Tihomir Varbanov

This paper investigates five different Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Condition-al Heteroscedacity (GARCH models (GARCH, exponential GARCH or EGARCH, integrated GARCH or IGARCH, Component GARCH or CGARCH and the Glosten-Jagannathan-Runkle GARCH or GJR-GARCH) along with six distributions (normal, Student’s t, GED and their skewed forms), which are used to estimate the price dynamics of the Bulgarian stock index SOFIX. We use the best model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data cover the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at analysing the SOFIX price and which distribution is most appropriate. The results, based on the BIC and AIC, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student’s t-distribution is preferred for modelling. From the results obtained, we can confirm that the CGARCH model specification supports a more appropriate description of SOFIX volatility than a simple GARCH model. We find that long-term shocks have a more persistent impact on volatility than the effect of short-term shocks. Furthermore, for the same magnitude, negative shocks to SOFIX prices have a more significant impact on volatility than positive shocks. According to the results, when predicting future values of SOFIX, it is necessary to include both a first-order autoregressive component and a first-order moving average in the mean equation. With the help of 5000 simulations, it is estimated that the chances of SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087.

This paper investigates five different GARCH models (GARCH, EGARCH, IGARCH, Component GARCH (CGARCH) and GJR-GARCH) along with six distributions (Normal, Student’s t, GED and their skewed forms), which are used to forecast the volatility for the Bulgarian Stock index SOFIX. We use a GARCH model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data covers the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at forecasting the volatility of SOFIX and which distribution is most appropriate. The results, based on BIC and AIC information criteria, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student t-distribution is preferred for forecasting. With the help of 5000 simulations, it is estimated that the chances of Index SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087.

Purpose: The aim of the research is to study the various aspects of the circular economy in Bulgaria and the countries of the European Union. Method: The article evaluates the circular economy by applying different statistical analysis approaches: multivariate statistical methods, convergence analysis and cross-correlation analysis. Results and conclusion: First, as a result of the conducted dynamic classification of EU countries, it was found that the transition to a circular economy is most advanced in Germany, the Netherlands, Belgium, Spain, Italy and Luxembourg. Second, according to each of the indicators included in the analysis, the absence of a process of general convergence and the presence of club convergence between the EU-27 countries during the period 2012-2019 was established. Convergence among countries in four of the clubs formed is relative, while in the others there is a process of transitional divergence and phase reversal. Third, based on the cross-correlation analysis, we find no relationship between generated and recycled packaging waste in Bulgaria from 2005 to 2019. Between these indicators in the European Union for the same period, there is reason to argue that there is a relationship that occurs within the current year. Fourth, the values of the indicators of waste utilization and rendering waste harmless clearly show that in Bulgaria the waste from economic activities is mainly landfilled, and this is associated with additional costs and leads to environmental pollution. Fifth, the taxonomic analysis shows the existence of minimal differences between the Bulgarian districts in terms of municipal solid waste management.

The article clarifies the essence of the indicators that characterise the principles on which the European Pillar of Social Rights is built, and the information provision of their statistical survey is presented. Official statistics published by Eurostat are used. The objective internal regularities of the time series for Bulgaria for the period 2005-2018 are established by using the autodetermination coefficient, while the viability of constructing univariate models for forecasting purposes is assessed. A cluster analysis has been applied for 2010 and 2018, as a result of which homogenous groups of EU countries have been established and the factors most significant for their formation have been identified. The survey is a preliminary assessment of both the dynamics of the indicators for Bulgaria and the social cohesion in the EU. The derived results can serve as information and analytical bases both for identifying appropriate methods for convergence analysis and for revealing the possibilities of cluster analysis for its evaluation.