Abstract: This paper deals with econometric analysis of real
retail trade turnover. It is a part of an extensive scientific research
about modern trends in Croatian national economy. At the end of the
period of transition economy, Croatia confronts with challenges and
problems of high consumption society. In such environment as
crucial economic variables: real retail trade turnover, average
monthly real wages and household loans are chosen for consequence
analysis. For the purpose of complete procedure of multiple
econometric analysis data base adjustment has been provided.
Namely, it has been necessary to deflate original national statistics
data of retail trade turnover using consumer price indices, as well as
provide process of seasonally adjustment of its contemporary
behavior. In model establishment it has been necessary to involve the
overcoming procedure for the autocorrelation and colinearity
problems. Moreover, for case of time-series shift a specific
appropriate econometric instrument has been applied. It would be
emphasize that the whole methodology procedure is based on the real
Croatian national economy time-series.
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).