Performance Classification of Ornstein-Uhlenbeck-Type Models Using Fractal Analysis of Time Series Data
This dissertation aims to assess the performance of Ornstein-Uhlenbeck models by examining the fractal characteristics of time series data from various sources, including finance, volcanic and earthquake events, US COVID-19 reported cases and deaths, and two simulated time series with differing properties. The time series data is categorized as either a Gaussian or a L´evy process (L´evy walk or L´evy flight) by using three scaling methods: Rescaled range analysis, Detrended fluctuation analysis, and Diffusion entropy analysis. The outcomes of this analysis indicate that the financial indices are classified as L´evy walks, while the volcanic, earthquake and COVID-19 data are classified as L´evy flights. The two simulated Brownian motions are classified as Gaussian processes, as expected. The simulation results of the time series using Ornstein-Uhlenbeck models emphasize the need for selecting an appropriate background driving process, combining solutions of Ornstein-Uhlenbeck-type SDEs, and considering the correlations between time series events to improve the performance of the Ornstein-Uhlenbeck type models.
Asante, Peter Kwadwo, "Performance Classification of Ornstein-Uhlenbeck-Type Models Using Fractal Analysis of Time Series Data" (2023). ETD Collection for University of Texas, El Paso. AAI30417375.