Fast Computation of the Kullback-Leibler Divergence and Exact Fisher Information for the First-Order Moving Average Model

Abstract

In this note expressions are derived that allow computation of the Kullback-Leibler (K-L) divergence between two first-order Gaussian moving average models in On(1) time as the sample size n →∞. These expressions can also be used to evaluate the exact Fisher information matrix in On(1)time, and provide a basis for an asymptotic expression of the K-L divergence.