Maximum Likelihood in Three-Way Contingency Tables

Abstract

Ansley and Kohn (1983) have shown that the Kalman filter can be used to calculate the exact likelihood function of a vector autoregressive moving average (ARMA) process when not all the observations are known. When there are no missing obser- vations the Chandrasekhar algorithm (see Schweppe (1965), Morf et al. (1974) and Shea (1987)) is much quicker than that of Ansley and Kohn (1983) except for an ARMA(2, 1) process and a couple of low order AR processes. A subroutine which computes the log-likelihood function, using the Chandrasekhar algorithm, is presented here. An efficient method of computing the likelihood function and its derivatives for a univariate ARMA process is discussed in Kohn and Ansley (1985).