MAXIMUM LIKELIHOOD ESTIMATION AND INFERENCE ON COINTEGRATION — WITH APPLICATIONS TO THE DEMAND FOR MONEY¶
Why this mattered¶
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Abstract¶
This paper gives a systematic application of maximum likelihood inference concerning cointegration vectors in non-stationary vector valued autoregressive time series models with Gaussian errors, where the model includes a constant term and seasonal dummies. The hypothesis of cointegration is given a simple parametric form in terms of cointegration vectors and their weights. The relation between the constant term and a linear trend in the non-stationary part of the process is discussed and related to the weights. Tests for the presence of cointegration vectors, both with and without a linear trend in the non-stationary part of the process are derived. Then estimates and tests under linear restrictions on the cointegration vectors and their weights are given. The methods are illustrated by data from the Danish and the Finnish economy on the demand for money. Copyright 1990 by Blackwell Publishing Ltd
Related¶
- cite → Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models — Johansen and Juselius use Johansen's Gaussian VAR likelihood framework for estimating and testing cointegration vectors in their money-demand application.
- cite → Co-Integration and Error Correction: Representation, Estimation, and Testing — Johansen and Juselius apply Engle and Granger's cointegration and error-correction representation to model long-run money-demand relationships.
- cite → Statistical analysis of cointegration vectors — Johansen and Juselius build directly on Johansen's statistical analysis of cointegration vectors to perform maximum-likelihood inference in vector autoregressions.
- cite ← Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models — Johansen's 1991 paper extends maximum-likelihood inference for cointegration developed in Johansen and Juselius's 1990 money-demand application.