Financial time-series data often exhibit statistically significant skewness and heavy tails, and numerous flexible distributions have been proposed to model them. In the context of the Log-linear Realized GARCH model with Skew-t (ST) distributions, our objective is to explore how the choice of prior distributions in the Adaptive Random Walk Metropolis method and initial parameter values in the Generalized Reduced Gradient (GRG) Solver method affect ST parameter and log-likelihood estimates. An empirical study was conducted using the FTSE 100 index to evaluate model performance. We provide a comprehensive step-by-step tutorial demonstrating how to perform estimation and sensitivity analysis using data tables in Microsoft Excel. Among seven ST distributions—namely, the asymmetric, epsilon, exponentiated half-logistic, Hansen, Jones–Faddy, Mittnik–Paolella, and Rosco–Jones–Pewsey distributions—Hansen’s ST distribution is found to be superior. This study also applied the GRG method to estimate new approaches, including Realized Real-Time GARCH, Realized ASHARV, and GARCH@CARR models. An empirical study showed that the GARCH@CARR model with the feedback effect provides the best goodness of fit. Out-of-sample forecasting evaluations further confirm the predictive dominance of models incorporating real-time information, particularly Realized Real-Time GARCH for volatility forecasting and Realized ASHARV for 1% VaR estimation. The findings offer actionable insights for portfolio managers and risk analysts, particularly in improving volatility forecasts and tail-risk assessments during market crises, thereby enhancing risk-adjusted returns and regulatory compliance. Although the GRG method is sensitive to initial values, its presence in the spreadsheet method can be a powerful and promising tool in working with probability density functions that have explicit forms and are unimodal, high-dimensional, and complex, without the need for programming experience.

In this paper, time series of length T are seen as frequency distributions. Each distribution is defined with respect to a statistical variable having T observed values. A methodological system based on Gini’s approach is put forward, so the statistical model through which time series are handled is a frequency distribution studied inside a linear system. In addition to the starting frequency distributions that are observed, other frequency distributions are treated. Thus, marginal distributions based on the notion of proportionality are introduced together with joint distributions. Both distributions are statistical models. A fundamental invariance property related to marginal distributions is made explicit in this research work, so one can focus on collections of marginal frequency distributions, identifying multiple frequency distributions. For this reason, the latter is studied via a tensor. As frequency distributions are practical realizations of nonparametric probability distributions over R, one passes from frequency distributions to discrete random variables. In this paper, a mathematical model that generates time series is put forward. It is a stochastic process based on subjective previsions of random variables. A subdivision of the exchangeability of variables of a statistical nature is shown, so a reinterpretation of principal component analysis that is based on the notion of proportionality also characterizes this research work.

This article introduces a novel approach to decomposing the Blinder–Oaxaca gender wage gap using pseudo-panel data. In many developing countries, panel data are not available; however, understanding the evolution of the gender wage gap over time requires tracking individuals longitudinally. When individuals change across time periods, estimators tend to be inconsistent and inefficient. To address this issue, and building upon the traditional Blinder–Oaxaca methodology, we propose an alternative procedure that follows cohorts over time rather than individuals. This approach enables the estimation of both the explained and unexplained components—“endowment effect” and “remuneration effect”—of the wage gap, along with their respective standard errors, even in the absence of true panel data. We apply this methodology to the case of Colombia, finding a gender wage gap of approximately 15% in favor of male cohorts. This gap comprises a −5.6% explained component and a 20% unexplained component without controls. When we control by informality, size of the firm and sector the gap comprises a −3.5% explained component and a 18.7% unexplained component.

Financial studies on the herding effect have been very popular for decades, as detecting herding behavior helps to explain price deviations and market inefficiencies. However, studying the herding effect as a single influencing factor is believed to be insufficient to explain the changes in investment behavior, as the herding effect itself may be caused by other influencing factors. In other words, the issue must be studied alongside other factors. In this study, we adopt the quantile regression model to comprehensively understand the herding effect’s influence on household investment in China, and the empirical results indicate that herding behavior leads to different investment outcomes for households in different scenarios. In this analysis, we consider a variety of household characteristics, such as income level and risk tolerance, to provide a nuanced understanding of investment behavior. Additionally, in this study, we explore the interaction between herding behavior and macroeconomic variables. Nevertheless, the results suggest that, if herding behavior can be reduced by the head of the household, profitability can be increased, or at the very least, losses can be reduced.

Microfinance aims to promote financial inclusion among underprivileged individuals, particularly through progressive microcredit, which enables borrowers to access increasing loan amounts over time. This study examines the conditions under which progressive microcredit positively impacts both small business performance and household well-being, considering borrower characteristics and business activity conditions. Using a dataset of 278 households across 110 administrative sectors in Tunisia from 2012 to 2020, this study employs two-stage least squares (2SLS) and three-stage least squares (3SLS) econometric techniques to estimate simultaneous equation models. The findings reveal that the cumulative amount of progressive microcredit received is mainly determined by project capital, suggesting that businesses with higher capital requirements tend to secure larger loans over successive cycles. Household well-being is significantly influenced by progressive microcredit, household income, net business benefit, rate of development index, and homeownership. Meanwhile, business profitability is driven by project capital and total fixed assets, highlighting the long-term impact of microcredit. The results highlight the critical role of microfinance in enabling small-scale entrepreneurs to expand their businesses while simultaneously improving household financial security. By promoting sustainable income generation, progressive microcredit serves as a key instrument in poverty alleviation and economic stability. This study underscores the necessity for microfinance institutions (MFIs) to tailor their lending strategies, ensuring optimal loan progression that balances business expansion with financial sustainability. Additionally, policymakers should refine microcredit frameworks to enhance accessibility and long-term economic benefits for low-income borrowers. Overall, these insights contribute to the broader discourse on financial inclusion and sustainable development, emphasizing that progressive microcredit not only facilitates entrepreneurship, but also serves as a driver of socioeconomic mobility.

