Naslov
Numerical Optimization within Vector of Parameters Estimation in Volatility Models.

Autori
Arnerić, Josip ; Rozga, Ante

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of International Conference on Statistics and Mathematics / - Dubai, 2009, 632-636

Skup
International Conference on Statistics and Mathematics

Mjesto i datum
Dubai, Ujedinjeni Arapski Emirati, 26.01.2009. - 29.01.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Heteroscedasticity; Log-likehood Maximization; Quasi-Newton iteration procedure; Volatility

Sažetak
In this paper usefulness of quasi-Newton iteration procedure in parameters estimation of the conditional variance equation within BHHH algorithm is presented. Analytical solution of maximization of the likelihood function using first and second derivatives is too complex when the variance is time-varying. The advantage of BHHH algorithm in comparison to the other optimization algorithms is that requires no third derivatives with assured convergence. To simplify optimization procedure BHHH algorithm uses the approximation of the matrix of second derivatives according to information identity. However, parameters estimation in a/symmetric GARCH(1, 1) model assuming normal distribution of returns is not that simple, i.e. it is difficult to solve it analytically. Maximum of the likelihood function can be founded by iteration procedure until no further increase can be found. Because the solutions of the numerical optimization are very sensitive to the initial values, GARCH(1, 1) model starting parameters are defined. The number of iterations can be reduced using starting values close to the global maximum. Optimization procedure will be illustrated in framework of modeling volatility on daily basis of the most liquid stocks on Croatian capital market: Podravka stocks (food industry), Petrokemija stocks (fertilizer industry) and Ericsson Nikola Tesla Stocks

Izvorni jezik
Engleski

Znanstvena područja
Ekonomija

POVEZANOST RADA