In the paper an approach to decision making in situations with non-point-like characterisation and subjective evaluation of the actions is considered. The decision situation is represented mathematically as fuzzy multiobjective linear programming (fMOLP) model, where we apply the reduced fuzzy matrices instead of fuzzy classical numbers. The fMOLP model with reduced parameters is decomposable into the set of point-like models and the point-like models enable effective construction of an optimisation procedure – fBIP, see Wojewnik (2006ab), extending the bireference procedure by Michalowski and Szapiro (1992). The approach is applied to a fuzzy optimization problem in the area of telecommunication services.
This paper points out that the ARMA models followed by GARCH squares are volatile and gives explicit and general forms of their dependent and volatile innovations. The volatility function of the ARMA innovations is shown to be the square of the corresponding GARCH volatility function. The prediction of GARCH squares is facilitated by the ARMA structure and predictive intervals are considered. Further, the developments suggest families of volatile ARMA processes.
The Walters critique of EMU presumed that pro-cyclical country-specific real interest rates would incorporate significant macroeconomic instability in an environment of asymmetric shocks. The literature on optimum currency areas suggests a number of criteria to minimize this risk, such as market flexibility, high degrees of openness, financial integration or similarity in inflation rates. In this paper, we argue that an essential part of macroeconomic volatility in a monetary union’s member country also depends on the mechanism of forming expectations. This is mainly due to (i) the construction of ex ante countryspecific real interest rate, implying a strong or weak negative correlation with current inflation rate and (ii) anticipated (and hence smoothed) loss in competitiveness and boom-bust cycle. In a 2-region 2-sector New Keynesian DSGE model, we apply 5 different specifications of ex ante real interest rates, based on commonly considered types of expectations: rational, adaptive, static, extrapolative and regressive, as well as their hybrids. Our simulations show that rational expectations dominate the other specifications in terms of minimizing the volatility of the most macroeconomic variables. This conclusion is generally insensitive to which group of agents (producers or consumers) and which region (home or foreign) forms the expectations. It also turns out that for some types of expectations the Walters critique indeed applies, i.e. the system does not fulfil the Blanchard-Kahn conditions or the system’s companion matrix has explosive eigenvalues.
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