Using Cointegration Restrictions to Improve Inference in Vector Autoregressive Systems

Abstract

An improved way of dealing with uncertain prior information in the context of vector autoregressive systems of equations is proposed. The procedure is appropriate when inference about parameters of a cointegrated system is the aim of the analysis. The estimator uses uncertain prior information about the existence of trends and co-trends in the time series to improve parameter estimation within these systems. The improved estimator eliminates the need to carry out the unit root, cointegration, and parameter restriction pretests and is shown in our Monte Carlo experiments to have good statistical properties in small samples. The pretest, maximum likelihood, and restricted maximum likelihood estimators are compared to the proposed estimator based on squared error risk, mean square error of prediction risk, and out-of-sample root-mean-square forecast error. The Monte Carlo simulations are based on actual economic data collected for eurodollar futures contracts. The evidence suggests that the parameters of vector autoregressive systems can be estimated with lower mean square error with the new estimator even when prior guesses about the nature of the cointegrating vector(s) are incorrect. In-sample prediction is likewise improved. The Monte Carlo simulations are based on eurodollar spot and futures market data that has been used to test the “unbiased expectations” hypothesis.