Inverse Gaussian Ornstein-Uhlenbeck Applied to Modeling High Frequency Data
Abstract
With about 226050 estimated deaths worldwide in 2010, earthquake is considered as one of the disasters that record a great number of deaths. This thesis develops a model for the estimation of magnitude of future seismic events. We propose a stochastic differential equation arising on the Ornstein-Uhlenbeck processes driven by Inverse Gaussian (a,b) process. Inverse Gaussian (a,b) Ornstein-Uhlenbeck processes offer analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to geophysics and financial stock market by fitting the superposed Inverse Gaussian (a,b) Ornstein-Uhlenbeck model to earthquake and financial time series.
Subject Area
Applied Mathematics
Recommended Citation
Kusi, Emmanuel Kofi, "Inverse Gaussian Ornstein-Uhlenbeck Applied to Modeling High Frequency Data" (2019). ETD Collection for University of Texas, El Paso. AAI22587598.
https://scholarworks.utep.edu/dissertations/AAI22587598