The Inverse Kullback–Leibler Method for Fitting Vector Moving Averages

Abstract

A new method for the estimation of a vector moving average (VMA) process is presented. The technique uses Kullback–Leibler discrepancy with inverse spectra, and yields a Yule–Walker system of equations in inverse autocovariances for the VMA coefficients. This provides a direct formula for the coefficients, which always results in a stable matrix polynomial. The paper provides asymptotic results, as well as an analysis of the method's performance, in terms of speed, bias, and precision. Applications to preliminary estimation of VMA models are discussed, and the method is illustrated on retail data.