A structured state space approach to computing the likelihood of an ARIMA process and its derivatives

Abstract

Kohn and Ansley (1984a) define a likelihood for a general nonstationary Gaussian ARIMA process having missing observations anywhere in the series, and obtain a modified Kalman filter algorithm to compute the likelihood.This paper shows how to efficiently implement the modified Kalman filter and its derivatives so as to compute the Kohn and Ansley (1984a) likelihood and its first two derivatives.We do so by demonstrating that most of the computation is done by a set of basic algorithms.