Theses and Dissertations

Date of Award

5-1-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Zhuanzhuan Ma

Second Advisor

Hyung Won Kim

Third Advisor

Tamer Oraby

Abstract

Financial markets often undergo abrupt structural changes driven by political, economic, and geopolitical events, leading to substantial volatility. Detecting such change-points is crucial for identifying structural breaks, improving risk management, and enhancing forecasting performance in financial time series. This study proposes a Bayesian change-point detection framework that incorporates both the t-shrinkage prior and the Horseshoe shrinkage prior. These priors enforce strong regularization on successive differences in mean parameters, enabling the identification of piecewise constant structures in time series data. Posterior inference is conducted using Markov Chain Monte Carlo (MCMC) methods, specifically a Gibbs sampling algorithm, which iteratively samples from the conditional posterior distributions of all model parameters. This approach allows for efficient and accurate estimation of change-points. The proposed method is evaluated using both simulated datasets and real financial data. Empirical applications include cumulative returns from the Standard & Poor’s 500 Index (S&P 500) spanning January 3, 2022 to February 2, 2026, and Bitcoin-USD data from January 2, 2025 to February 2, 2026.

Comments

Copyright 2026 Yosalin Sanchez. All Rights Reserved. https://proquest.com/docview/3371131635

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