Award Date


Degree Type


Degree Name

Master of Science (MS)


Mathematical Sciences

First Committee Member

Chih-Hsiang Ho

Second Committee Member

Amei Amei

Third Committee Member

Kaushik Ghosh

Fourth Committee Member

Hualiang Teng

Number of Pages



The financial health of the banking industry is an important prerequisite for economic stability and growth. Bank failures in the United States have run in cycles largely associated with the collapse of economic bubbles. The number of bank failures has increased dramatically over the last thirty years (Halling and Hayden, 2007). In this thesis, we try to address the following two questions: 1) What is the relationship, if any, between a bank's asset size and its likelihood of failures? 2) How can we use statistical tools to predict the numbers of bank failures in the future? Various modeling techniques are proposed and applied to bank failure data from Federal Deposit Insurance Corporation. For the first question, we find that there is a relationship between bank size and bank failure status based on the Pearson's chi-square test. To answer the second question, first, logistic regression is applied to the bank failure data, and the corresponding prediction rule and prediction results are obtained. Second, we develop the empirical recurrence rate (Ho, 2008) and empirical recurrence rates ratio time series for the given data, and also perform corresponding theoretical and graphical analysis on both of them. We obtained much valuable information on the reason for, time period of, and trends of bank failures in the past thirty years. We perform pairwise bank failure rate comparisons using the conditional test (Przyborowski and Wilenski, 1940). Additionally, based on the smooth behavior of empirical recurrence rate and empirical recurrence rates ratio time series, we apply autoregressive fractional integrated moving average models to both of the series for forecasting purposes. Finally, some interesting results are discussed.


Bank assets; Bank failures; Bank failures – Forecasting; Business enterprises – Size; United States


Analysis | Applied Statistics | Economic Policy | Finance | Finance and Financial Management