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.

Maximum Likelihood Estimation and Inference on Cointegration with Applications to the Demand for Money [статья]

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.
ресурс содержит гиперссылку на сайт, на котором можно найти дополнительную информацию

ресурс содержит гиперссылку на сайт, на котором можно найти дополнительную информацию

Practitioners' Corner: Double Length Artificial Regressions [статья]

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.
ресурс содержит гиперссылку на сайт, на котором можно найти дополнительную информацию