A first order continuous time VAR with random coefficients

Abstract

This article considers a first order continuous time vector autoregression with random coefficients. We discuss some difficulties that arise when the exact discrete analogue is used for estimating the continuous time parameters and provide an estimation method based on an approximate discrete model. Some expressions for the estimator of the drift parameter matrix, for its approximated bias and for the covariance matrix of the parameter estimates are derived. The finite sample performance of the proposed method is studied by a Monte Carlo experiment. We also illustrate the advantages of our model in an application on the expectations theory of the term structure of interest rates. Results show that the performance of the proposed methodology is good, and allowing for time variation on coefficients results in large reductions in the root mean square error of the parameter estimates.