The untapped potential of wave energy offers another alternative to diversifying renewable energy sources and addressing climate change by reducing CO2 emissions. However, development costs to mature the technology remain significant hurdles to adoption at scale and the technology often must compete against other marine energy renewables such as offshore wind. Here, we conduct a real option valuation that includes the uncertain market price of wholesale electricity and managerial flexibility expressed in determining future optimal decisions. We demonstrate the probability that the project’s embedded compound real option value can turn a negative net present value wave energy project to a positive expected value. This change in investment decision uses decision tree analysis, where real options are developed as decision nodes, and models the uncertainty as a risk-neutral stochastic process using chance nodes. We also show how our results are analogous to a financial out-of-the-money call option. Our results highlight the distribution of outcomes and the benefit of a staged long-term investment in wave energy systems to better understand and manage project risk, recognizing that these probabilistic results are subject to the ongoing evolution of wholesale electricity prices and the stochastic process models used here to capture their future dynamics. Lastly, we show that the near-term optimal decision is to continue to fund ongoing development of a reference architecture to a higher technology readiness level to maintain the long-term option to deploy such a renewable energy system through private investment or private–public partnerships.

Aim: The aim of the article was to analyse the level and structure of household indebtedness in selected European countries over two periods: 2018–2019 and 2020–2022. The research focused on two key objectives: (1) a comparative analysis of the forms of indebtedness among households in different European countries, and (2) a comparative analysis of the euro area and non-euro area EU Member States with respect to the level and structure of household debt. Methodology: The study is based on secondary data from Eurostat concerning the financial resources and debt levels of European households. The analysis covered two distinct time periods (2018–2019 and 2020–2022) and compared the prevalence and structure of different debt instruments. The research included descriptive and comparative methods, examining household behaviour in euro area and non-euro area countries. Results: The analysis showed that there were no statistically significant differences between euro area and non-euro area households in terms of asset and debt categories. In the euro area, households more frequently used short-term and long-term loans, while they were less likely to invest in quoted shares and bonds. In non-euro area countries, short-term loans dominated, suggesting a stronger tendency to use quick access financing tools. Debt securities and long-term loans were less prevalent in these countries. Implications and recommendations: The findings suggest that household debt preferences were relatively stable across Europe, with minor regional differences. Policymakers should consider these patterns when designing financial literacy programmes and credit regulations. Future research could focus on the behavioural factors influencing household debt decisions and investigate the impact of macroeconomic changes on these trends. Originality/value: This study contributes to the literature by offering a comparative perspective on household indebtedness in euro area and non-euro area countries, using up-to-date Eurostat data across two relevant time frames. It provides insights into the structure of household liabilities and the regional differences in debt preferences.

Aim: This study examines the practical impact of measurement scale choices, particularly logarithmic transformations, on the accuracy, reliability, and interpretability of econometric models using macroeconomic indicators from the MENA region. Methodology: Using real-world MENA data, multiple techniques (OLS, Fixed Effects, Random Effects, GMM) were applied with both raw and log-transformed variables to compare outcomes for variance stability, normality, stationarity, and heteroskedasticity. Results: Log transformations substantially improve model diagnostics by stabilising variance, enhancing normality, and reducing heteroskedasticity, yielding more precise estimates. However, they alter coefficient interpretation, highlighting a trade-off between statistical robustness and economic meaning. Implications and Recommendations: The findings underscore the critical need for appropriate data transformations to ensure valid and interpretable results, offering practical guidance for researchers and policymakers in model specification for policy analysis and forecasting. Originality/Value: This study provides a novel comparative exploration of transformation effects across methodologies and one of the few region-specific investigations using MENA data, delivering actionable insights for methodological and applied research.

Personal finance research often utilizes Likert-type items and Likert scales as dependent variables, frequently employing standard probit and ordered probit models. If inappropriately modeled, the “neutral” category of discrete dependent variables can bias estimates of the remaining categories. Through the utilization of hierarchical models, this paper demonstrates a methodology that accounts for the econometric issues of the neutral category. We then analyze the technique through an empirical exercise relevant to personal finance research using data from the National Financial Capability Study. We demonstrate that ignoring the “neutral” category bias can lead to incorrect inferences, hindering the progression of personal finance research. Our findings underscore the importance of refining statistical modeling techniques when dealing with Likert-type data. By accounting for the neutral category, we can enhance the reliability of personal finance research outcomes, fostering improved decision-relevant insights.

The COVID-19 (coronavirus disease of 2019) pandemic is over; however, the probability of such a pandemic is about 2% in any year. There are international negotiations among almost 200 countries at the World Health Organization (WHO) concerning a global plan to deal with the next pandemic on the scale of COVID-19, known as “Disease X”. We develop a nonlinear panel quasi-vector autoregressive (PQVAR) model for the multivariate t-distribution with dynamic unobserved effects, which can be used for out-of-sample forecasts of causes of death counts in the United States (US) when a new global pandemic starts. We use panel data from the Centers for Disease Control and Prevention (CDC) for the cross section of all states of the United States (US) from March 2020 to September 2022 regarding all death counts of (i) COVID-19 deaths, (ii) deaths that medically may be related to COVID-19, and (iii) the remaining causes of death. We compare the t-PQVAR model with its special cases, the PVAR moving average (PVARMA), and PVAR. The t-PQVAR model provides robust evidence on dynamic interactions among (i), (ii), and (iii). The t-PQVAR model may be used for out-of-sample forecasting purposes at the outbreak of a future “Disease X” pandemic.