Term of Award

Fall 2017

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)


Department of Mathematical Sciences

Committee Chair

Tharanga Wickramarachchi

Committee Member 1

Stephen Carden

Committee Member 2

Arpita Chatterjee


This thesis explores how arc length can be modeled and used to measure the risk involved with a financial time series. Having arc length as a measure of volatility can help an investor in sorting which stocks are safer/riskier to invest in. A Gamma autoregressive model of order one(GAR(1)) is proposed to model arc length series. Kernel regression based bias correction is studied when model parameters are estimated using method of moment procedure. As an application, a model-based clustering involving thirty different stocks is presented using k-means++ and hierarchical clustering techniques.

Research Data and Supplementary Material