Juan Evangelista Trinidad Segovia – författare

This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithmsfor properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes.This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.

Bringing together a distinguished group of contributors, this volume in honor of José García Pérez provides a comprehensive overview of the latest advances in quantitative methods for business and economics, including distribution theory, econometrics, behavioral finance, financial networks and economic applications, as well as parallels exploring José García Pérez's research interests.Contemporary challenges in this field include evaluating the robustness of structural econometric analyses under collinearity, identifying the connections between long-term memory and financial performance, and treating multicollinearity in the Nelson-Siegel model. To tackle these problems, this book offers a wealth of innovative approaches, methodologies, and theoretical frameworks. For example, it presents new probability distributions, explores the application of partial least structural equation modeling in economics, discusses the theoretical-practical approach to portfolio management in sustainable finance and Environmental, Social and Governance, and reviews the application and usefulness of state-of-the-art machine learning and artificial intelligence in applied finance.The book serves as a valuable resource for researchers and practitioners in econometrics, finance, and economics, providing a comprehensive yet accessible resource for further exploration and study. In honoring José García Pérez, it not only pays tribute to a distinguished scholar but will also act as a catalyst for continued exploration and advancement in the dynamic and evolving landscape of quantitative methods for economics and business.