Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

G. Geoffrey Booth


This dissertation investigates the nonlinear dynamics of the returns generation process of individual stocks listed on national market system from national association of security dealers automated quotation system (NASDAQ/NMS) and compares them to a similar sample from New York Stock Exchange (NYSE). One of the most prominent tools that has emerged for characterizing nonlinear processes is the Autoregressive Conditional Heteroscedasticity (ARCH) model, and its various extensions, the most significant being the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. From the stocks listed on the Center for Research in Security Prices (CRSP) tapes, a group of NASDAQ/NMS and NYSE stocks are chosen for the analysis. Weekly data for the years 1982 to 1988 are used for this study. Various forms of existing GARCH models are applied on the same data set with conditional error distributions of normal, Student-t, power exponential and mixed jump-diffusion process. Although attempts at exploring the relative merits of the models have been made on the foreign exchange market, no such study exists for individual stock returns. The performance of each model is evaluated by several diagnostics on the respective error distributions and evaluation of log likelihood values. In a simulation study on non-nested testing GARCH-PE is found to be more flexible as compared to GARCH-T. Only 36% stocks of the given sample from each market can be modeled using GARCH. However, on forming portfolios, three out of four can be modeled using GARCH.