Arch models

This chapter evaluates the most important theoretical developments in ARCH type modeling of time-varying conditional variances. The coverage include the specification of univariate parametric ARCH models, general inference procedures, conditions for stationarity and ergodicity, continuous time methods, aggregation and forecasting of ARCH models, multivariate conditional covariance formulations, and the use of model selection criteria in an ARCH context. Additionally, the chapter contains a discussion of the empirical regularities pertaining to the temporal variation in financial market volatility. Motivated in part by recent results on optimal filtering, a new conditional variance model for better characterizing stock return volatility is also presented.