The Power Function Of The Likelihood Ratio Test For Cointegration

The Power Function of the Likelihood Ratio Test for Cointegration

Econometric Decision Models

This volume contains a refereed selection of revised papers which were originally presented at the Second International Conference on Econometric Decision Models, University of Hagen (FernUni versitat). The conference was held in Haus Nordhelle, a meeting place in the mountainous area " Sauerland" , some 50 kilometers south of Hagen, on August 29 - September 1, 1989. Some details about this conference are given in the first paper, they need not be repeated here. The 40 papers included in this volume are organized in 10 "parts", shown in the table of contents. Included are such "fashionable" topics like "optimal control", "cointegration" and "rational expec tations models". In each part, the papers have been arranged alphabetically by author, unless there were good reasons for a different arrangement. To facilitate the decision making of the readers, all papers (except a few short ones) contain an abstract, a list of keywords and a table of contents. At the end of the proceedings volume, there is a list of authors. More than ten years ago, I began to organize meetings of econometricians, mainly called "seminar" or " colloquium". One major purpose of these meetings has always been to improve international cooperation of econometric model builders (and model users) from "the East" and "the West". Unprecedented changes to the better have taken place recently ("perestroika"). For a large fraction of participants from the Soviet Union, the 1989 conference was the first conference in a Western country.

Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

This book gives a detailed mathematical and statistical analysis of the cointegrated vector autoregresive model. This model had gained popularity because it can at the same time capture the short-run dynamic properties as well as the long-run equilibrium behaviour of many non-stationary time series. It also allows relevant economic questions to be formulated in a consistent statistical framework. Part I of the book is planned so that it can be used by those who want to apply the methods without going into too much detail about the probability theory. The main emphasis is on the derivation of estimators and test statistics through a consistent use of the Guassian likelihood function. It is shown that many different models can be formulated within the framework of the autoregressive model and the interpretation of these models is discussed in detail. In particular, models involving restrictions on the cointegration vectors and the adjustment coefficients are discussed, as well as the role of the constant and linear drift. In Part II, the asymptotic theory is given the slightly more general framework of stationary linear processes with i.i.d. innovations. Some useful mathematical tools are collected in Appendix A, and a brief summary of weak convergence in given in Appendix B. The book is intended to give a relatively self-contained presentation for graduate students and researchers with a good knowledge of multivariate regression analysis and likelihood methods. The asymptotic theory requires some familiarity with the theory of weak convergence of stochastic processes. The theory is treated in detail with the purpose of giving the reader a working knowledge of the techniques involved. Many exercises are provided. The theoretical analysis is illustrated with the empirical analysis of two sets of economic data. The theory has been developed in close contract with the application and the methods have been implemented in the computer package CATS in RATS as a result of a rcollaboation with Katarina Juselius and Henrik Hansen.