Measuring Volatility Dynamics

Recently there has been a great deal of interest in modeling volatility fluctuations. ARCH models, for example, provide parsimonious approximations to volatility dynamics. Here we provide a selective amount of certain aspects of conditional volatility modeling that are of particular relevance in macroeconomics and finance. First, we sketch the rudiments of a rather general univariate time- series model, allowing for dynamics in both the conditional mean and variance. Second, we discuss both the economic and statistical motivation for the models, we characterize their properties, and we discuss issues related to estimation and testing. Finally, we discuss a variety of applications and extensions of the basic models.