GENERAL INFORMATION
| Info-AJIRAS-® Journal ISSN 2429-5396 (Online) / Reference CIF/15/0289M |
American Journal of Innovative Research & Applied Sciences
Authors Contact
*Correspondant author and authors Copyright © 2020:
| Wafaa Kaikani *1.2 | Asmaa Naim 1.2 | and | Hamouda Boussen 3 |
Affiliation.
1. Faculté de médecine | Université Mohammed VI des Sciences de la Santé | MAROC |
2. Hôpital Universitaire International Cheikh Khalifa | Maroc |
3. Hôpital A Mami | Ariana | Tunis |
This article is made freely available as part of this journal's Open Access: ID | Wafaa-Ref.4-ajiras070220 |
| MARCH | VOLUME 10 | ISSUE 3 | 2020 |
| ARTICLES | Am. J. innov. res. appl. sci. Volume 10, Issue 2 Pages 93-105 (March 2020)
| Wafaa Kaikani *1.2 | Asmaa Naim 1.2 | and | Hamouda Boussen 3 |. Am. J. innov. res. appl. sci. 2020; 10(3):99-105.
ABSTRACT
Background: Maximum likelihood estimation (MLE) is often used in econometric and other statistical models despite its computational considerations and because of its strong theoretical appeal. Objectives: Non-linear optimization discipline provides feasible alternative methods for calculating MLE’s, especially when special structure may be exploited, as for example in probabilistic choice models. Methods: may be exploited, as for example in probabilistic choice models. This paper examines estimation of parameters of financial time series model named GARCH(p,q) using four numerical optimization methods and gives numerical comparisons of these methods. Results: Among the issues considered in this paper are theoretical background of MLE. Also methods of approximating the Hessian are presented. These include (DFP and BFGS) and statistical approximations (BHHH). Conclusions: In our case of GARCH (p, q) NR has approved to be the fastest in convergence according to the number of iterations followed by BHHH algorithm, BFGS and DFP is the last position rank.
Keywords: GARCH(p,q), Log-likelihood, Numerical optimization, BHHH, Newton-Raphson, BFGS, DFP.
Background: Maximum likelihood estimation (MLE) is often used in econometric and other statistical models despite its computational considerations and because of its strong theoretical appeal. Objectives: Non-linear optimization discipline provides feasible alternative methods for calculating MLE’s, especially when special structure may be exploited, as for example in probabilistic choice models. Methods: may be exploited, as for example in probabilistic choice models. This paper examines estimation of parameters of financial time series model named GARCH(p,q) using four numerical optimization methods and gives numerical comparisons of these methods. Results: Among the issues considered in this paper are theoretical background of MLE. Also methods of approximating the Hessian are presented. These include (DFP and BFGS) and statistical approximations (BHHH). Conclusions: In our case of GARCH (p, q) NR has approved to be the fastest in convergence according to the number of iterations followed by BHHH algorithm, BFGS and DFP is the last position rank.
Keywords: GARCH(p,q), Log-likelihood, Numerical optimization, BHHH, Newton-Raphson, BFGS, DFP.
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