ASYMPTOTIC FILTERING THEORY FOR UNIVARIATE ARCH MODELS

Many researchers have employed ARCH models to estimate conditional var iances and covariances. How successfully can ARCH models carry out thi s estimation when they are misspecified? This paper employs continuous record asymptotics to approximate the distribution of the measurement error. This allows us to (a) compare the efficiency of various ARCH m odels, (b) characterize the impact of different kinds of misspecificat ion (e.g., ''fat-tailed'' errors, misspecified conditional means) on e fficiency, and (c) characterize asymptotically optimal ARCH conditiona l variance estimates. We apply our results to derive optimal ARCH filt ers for three diffusion models, and to examine in detail the filtering properties of GARCH(1,1), AR(1) EGARCH, and the model of Taylor (1986 ) and Schwert (1989).