Date of Award
Doctor of Philosophy
The main purpose of this thesis is to examine and compare the Mixture of Distributions Hypothesis versus Autoregressive Conditional Heteroscedasticity (ARCH) models as an explanation for the distribution of stock returns and the relationship of returns to measures of trading activity. The conjecture has been made by Lamoureux and Lastrapes, (1990a), that ARCH modelling of stock returns does not contribute any information if a variable representing the rate of flow of information is accounted for in the variance of the stock return. This thesis directly challenges this conjecture.;Three measures of trading activity, namely, the number of intraday changes in the bid-ask quotes, the number of daily transactions, and the volume of shares traded, are examined and the relationship of these variables to the variance of stock returns is studied. These variables are used as proxies for the rate of flow of information about a specific stock and are modelled using both Exponential ARCH, (EARCH), and Generalized ARCH, (GARCH), models. The data sample consists of daily returns and daily trading activity variable data for twenty securities traded on the Toronto Stock Exchange and twenty securities traded on the New York Stock Exchange.;The results of this thesis show that when stock returns are modelled using a GARCH model that the addition of a trading activity variable in the variance portion of the GARCH model renders the ARCH components insignificant. However when the more general EARCH model is utilized, then both the ARCH components and the trading activity variable become significant. These results contradict the results of Lamoureux and Lastrapes and show the limitations of using the GARCH model to model stock returns over an extended period of time. Model selection criteria always select an EARCH model over a GARCH model demonstrating the superiority of EARCH modelling.;Concerning the trading activity variables, the results of this thesis show that the number of changes in the intraday quotes for a stock is the best measure for modelling the rate of flow of information about a specific stock. This conclusion is particularly strong for the Canadian stocks in the sample. The results on the proper trading activity variable to use is more mixed for the American data although changes in quotes is still shown to be preferred.;The results of this thesis are important for both modelling volatility of stock returns and for determining the distribution of stock returns. An accurate knowledge of the distribution of stock returns is critical for testing hypotheses concerning stock market variables, especially in an event study setting.
Nason, Richard Ronald, "Heteroscedasticity In Returns: Arch Effects Versus The Mixture Of Distributions Hypothesis" (1993). Digitized Theses. 2241.