressive (VAR) model, the hypothesis of cointegration
is formulated as the hypothesis of reduced rank of the long-run impact matrix. This
is given in a simple parametric form that allows the application of the method of
maximum likelihood and likelihood ratio tests. In this way, one can derive estimates
and test statistics for the hypothesis of a given number of cointegration vectors,
as well as estimates and tests for linear hypotheses about the cointegration vectors
and their weights. The asymptotic inferences concerning the number of cointegrating
vectors involve nonstandard distributions. Inference concerning linear restrictions
on the cointegration vectors and their weights can be performed using the usual chi
squared methods. In the case of linear restrictions on beta, a Wald test procedure
is suggested. The proposed methods are illustrated by money demand data from the
Danish and Finnish economies.


Опубликовано на портале: 01-07-2004
Russell Davidson, James G. MacKinnon
Oxford Bulletin of Economics and Statistics.
1988.
Vol. 50.
No. 2.
P. 203-218.
Recently, applied econometricians have become familiar with the idea that artificial
regressions may offer a convenient way to compute many test statistics. One well-known
family of artificial regressions is the outer product of the gradient (OPG) family.
However, available evidence indicates that using tests based on the OPG regression
can be very misleading. A procedure that often can replace it is the double-length
artificial regression (DLR), which can be considered as a generalization of both
the Gauss-Newton regression and the squared-residuals regression. A discussion includes
applications to the nonlinear regression model as well as tests for functional form.
DLRs potentially are very useful. While they generally have good finite-sample properties,
they are applicable to far more situations than Gauss-Newton and squared-residuals
artificial regressions. They also can be used as part of maximization algorithms
and should be considered to routinely test regression equations for functional form.

