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

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
O

_n
(1) time as the sample size n ¿ ¿. These expressions can also be used to evaluate the exact Fisher information matrix in O
_n
(1) time, and provide a basis for an asymptotic expression of the K-L divergence.