\thanks{The first author  was supported in part by the Serbian Ministry of Education, Science and Technological Development (No. \#OI\,174015).
The second author  was supported  by the Serbian Ministry of Education, Science and Technological Development (No. \#OI\,174007).}

The procedure of estimating parameters of Stochastic Volatility (SV) models, because of their specific structure, is much more complex than with the most similar nonlinear stochastic models. In this paper, the Empirical Characteristic Function (ECF) method is described in parameter estimations of the so-called standard SV model introduced by Taylor \cite{Taylor},  as well as the original thresholds modification of this model, named the Split-SV model, introduced in \cite{Split-SV}. The estimation procedure of the both of previously-mentioned models is based on minimization of the objective function which, in fact, represents the double integral with respect to the some weight function $g:\mathbb R^2\rightarrow\mathbb R$. In our investigation we consider some typical, exponential classes of the weight functions $g(u_1,u_2)$. These exponential functions put more weight around the origin, which is in accordance to the fact that Characteristic Functions (CFs) contains the most of information around this point. On the other hand, an exponential weight function has the numerical advantage, because the objective function of the ECF method (i.e., the appropriate double integral) can be numerically approximated by using some of $N$-point cubature formulas. For this purpose, we use  different types of cubature formulas, whose have been realized by authorized {\sc Mathematica}  package {\tt  OrthogonalPolynomials} (see \cite{OrtPol,OrtPol2}). Consequently, the objective function is minimized with respect to $\theta$ by a Nelder-Mead method, and  estimation procedures are realized by the original authors' codes written in statistical programming language ``R''. Using these procedures, by different choices of  weight functions, it is examined the performance of the ECF method, by statistical and numerical aspects. The numerical simulation of the obtained estimates is given, also. Finally, the standard SV model, and the Split-SV model as its alternative, are applied for fitting  the empirical data: the daily returns of the exchange rates of GBP and USD per euro, and the efficiency of their fitting is compared.

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\bibitem{OrtPol} Cvetkovi\'c, A. S., Milovanovi\'c, G. V., 2004. The Mathematica Package ``OrthogonalPolynomials''. Facta Univiversitatis-Series: Mathematics \& Informatics 19, 17--36.

\bibitem{OrtPol2}Milovanovi\'c, G. V., Cvetkovi\'c, A. S., 2012. Special classes of orthogonal polynomials and corresponding quadratures of Gaussian type. Mathematica Balkanica 26, 169--184.

\bibitem{Split-SV} Popovi\' c, B. \v C., Stojanovi\' c, V., 2011. The Distribution of Split-SV(1) Model. Proceeding of the 2th International Conference MIT 2011, 335--340.

\bibitem{Taylor} Taylor, S. J., 1986. Modelling financial time series. John Wiley \& Sons, Chichester.

\end{thebibliography}