Inverse Gaussian Ornstein-Uhlenbeck Applied to Modeling High Frequency Data

Emmanuel Kofi Kusi, University of Texas at El Paso

Abstract

With about 226050 estimated deaths worldwide in 2010, an earthquake is considered as one of the disasters that records 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 IG(a,b) process. IG(a,b) Ornstein-Uhlenbeck processes offers 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 markets by fitting the superposed IG(a,b) Ornstein-Uhlenbeck model to earthquake and financial time series.

Subject Area

Applied Mathematics|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. AAI22617710.
https://digitalcommons.utep.edu/dissertations/AAI22617710

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