Approximation of likelihood function for multiple autoregressive moving average stationary models.

Olorunsola E. Olowofeso; A. B. Fagbohun; Khogali A. Khogali

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Approximation of likelihood function for multiple autoregressive moving average stationary models.

Author(s)

Olorunsola E. Olowofeso Mathematical Sciences Department, Federal University of Technology, P.M.B. 704, Akure, Ondo State, Nigeria

A. B. Fagbohun Mathematics Department, Obafemi Awolowo University Ile-Ife, Osun State, Nigeria

Khogali A. Khogali Mathematics Department, University of Nairobi P.O. Box. 30197, Nairobi, Kenya

Abstract

This work extend the computable likelihood function (LF) proposed by Hilmer and Tiao (1979). The work provides three alternative expressions for the likelihood function free from pre-period values for vector Autoregressive Moving Average (ARMA). The first function is based on shifting the vector of observations in such a manner to avoid the incorporation of the pre-period values in the likelihood function. Based on the concept of domination probability which factorises the likehood function into marginal and conditional likelihood factors; two further approximations of the likelihood function were provided. This second approximations suggest the use of the density function of MA (p) to approximate the likelihood function of vector ARMA (p, q) based on n – p - q observations rather than n observations. The third approximation attempts to trace the factorization of the density function of the observations. The simulation results of estimates of the parameters for vector Autoregressive Integrated Moving Average of known orders for the Likelihood functions using S-PLUS 2000 professional software are presented.

Publication Details

Page(s) 257-276

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 22, Issue: 3, Year: 2006

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