Numerical Optimization within Vector of Parameters Estimation in Volatility Models. (CROSBI ID 552738)
Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Arnerić, Josip ; Rozga, Ante
engleski
Numerical Optimization within Vector of Parameters Estimation in Volatility Models.
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
Heteroscedasticity; Log-likehood Maximization; Quasi-Newton iteration procedure; Volatility
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Podaci o prilogu
632-636.
2009.
objavljeno
Podaci o matičnoj publikaciji
Proceedings of International Conference on Statistics and Mathematics
Dubai:
2070-3740
Podaci o skupu
International Conference on Statistics and Mathematics
predavanje
26.01.2009-29.01.2009
Dubai, Ujedinjeni Arapski Emirati