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  | ARTICLES | Am. J. innov. res. appl. sci. Volume 10,  Issue 3, Pages 121-129 (March 2020)
Revew Article 2
 
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American Journal of innovative
Research & Applied Sciences 
ISSN  2429-5396 (Online)
OCLC Number: 920041286
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| IMPACT FACTOR AND INDEXING | | PUBLICATION FEE |
| MARCH | VOLUME 10 | N° 3 | 2020 |
| Info-AJIRAS-® Journal ISSN 2429-5396 (Online) / Reference  CIF/15/0289M |
  American Journal of Innovative Research & Applied Sciences
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.
*Corresponding author Author & Copyright Author © 2020: | Moulay El Mehdi Falloul |. All Rights Reserved. All articles published in American Journal of Innovative Research
and Applied Sciences are the property of Atlantic Center Research Sciences, and is protected by copyright laws CC-BY. See: http://creativecommons.org/licenses/by-nc/4.0/
Authors Contact

*Correspondant author and authors Copyright © 2020:

| Moulay El Mehdi Falloul 1* | Ayoub Razouk 2 | and | Youness Saoudi 2 |. 

 
Affiliation.

1. Sultan Moulay Slimane University | department of Economics | Beni Mellal | Faculty polidisciplinary | Morocco |
2. Mohamed V University | Decision aid and computing | ENSIAS | Morocco |

This article is made freely available as part of this journal's Open Access: ID | Moulay-Ref.6-ajira250220 |
NUMERICAL OPTIMIZATION METHODS FOR FINANCIAL TIME SERIES GARCH (P,Q) MODEL, A COMPARATIVE APPROACH

| Moulay El Mehdi Falloul 1* | Ayoub Razouk 2 | and | Youness Saoudi 2 |. Am. J. innov. res. appl. sci. 2020; 10(3)121-129.
 
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XML FILE  |   | Received | January 22, 2020 | | Accepted | March 07, 2020 |  | Published | March 14, 2020 |