Estimating parameters of a multiple autoregressive model by the modified maximum likelihood method

Türker Bayrak Ö., Akkaya A.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.233, no.8, pp.1763-1772, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 233 Issue: 8
  • Publication Date: 2010
  • Doi Number: 10.1016/j.cam.2009.09.013
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1763-1772
  • Keywords: Autoregression, Student's t, Generalized Logistic, Modified likelihood, Non-normality, LINEAR-REGRESSION MODEL, TIME-SERIES MODELS, NONNORMAL SITUATIONS, ROBUST ESTIMATION, DISTRIBUTIONS
  • Middle East Technical University Affiliated: Yes

Abstract

We consider a multiple autoregressive model with non-normal error distributions, the latter being more prevalent in practice than the usually assumed normal distribution. Since the maximum likelihood equations have convergence problems (Puthenpura and Sinha, 1986) [11], we work Out modified maximum likelihood equations by expressing the maximum likelihood equations in terms of ordered residuals and linearizing intractable nonlinear functions (Tiku and Suresh, 1992) [8]. The solutions, called modified maximum estimators, are explicit functions of sample observations and therefore easy to compute. They are under some very general regularity conditions asymptotically unbiased and efficient (Vaughan and Tiku, 2000) [4]. We show that for small sample sizes, they have negligible bias and are considerably more efficient than the traditional least Squares estimators. We show that Our estimators are robust to plausible deviations from an assumed distribution and are therefore enormously advantageous as compared to the least squares estimation. We give a real life example. (C) 2009 Elsevier B.V. All rights reserved.