Assessment and Analysis of Trading Volume and Return Volatility Relationship on Dow Jones Index Using Stable Paretian GARCH and Threshold GARCH Models

Many models in finance are often based on the assumption that the random variables follow a
Gaussian distribution. It is now well known that empirical data have frequently occurring extreme
values and cannot be modeled with the Gaussian distribution. The stable distributions, a class of
probability distributions that allow skewness and heavy tails, have received great interest in the last
decade because of their success in modeling financial data that depart from the Gaussian distribution.
This paper examines the volatility of Dow Jones Industrial Average stock returns and the trading
volume by employing stable Paretian GARCH and Threshold GARCH (TGARCH) models. Our results
indicate that the trading volume significantly contributes to the volatility of stock returns. Additionally,
strong leverage effects exist with negative shocks having a larger impact on volatility than positive
shocks. The likelihood ratio tests and goodness of fit support the use of stable Paretian GARCH and
TGARCH models over Gaussian models.