Recursive Estimation in Cointegrated VAR-Models

Some methods for the evaluation of parameter constancy in cointegrated vector autoregressive (VAR) models are discussed. Two different ways of re-estimating the VAR-model are proposed; one in which all parameters are estimated recursively based upon the likelihood function for the first observations, and another in which the cointegrating relations are estimated recursively from a likelihood function, where the short-run parameters have been concentrated out. We suggest graphical procedures based on recursively estimated eigenvalues to evaluate the constancy of the long-run parameters in the model. Specifically, we look at the time paths of the eigenvalues using a new result on the asymptotic distribution of the estimated eigenvalues. Furthermore, we show that the fluctuation test by Ploberger et al. (1989) and the Lagrange multiplier (LM) type test for constancy of parameters by Nyblom (1989) can be applied to test the constancy of the long-run parameters in the cointegrated VAR-model. All results are illustrated using a model for the term structure of interest rates on US Treasury securities.