Exploring the Fractal Geometry of Financial Time Series

Abstract

Fractal geometry has emerged as a powerful tool for understanding complex and irregular structures in various domains, including finance. In this paper, we delve into the application of fractal geometry to analyze financial time series data. We begin by providing an overview of fractal geometry concepts and its relevance to understanding the dynamics of financial markets. Subsequently, we explore different fractal dimensions and their implications for characterizing the self-similarity and scaling properties of financial time series. We investigate how fractal geometry can be used to detect patterns, trends, and anomalies in financial data, offering insights into market behavior and potential forecasting capabilities. Furthermore, we discuss the challenges and limitations associated with applying fractal geometry to financial time series analysis, such as data noise, non-stationarity, and parameter estimation. Finally, we conclude with future directions and potential avenues for further research in this exciting and interdisciplinary field at the intersection of mathematics and finance.