Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Kandethody Ramachandran, Ph.D.

Committee Member

Lu Lu, Ph.D.

Committee Member

Dan Shen, Ph.D.


Risk, Time Series, Rainfall, Tourism


The objectives of the study are to review and evaluate four basic risk models that are commonly used in investment science; statistically investigate the risk factor in Capital Asset Pricing Model (CAPM) that is used to reflect the safety of an investment decision in stocks; explore the statistical distribution of monthly precipitation in Belize and to forecast tourist arrivals using statistical time series modelling techniques.

The risk models are the Capital Asset Pricing Model (Sharpe-Linter Version), Capital Asset Pricing Model (Conditional Version), Arbitrage Pricing Theory, and Fama–French three-factor model adopted in empirical investigations of asset pricing. The underlying assumptions of using these models are reviewed, and the statistical procedures to evaluate their robustness are reviewed.

It will be shown that the present manner of determining this risk factor is quite sensitive and misleading. We introduce a statistical procedure for obtaining a more robust measure of the risk factor commonly referred to as CAPM beta.

Changes in the hydrological cycle will generate repercussions in all sectors. It is therefore imperative that Belize’s water resources be managed in an integrated manner, responding to the requirements of all sectors. Daily rainfall data have been collected for a period of 51 years (1960– 2011) from The National Meteorological Service of Belize. The Wakeby distribution adequately fit the monthly rainfall data producing a suitable model based on the Kolmogorov – Smirnov test.

Tourism is vitally important to the entire Belize’s economy, contributing 50% of Belize's gross domestic product in 2015. It is the foremost foreign exchange earner in this small economy, followed by exports of marine products, citrus, cane sugar, bananas, and garments. The tourist sector is not without its vulnerabilities and is subject to international economic vagaries. In order to meet the expected future demands on the industry in terms of service delivery it is important that the sector understands the significance of forecasting.