Statistika, 102(3): 369-381
https://doi.org/10.54694/stat.2022.19

Abstract
This paper examines the role of factors which could have influenced subjective well-being (SWB) in European countries at a national level between 2010 and 2019. Macroeconomic variables in much of the existing literature have looked at GDP, inflation, government size and expenditure and their relationship to SWB. The current analysis included corruption, property rights, poverty, life expectancy, working time and emissions to enrich the existing body of literature. The World Happiness Index (WHI) is used to measure SWB in this study. The correlation analysis in this study shows a high level of correlation between WHI and the Human Development Index (HDI) which suggests the WHI is a suitable proxy for measuring subjective well-being. Next, the fixed and random effects models were estimated since the dataset was longitudinal, and we have also compared panel regression models with OLS regression models. This analysis revealed positive relationships of GDP, income and property rights on WHI, while poverty and unemployment impact WHI negatively, thus we can conclude positive relationship between material aspects of life and subjective well-being. Corruption and working time impact SWB in a negative way while the impact of life expectancy is positive. The regression models with inflation and emissions were not found to be significant in the research. The results were compared with existing studies based on individual as well as aggregated data. Similarities in results prove that it is possible to analyze determinants of SWB from aggregated data on national level. At the end, we formulate proposals for improving quality of life in the analyzed countries.

Panel data models, quality of life, World Happiness Index, macroeconomic factors, correlation analysis

Statistika, 102(4): 382-395
https://doi.org/10.54694/stat.2022.6

Abstract
The article offers the results of statistical analysis of data on the highest wages of employees in the Slovak Republic in 2020. Descriptive analysis of sample data is supplemented by generalizing the results to the population of all employees whose salary exceeds the 99th percentile of the sample, by selected methods of statistical inference, which are probability models of the highest wages and analysis of variance. The analysis focuses on assessing the significance of the impact of selected demographic and social factors on the highest salaries of employees in SR in 2020 and their differences. The investigated factors there are gender, level of education, region of residence, the label of occupation, and age category. The article also focuses on inequalities in the number of employees at different levels of the monitored factors. The obtained results of the analysis are compared with the results of similar analysis from 2010. 

Keywords
The highest wages, factors, descriptive characteristics, probability models, analysis of variance, comparisons

Statistika, 102(4): 396-408
https://doi.org/10.54694/stat.2022.4

Abstract
The paper focuses on visualization methods suitable for outcomes of cluster analysis of categorical data (nominal data, specifically). Since nominal data have no inherent order, their graphical representation is often challenging or very limited. This paper aims to provide a list of common visualization methods in the domain of cluster analysis of objects characterized by nominal variables. Firstly, the various plot types (such as clustering scatter plot, dendrogram, icicle plot) for cluster analysis are presented, and their suitability for presenting clusters of nominal data is discussed. Then, we study approaches of sorting nominal values on chart axes in such a way that would improve visualization of the data. Lastly, we introduce a simple alternative to cluster scatter plot for nominal data, that makes the final visualization of clustering solution more efficient since the pattern and groups in data are now more apparent. The suggested method is demonstrated in illustrative examples.

Keywords
Cluster analysis, nominal data, hierarchical clustering, visualization

Statistika, 102(4): 409-425
https://doi.org/10.54694/stat.2022.20

Abstract
The aim of this paper is to present the use of simulations of non-homogeneous Markov chains in discrete time in the context of the problem of long-term care delivery. The object of investigation is to model the distribution of clients into different states during specified time steps, then to estimate the average time a client stays in a given state, as well as to estimate the insurance premiums. Within the use of the Monte Carlo simulation method, the focus is on providing approaches that ensure more accurate results in the context of the number of simulations performed. Based on the statistical processing of the data obtained from the simulations, it is possible to obtain the information necessary for the provision of resources for the provision of health care and for the determination of the aforementioned premiums. For the implementation of the above techniques and their graphical presentation available packages such as markovchain, ggplot2 or custom code created using the R language were used.

Long-term care insurance, Markov Chains, multi-state models, simulations, Monte Carlo Method, markovchain package

Statistika, 102(4): 426-442
https://doi.org/10.54694/stat.2022.16

Abstract
Economy digitalization has become a trend during the pandemic. The banking sector was also one of the first to face the need to accelerate digitalization. This work is devoted to developing a digitalization index for both the banking sector and an individual bank based on a set of indicators calculated according to data from the World Bank and data from commercial banks. At a macro level, the study concluded that the pandemic has accelerated the digitalization of the banking sector in all the monitored countries; however, a significant increase was observed in countries with lower index values in the pre-pandemic period. At the micro-level, the study showed that digital banks had benefited from digitalization more during the pandemic, unlike classical banks.

Keywords
Digitalization, financial innovation, digital transformation, digital banking, fintech

Statistika, 102(4): 443-453
https://doi.org/10.54694/stat.2022.18

Abstract
Many game development companies use game data analysis for mining insights about users' behaviour and possible product growth. One of the most important analysis tasks for game development is user churn prediction. Effective churn prediction can help hold users in the game by initiating additional actions for their engagement. We focused on high-value user churn prediction as it is of particular interest for any business to keep paying customers satisfied and engaged. We consider the churn prediction problem as a classification problem and conduct the random undersampling approach to address imbalanced class distribution between churners and active users. Based on our real-life data from a freemium casual mobile game, although the best model was chosen as the final classification algorithm for extracted data, we can definitely say there is no general solution to the stated problem. Model performance highly depends on the churn definition, user segmentation and feature engineering, it is therefore necessary to havea custom approach to churn analysis in each specific case.

Keywords
Churn prediction, mobile games, classification models, resamlpling methods, imbalanced class distribution, machine learning

Statistika, 102(4): 454-470
https://doi.org/10.54694/stat.2022.17

Abstract
In this paper, a novel market risk tracking and prediction strategy is introduced. Our approach takes volatility clustering into account and allows for the possibility of regime shifts in the intra-portfolio's latent correlation structure. The proposed specification combines hidden Markov models (HMM) with latent factor models that takes into account the presence of both the conditional skewness and leverage effects in stock returns.
A computationally efficient expectation-maximization (EM) algorithm based on the Viterbi decoder is developed to estimate the model parameters. Using daily exchange rate data of the Tunisian dinar versus the currencies of the main Tunisian government's creditors, during the 2011 revolution period, the model parameters are estimated. Then, the suitable model is used in conjunction with a Monte Carlo simulation strategy to predict the Value-at-Risk (VaR) of the Tunisian government's foreign debt portfolio. The backtesting results indicate that the new approach appears to give a good fit to the data and can improve the VaR predictions, particularly during financial instability periods.

Keywords
Factor analysis, volatility clustering, hidden Markov models, Viterbi-EM algorithm, portfolio’s Value-at-Risk