We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Teräsvirta (2009), ČiŽek and Spokoiny (2009) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible time variability of the unconditional variance. The function proposed in this paper can be interpreted as a finite Fourier approximation of an Almost Periodic (AP) function as defined by Corduneanu (1989). The resulting model has a particular form of a GARCH process with time varying parameters, intensively discussed in the recent literature.

In the empirical analyses we apply a generalisation of the Bayesian AR(1)-GARCH model for daily returns of S&P500, covering the period of sixty years of US postwar economy, including the recently observed global financial crisis. The results of a formal Bayesian model comparison clearly indicate the existence of significant long term cyclical patterns in volatility with a strongly supported periodic component corresponding to a 14 year cycle. Our main results are invariant with respect to the changes of the conditional distribution from Normal to Student-tand to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.

A heterogeneous Bertrand duopoly game with bounded rational and adaptive players manufacturing differentiated products is subject of investigation. The main goal is to demonstrate that participation of one bounded rational player in the game suffices to destabilize the duopoly. The game is modelled with a system of two difference equations. Evolution of prices over time is obtained by iteration of a two dimensional nonlinear map. Equilibria are found and local stability properties thereof are analyzed. Complex behavior of the system is examined by means of numerical simulations. Region of stability of the Nash equilibrium is demonstrated in the plane of the speeds of adjustment. Period doubling route to chaos is presented on the bifurcation diagrams and on the largest Lyapunov characteristic exponent graph. Lyapunov time is calculated. Chaotic attractors are depicted and their fractal dimensions are computed. Sensitive dependence on initial conditions is evidenced.

The paper investigates the mechanisms behind the formation and maintenance of those migrants’ social ties which translate into a particular composition of the network and become a source of social capital. Based on a number of in-depth interviews with Ukrainian migrants in Warsaw, we find that Ukrainian migrants’ networks are based primarily on ties homogenous in regard to nationality, level of education and character of work. The institutional context of social interaction determines with whom migrants form relations and whether these ties become a source of social advancement. The studied migrants do form bridging ties with more experienced, as well as socially and legally embedded persons, mainly other migrants, receiving both instrumental and emotional support.

This paper describes the spatial differentiation of topoclimatic conditions in the vicinity of the Arctowski Station (King George Island, Antarctica) during the summer season of the 2006/2007. The measurement stations were located in the Point Thomas oasis as well as on the Ecology Glacier and Warszawa Icefield. The paper analyses meteorological elements such as air temperature, air humidity (eight sites) and wind direction and velocity (three sites). Significant topoclimatic diversities resulting from denivelation, exposure, ground properties and local air circulation were recorded in the study area.