Modeling Volatility Dynamics

Abstract

Good macroeconomic and financial theorists, like all good theorists, want to get the facts straight before theorizing; hence, the explosive growth in the methodology and application of time-series econometrics in the last twenty-five years. Many factors fueled that growth, ranging from important developments in related fields (see Box and Jenkins, 1970) to dissatisfaction with the “incredible identifying restrictions” associated with traditional macroeconometric models (Sims, 1980) and the associated recognition that many tasks of interest, such as forecasting, simply do not require a structural model (see Granger and Newbold, 1979). A short list of active subfields includes vector autoregressions, index and dynamic factor models, causality, integration and persistence, cointegration, seasonality, unobserved-components models, state-space representations and the Kalman filter, regime-switching models, nonlinear dynamics, and optimal nonlinear filtering. Any such list must also include models of volatility dynamics. Models of autoregressive conditional heteroskedasticity (ARCH), in particular, provide parsimonious approximations to volatility dynamics and have found wide use in macroeconomics and finance¹. The family of ARCH models is the subject of this chapter.