The objective of this research paper is to apply a mathematical model to estimate and predict the economic growth of the Caspian countries in the period from 1995 to 2022. We use multiple regression by applying the OLS method to estimate the impact of global oil price, energy resource production per capita, trade, and renewable energy on GDP per capita. The mathematical approach uses fixed and random effects models to assess the overall impact of the independent variables on economic growth in this region and over the period analysed. This study also aims to investigate whether the explanatory variables are cointegrated in the long run; as such, we carry out several mathematical cointegration tests, namely the Pedroni and Johansen tests. The mathematical analysis is completed by the estimation of short- and long-run parameters using the stochastic VAR/VEC models, the impulse response function, and the causality test to assess economic growth in this region. This study’s main finding is that GDP per capita is increasingly influenced by its previous values, which is confirmed by considering lag 1 and lag 2. The results of the Granger causality tests identify several bidirectional relationships between GDP per capita and oil and gas production. These relationships are clearly positive evidence of the growth trend and progress of economic activity in the Caspian region. The practical implications of the study aim to promote and support the use of renewable energy sources. In this sense, policymakers in the Caspian countries should create favourable conditions for the transition to a green economy. An important aspect is the efforts of the government authorities to make their policies more environmentally friendly, as decarbonisation is a good practice in the current context of sustainability and related choices. As the Caspian countries are heavily dependent on conventional energy production, it is essential for them to increase their export earnings from energy resources via diversifying and strengthening new energy opportunities and partnerships.

The transition to a circular economy is imperative in order to confer considerable benefits upon the environment, the economy, and society. The present study aimed to analyse the interdependence and causal relationships between recyclable material consumption as the dependent variable and other independent variables, including the raw material footprint, the trade in recyclable materials, greenhouse gas emissions, investments in the circular economy sectors, the real GDP per capita, renewable energy sources, the circular material use rate, and the population within the 27 EU Member States from 2013 to 2021. In order to achieve the objective, a two-stage economic model was constructed using a panel approach. The research findings indicate a direct and positive correlation between the consumption of recyclable materials and all the aforementioned independent variables, with the exception of greenhouse gas emissions. This study confirms that innovation and investment significantly reduce environmental degradation, and, moreover, the efficiency of investment remains unaffected. A further relationship that emerged from this study is that developed countries have higher resource consumption, which is consistent with the cause of increased consumption being the rapid growth of the middle class around the world. The main conclusion is that Europe cannot achieve sustainable development without a circular economy.

In the financial sphere, volatility is a key factor. This study aims to analyse and predict the volatility associated with Bitcoin’s daily returns between January 2019 and August 2025. Using the GARCH (1,1) autoregressive model sequentially with normal, Student’s t and generalised error (GE) distributions in sequence demonstrates an understanding of the volatility transmission mechanism of this innovative financial asset within the context of the complex investment process. The empirical evidence obtained indicates a tendency for negative daily Bitcoin returns, reflecting persistent and high volatility during the analysed period. Furthermore, predictive analysis suggests that this high volatility is due to economic and financial uncertainty caused by the pandemic, high inflation rates, and the war between Russia and Ukraine. Conversely, predictive analysis shows that Bitcoin is becoming a risk diversification option and is currently playing the role of a risk diversifier, targeting long-term reverse volatility of approximately 4.89%. Finally, the study emphasises that investors are paying much closer attention to, and are much more concerned about, changes in the cryptocurrency market.

This article presents the quality function deployment (QFD) method, also called the “Quality House.” This method transforms customer requirements into identifiable and measurable compliance specifications for service design. The Quality House provides a framework for translating customer satisfaction into identifiable and measurable compliance specifications for service design. Customer expectations were initially formulated in relation to the five dimensions of service quality: trust, solicitude, safety, tangibility, and empathy. To exemplify the QFD method, choose the online bank banking service (ING), called Home' Bank. The purpose of the article is to implement methods of measuring the quality of the banking services in order to maximize the level of cost-effectiveness of the organization.