Research background: On 11 March 2020, the Covid-19 epidemic was identified by the World Health Organization (WHO) as a global pandemic. The rapid increase in the scale of the epidemic has led to the introduction of non-pharmaceutical countermeasures. Forecast of the Covid-19 prevalence is an essential element in the actions undertaken by authorities. Purpose of the article: The article aims to assess the usefulness of the Auto-regressive Integrated Moving Average (ARIMA) model for predicting the dynamics of Covid-19 incidence at different stages of the epidemic, from the first phase of growth, to the maximum daily incidence, until the phase of the epidemic's extinction. Methods: ARIMA(p,d,q) models are used to predict the dynamics of virus distribution in many diseases. Model estimates, forecasts, and the accuracy of forecasts are presented in this paper. Findings & Value added: Using the ARIMA(1,2,0) model for forecasting the dynamics of Covid-19 cases in each stage of the epidemic is a way of evaluating the implemented non-pharmaceutical countermeasures on the dynamics of the epidemic.

On 11 March 2020, the WHO declared the COVID-19 epidemic to be a global pandemic. This was a consequence of the rapid increase in the number of people with positive test results, the increase in deaths due to COVID-19, and the lack of pharmaceutical drugs. Governments introduced national lockdowns, which have impacted both energy consumption and economies. The purpose of this paper is to answer the following question: do COVID-19 lockdowns affect the business cycle? We used the cycle clock approach to assess the magnitude of decrease in electricity consumption in the three waves of the epidemic, namely, April 2020, November 2021, and April 2021. Additionally, we checked the relation between energy consumption and GDP by means of spectral analysis. Results for selected 28 European countries confirm an impact of the introduced non-pharmaceutical interventions on both energy consumption and business cycle. The reduction of restrictions in subsequent pandemic waves increased electricity consumption, which suggests movement out of the economic recession.

Inflation is an indicator that signals emerging crises. The period of 2001–2024 witnessed numerous crises. Energy crises affect countries to varying degrees, making it important to identify those most sensitive to inflationary changes in energy prices. This study aims to assess the similarity in the dynamics of the annual inflation rates for the electricity, gas, and other fuels category (HICP—COICOP group 04.5) across Europe. In particular, we identify sub-periods and countries in which inflation indicators either led price changes in Poland or followed the inflation dynamics observed in Poland. This assessment of leading and lagging inflation dynamics is conducted using wavelet analysis, specifically analysis of the wavelet coherence with a phase difference, for Poland and 27 European countries. The analysis addresses two main questions. First, was there statistically significant coherence (correlation in the frequency domain over specific sub-periods) in energy price inflation processes between Poland and other countries? Second, which countries exhibited energy price inflation dynamics that led or lagged behind the pattern in Poland? For many countries, coherence with Poland was not significant in regard to short-term fluctuations (2–6 months) but became significant over longer time scales. Furthermore, at longer periodicities, Poland’s energy inflation dynamics were synchronous with those of many European countries, especially during the period of Russian aggression against Ukraine. This analysis identifies statistically significant coherence between Poland and the chosen European countries. Germany and Lithuania frequently led Polish energy price inflation, whereas other countries, such as Bulgaria and Spain, often lagged behind. These results reveal dynamic patterns in the time–frequency co-movements of energy inflation across Europe.

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players' payoffs do not exceed the non-deviating player payoff more than a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale's good strategies described in \cite{smale}, where the repeated Prisoner's Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.

We propose to apply a time-series-based nonlinear mechanism in the threshold autoregression (TAR) form in order to examine business cycles in Central and Eastern European economies and compare them to the entire EU business cycle. The threshold variables, such as consumer price index, short and long interest rates, unemployment rate and an exchange rate vs. the U.S. Dollar, have been considered. The purpose of the paper is to model and to predict business cycles in Central and East European (CEE) economies (the EU Member States) and compare them to business cycles of the entire EU28 area and Eurozone EU19. We found that the exogenous mechanism played an important role in diagnosing the phases of business cycles in CEE economies, which is in line with the entire EU economic area. The results of business cycle forecasting using bootstrap technique are quite promising, while bootstrap confidence intervals are used for diagnosis.