Abstract: The current study investigates the behaviour of time-varying parameters that are based on the score function of the predictive model density at time t. The mechanism to update the parameters over time is the scaled score of the likelihood function. The results revealed that there is high persistence of time-varying, as the location parameter is higher and the skewness parameter implied the departure of scale parameter from the normality with the unconditional parameter as 1.5. The results also revealed that there is a perseverance of the leptokurtic behaviour in stock returns which implies the returns are heavily tailed. Prior to model estimation, the White Neural Network test exposed that the stock price can be modelled by a GAS model. Finally, we proposed further researches specifically to model the existence of time-varying parameters with a more detailed model that encounters the heavy tail distribution of the series and computes the risk measure associated with the returns.
Abstract: This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.
Abstract: This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.
Abstract: 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 (information-s-communications industry).