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.

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.

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.

The annual usage of heat for the demand of heating systems in municipal sector has been estimatedas about 650PJ. It is mostly addressed for the demand of central heating systems and hot waterconsumption. The mode of adopted solutions concerning regulation and control, as well as energymanagement system, essentially influence its consumption. In the case of residential buildings,the costs of energy constitute the greatest share related to the total cost of building maintenance. Providing buildings with modern digital systems for control and regulation of heating installationsis a basic condition enabling their rational usage. In currently employed solutions, algorithms PI or PID are usually applied. However, due to the non-linear properties of heating control systems, they do not secure proper quality. The sequences are often unstable and major control deviationsoccur. The application of neural networks is an alternative solution to those presently employed. They are especially recommended for adaptive control of non-stationary systems. Such cases occurin heating objects since they demonstrate non-linear properties with a great range of variability ofparameters; this especially refers to district heating equipped with flux-through heat exchangers.In this paper, a compile model of heating system control aided by neural networks is presented. The results of the investigation clearly prove the usefulness of such solutions, cause the qualityof control is much better than that one applied in traditional systems. Presently, works on theimplementation of the proposed solutions are under way.