Volatility clustering refers random or persistent nature of how market results drift together.
The ARCH/GARCH family models were used to examine the behavior of the volatility of the return. Factors like the weekend/holiday effect, leverage effects, and asymmetric response to news were looked at more closely. The GARCH model is a more generalized model of the ARCH model first introduced by professor, Robert Engle in 1982 to explain the volatility of inflation rates. The model is considered to be more appropriate for modeling high frequency financial assets and market return data. There are several versions of the GARCH model that have been proposed over the years. The ARCH process uses two equations, the mean and the variance equations. The model indicates that the conditional variance of a shock at time t is a function of the squares of past shocks, where the conditional variance needs to be nonnegative. The nonnegative aspect indicates that a positive or negative market move will result in a big increase in conditional variance. This process captures the conditional variance of financial market returns and it uses the assumption that today's conditional variance is a weighted average of past squared unexpected returns. Because ARCH model are difficult to estimate and has lagged forecasts, the GARCH model was proposed. It adds autoregressive terms to the equation and focuses on the time-varying variance of the distribution of returns.
Past studies suggest that volatility of returns is much higher in falling markets than it is in a rising market. That is the response to bad news has proven to be a greater magnitude that that of goods new in a market. In other words, the response to "good- news and "bad- news does not have a symmetric effect. This concept is referred to as the leverage effect. The asymmetric GARCH models are used to examine these leverage effects. Our authors chose to look at the TARCH and E-GARCH models.
