Abstract

In this work, we delved into advanced modeling of economic relationships using the Cobb–Douglas production function as a theoretical foundation. Our primary goal was to develop an innovative multiple linear regression model by introducing innovations based on the \(\alpha\)-stable distribution. By adapting the traditional multiple linear regression model, our approach incorporates the \(\alpha\)-stable distribution to better represent the complexity of relationships between economic variables. This modification enables a better fit for asymmetric distributions and scenarios where data exhibit heavy tails. To assess the performance of our model, we applied it to real financial data. This practical step allowed us to evaluate the effectiveness and predictive capability of our approach in a real-world context, thus offering fresh perspectives for financial data analysis.

中文翻译：

---

柯布-道格拉斯生产函数的统计建模：存在稳定分布噪声时的多元线性回归方法

 抽象的

在这项工作中，我们以柯布-道格拉斯生产函数作为理论基础，深入研究了经济关系的高级建模。我们的主要目标是通过引入基于 \(\alpha\) 稳定分布的创新来开发创新的多元线性回归模型。通过采用传统的多元线性回归模型，我们的方法结合了\(\alpha\)稳定分布，以更好地表示经济变量之间关系的复杂性。此修改可以更好地适应不对称分布和数据呈现重尾的场景。为了评估我们模型的性能，我们将其应用于真实的财务数据。这一实际步骤使我们能够在现实世界中评估我们方法的有效性和预测能力，从而为金融数据分析提供新的视角。