Stats

We present a new single-parameter bivariate copula, called the Stingray, that is dedicated to representing negative dependence, and it nests the Independence copula. The Stingray copula is generated in a relatively novel way; it has a simple form and is always defined over the full support, unlike many copulas that model negative dependence. We provide visualizations of the copula, derive several dependence properties, and compute basic concordance measures. We compare it with other copulas and joint distributions with respect to the extent of dependence it can capture, and we find that the Stingray copula outperforms most of them while remaining competitive with well-known, widely used copulas such as the Gaussian and Frank copulas. Moreover, we show, through simulation, that the dependence structure it represents cannot be fully captured by these copulas, as it is asymmetric. We also show how the non-parametric Spearman’s rho measure of concordance can be used to formally test the hypothesis of statistical independence. As an illustration, we apply it to a financial data sample from the building construction sector in order to model the negative relationship between the level of capital employed and its gross rate of return.

In recent years, the green financial market has been exhibiting heightened volatility daily, largely due to policy changes and economic shifts. To explore the broader potential of predictive modeling in the context of short-term volatility time series, this study analyzes how fine-tuning hyperparameters in predictive models is essential for improving short-term forecasts of market volatility, particularly within the rapidly evolving domain of green financial markets. While traditional econometric models have long been employed to model market volatility, their application to green markets remains limited, especially when contrasted with the emerging potential of machine-learning and deep-learning approaches for capturing complex dynamics in this context. This study evaluates the performance of several data-driven forecasting models starting with machine-learning models: regression tree (RT) and support vector regression (SVR), and with deep-learning ones: long short-term memory (LSTM), convolutional neural network (CNN), and gated recurrent unit (GRU) applied to over a decade of daily estimated volatility data coming from three distinct green markets. Predictive accuracy is compared both with and without hyperparameter optimization methods. In addition, this study introduces the quantile loss metric to better capture the skewness and heavy tails inherent in these financial series, alongside two widely used evaluation metrics. This comparative analysis yields significant numerical and graphical insights, enhancing the understanding of short-term volatility predictability in green markets and advancing a relatively underexplored research domain. The study demonstrates that deep-learning predictors outperform machine-learning ones, and that including a hyperparameter tuning algorithm shows consistent improvements across all deep-learning models and for all volatility time series.

In this study, a procedure to build Bayesian optimal designs using utility functions and exploiting existing data is proposed. The procedure is illustrated through a case study in the field of reliability, by applying a hierarchical Bayesian model and performing Markov Chain Monte Carlo simulations. Two innovative contributions are introduced: (i) the definition of specific utility functions that involve several key issues and (ii) the use of observational data. The use of observational data makes it possible to build the optimal design without additional costs for the company, while the definition of the utility functions accounts for the specific characteristics of the reliability study. Features like model residuals, i.e., discrepancies between observed and predicted response values, and the costs of the electronic component are addressed. Costs are also weighted considering the environmental impact. Satisfactory results are obtained and subsequently validated through an in-depth sensitivity analysis.