Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Dr. Colin Gallagher, Dr. Whitney Huang

Committee Member

Dr. William Bridges

Committee Member

Dr. Brook Russell


This dissertation delves into the concept of risk, specifically focusing on two prominent categories: financial risk and environmental risk.

Financial risk is the probability of unfavorable outcomes of an investment while environmental risk refers to the possible harm to the environment resulting from extreme weather events. More specifically, risk is the high (low) quantiles of the distribution of variables of interest. \\ To quantify and assess uncertainties in financial and environmental risk, robust and reliable methodologies are needed. The aim of this dissertation is to develop some risk assessment methods and compare them with the widely used methodologies in both finance and the environment. The exploration utilizes well-established metrics Value-at-risk (VaR) and expected shortfall (ES) for quantifying financial risk and Return Level (RL) or conditional quantiles for quantifying environmental risk. All of these concepts can be derived from conditional loss distribution as VaR and RL are the specific percentile of the loss distribution and ES is the expected value of all losses exceeding the VaR.

This study initiates by proposing a novel non-parametric local linear quantile autoregression (LLQAR) approach for financial risk. The performance of these methods is evaluated through a Monte Carlo simulation study and real-world data analysis, employing criteria such as root mean squared error and multiple backtests. The LLQAR method emerges as a competitive performer for estimating VaR and ES, especially for non-stationary data.Extending this scope to environmental risk, the study introduces two innovative novel models: SS-ARMA-GPD (Seasonally Standardized Auto Regressive Moving Average Generalized Pareto Distribution) and SS-LLQAR (Seasonally Standardized Local Linear Quantile Autoregressive) to estimate extreme wind speed particularly, one step ahead high conditional quantiles. To effectively model the time-varying conditional distribution, it is crucial to comprehend the temporal mean (e.g., seasonal variations) and the related dependence structures, including their respective distributions. These models consider temporal mean, seasonal variations, and dependence structures in the data. A Monte Carlo simulation study and an application to real daily wind speed data are rigorously performed to investigate the estimation performance. Different evaluation metrics are employed to judge the estimation accuracy. Evaluation metrics and comparative analysis reveal the superior performance of SS-ARMA-GPD in simulation scenarios, while SS-LLQAR demonstrates comparable performance in real-world applications.

In summary, the dissertation contributes novel methodologies for risk estimation in both financial and environmental contexts. It highlights the promise of the non-parametric LLQAR method while suggesting areas for future refinement, such as improving bandwidth selection. The dissertation also suggests potential extensions to spatio-temporal data and the integration of machine learning and deep learning algorithms with the LLQAR approach for enhancing accuracy and adaptability.

Available for download on Tuesday, December 31, 2024