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

Lu Lu, Ph.D.

Committee Member

Kandethody Ramachandaran, Ph.D.

Committee Member

Yicheng Tu, Ph.D.


Asset Allocation, K-th Moving Average GARCH, MACBETH, Multi-Level Time Series Clustering


The Capital Asset Pricing Model combined with the Sharpe ratio is a standard method for choosing assets for selection in a portfolio. However, this method has many structural issues and was designed for a time when high dimensional computing was in its infancy. An alternative to these methods using a mix of Multi-Level Time Series Clustering, the MACBETH algorithm and traditional time series techniques was constructed that minimized data loss and allow for customized portfolio construction for investors with different risk profiles and specialized investment needs. It was shown that these methods are adaptable to cloud computing environments and allow for modular customization as needed, while also being quite powerful and adaptable as developed. These approaches extend the risk-return foundation of finance into a risk-return-suitability framework that is more in line with the methods being used by most financial practitioners and regulators.

In addition to methods for portfolios, new techniques for the selection, screening, and analysis of individual assets were developed. The K-th Moving Average approach to ARIMA forecasting (2007) was extended for volatility forecasting to allow for estimation in a GARCH environment. New analysis techniques to combine these methods with machine learning methods were also developed and shown to yield unique insights into the decomposition of signal performance.

The new proposed approaches are data-driven analytical characterizations that combine theory and practice to generate new characterizations and insights into the workings of financial markets and systems by using a mix of existing methods with newly develvi oped techniques. These new methods develop allow for a more sophisticated approach to the understanding of risk and volatility on multiple levels with broad applications.