ResearchBib, Google Scholar, SIS database, i.f.s.i.j, Scribd, IISJ, Eurasian Scientific Journal Index (ESJI),Indianscience.in, arastirmax, Directory of Research Journals Indexing, Pak Academic Sesearch, AcademicKeays, CiteSeerX, UDL Library, CAS Abstracts, J-Gate, WorldCat, Scirus, IET Inspec Direct, and getCited
| ISSN: 2429-5396 (e) | https://www.american-jiras.com|| | Web Site Form: v 0.1.05 | JF 22 Cours, Wellington le Clairval, Lillebonne | France |
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.
American Journal of innovative Research & Applied Sciences
