On the Shape of the Likelihood/Posterior in Cointegration Models

Frank R. Kleibergen · Herman K. van Dijk

129 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Statistical Methods and Bayesian Inference Diverse Scientific and Economic Studies

Abstract

A vector autoregressive (VAR) model is specified with equation system parameters, which directly reflect the possible cointegrating nature of the analyzed time series. By using a flat/diffuse prior, we show that the marginal posteriors of the parameters of interest (multipliers of the cointegrating vectors) may be nonintegrable and favor difference stationary models in an undesired way. To choose between stationary, cointegrated, and difference stationary models in a meaningful way, the Jeffreys prior principle is used. We investigate the sensitivity of the posterior results with respect to the construction of the Jeffreys prior. In this context, we also analyze the effect of fixed and stochastic initial values. The theoretical results are illustrated by using a VAR model for shortand long–term interest rates in the United States.

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References

1987Co-Integration and Error Correction: Representation, Estimation, and Testing 1990MAXIMUM LIKELIHOOD ESTIMATION AND INFERENCE ON COINTEGRATION — WITH APPLICATIONS TO THE DEMAND FOR MONEY 1991Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models 1987Cointegration and Tests of Present Value Models 1993Introduction to Multiple Time Series Analysis 1988Testing for Common Trends 1991Optimal Inference in Cointegrated Systems 1991To criticize the critics: An objective bayesian analysis of stochastic trends

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2013Forecasting with Bayesian Vector Autoregression 2000US deficit sustainability: a new approach based on multiple endogenous breaks 2010Forecasting large datasets with Bayesian reduced rank multivariate models 1996Time-Series-Based Econometrics 2002Priors, posteriors and bayes factors for a Bayesian analysis of cointegration 2009Econometric Analysis with Vector Autoregressive Models

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