Date of Graduation


Document Type


Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level



Statistics and Analytics


Giovanni Petris

Committee Member

Avishek Chakraborty

Second Committee Member

Sean Plummer


This paper compares the predictive performance of two commonly used financial models, the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model, and the Stochastic Volatility model. Both techniques are used in the finance literature to model returns on an asset; the main difference between the two is that the former holds volatility as deterministic, whereas the latter treats it as a stochastic component. Three 10-year periods (2006-15, 2008-17, and 2010-19) of returns of the S&P-500 Index are used to train the two models. The parameter estimation is done using Hamiltonian Monte Carlo. Then, using Sequential Monte Carlo updates, returns for 2016, 2018, and 2020 are predicted, and their performance over different time frames—one month, one quarter, and one year—are compared using sum of squared errors (SSE). In addition, the percentage of observed returns for the three years that are captured between the 2.5 percentile and the 97.5 percentile of the predictions are compared. The results of the two models are practically indistinguishable by both criteria.