Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models / Søren Johansen
19 Oct 2012-
TL;DR: In this paper, the authors present the likelihood methods for the analysis of cointegration in VAR models with Gaussian errors, seasonal dummies, and constant terms, and show that the asymptotic distribution of the maximum likelihood estimator is mixed Gausssian.
Abstract: Presents the likelihood methods for the analysis of cointegration in VAR models with Gaussian errors, seasonal dummies, and constant terms. Discusses likelihood ratio tests of cointegration rank and find the asymptotic distribution of the test statistics. Shows that the asymptotic distribution of the maximum likelihood estimator is mixed Gausssian.
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TL;DR: In this paper, the authors developed a new approach to the problem of testing the existence of a level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend- or first-difference stationary.
Abstract: This paper develops a new approach to the problem of testing the existence of a level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend- or first-difference stationary. The proposed tests are based on standard F- and t-statistics used to test the significance of the lagged levels of the variables in a univariate equilibrium correction mechanism. The asymptotic distributions of these statistics are non-standard under the null hypothesis that there exists no level relationship, irrespective of whether the regressors are I(0) or I(1). Two sets of asymptotic critical values are provided: one when all regressors are purely I(1) and the other if they are all purely I(0). These two sets of critical values provide a band covering all possible classifications of the regressors into purely I(0), purely I(1) or mutually cointegrated. Accordingly, various bounds testing procedures are proposed. It is shown that the proposed tests are consistent, and their asymptotic distribution under the null and suitably defined local alternatives are derived. The empirical relevance of the bounds procedures is demonstrated by a re-examination of the earnings equation included in the UK Treasury macroeconometric model. Copyright © 2001 John Wiley & Sons, Ltd.
13,898 citations
TL;DR: In this article, the authors consider pooling cross-section time series data for testing the unit root hypothesis, and they show that the power of the panel-based unit root test is dramatically higher, compared to performing a separate unit-root test for each individual time series.
10,792 citations
01 Jan 2005
10,230 citations
TL;DR: In this paper, the authors show how to estimate VAR's formulated in levels and test general restrictions on the parameter matrices even if the processes may be integrated or cointegrated of an arbitrary order.
4,959 citations
TL;DR: This article examined the use of autoregressive distributed lag (ARDL) models for the analysis of long-run relations when the underlying variables are I(1) and I(0) regressors.
Abstract: This paper examines the use of autoregressive distributed lag (ARDL) models for the analysis of long-run relations when the underlying variables are I(1). It shows that after appropriate augmentation of the order of the ARDL model, the OLS estimators of the short-run parameters are p T -consistent with the asymptotically singular covariance matrix, and the ARDL-based estimators of the long-run coe¢cients are super-consistent, and valid inferences on the long-run parameters can be made using standard normal asymptotic theory. The paper also examines the relationship between the ARDL procedure and the fully modi
ed OLS approach of Phillips and Hansen to estimation of cointegrating relations, and compares the small sample performance of these two approaches via Monte Carlo experiments. These results provide strong evidence in favour of a rehabilitation of the traditional ARDL approach to time series econometric modelling. The ARDL approach has the additional advantage of yielding consistent estimates of the long-run coe¢cients that are asymptotically normal irrespective of whether the underlying regressors are I(1) or I(0). JEL Classi
cations: C12, C13, C15, C22. Key Words: Autoregressive distributed lag model, Cointegration, I(1) and I(0) regressors, Model selection, Monte Carlo simulation. ¤This is a revised version of a paper presented at the Symposium at the Centennial of Ragnar Frisch, The Norwegian Academy of Science and Letters, Oslo, March 3-5, 1995. We are grateful to Peter Boswijk, Clive Granger, Alberto Holly, Kyung So Im, Brendan McCabe, Steve Satchell, Richard Smith, Ron Smith and an anonymous referee for helpful comments. Partial
nancial support from the ESRC (Grant No. R000233608) and the Isaac Newton Trust of Trinity College, Cambridge is gratefully acknowledged.
4,711 citations
References
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TL;DR: In this paper, the authors consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors, and derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions.
16,189 citations
TL;DR: In this paper, the authors present an examination of such models for variables integrated at most of order one, when tests for cointegration involve statistics with non-standard asymptotic distributions.
Abstract: 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.
2,831 citations
TL;DR: In this article, the authors consider estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots and show that parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distributions, converging at the rate T'/2.
Abstract: This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general formulation, the variable might be integrated or cointegrated of arbitrary orders, and might have drifts as well. We show that parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distributions, converging at the rate T'/2. In general, the other coefficients (including the coefficients on polynomials in time) will have nonnormal asymptotic distributions. The results provide a formal characterization of which t or F tests-such as Granger causality tests-will be asymptotically valid, and which will have nonstandard limiting distributions.
2,529 citations
TL;DR: In this paper, it was suggested that some aspects of this practice should be brought out into the open, and the type of equations to be considered are generating equations, so that a simulation of the explanatory side should produce the major properties of the variable being explained.
2,482 citations