The Econometric Society An International Society for the Advancement of Economic Theory in its Relation to Statistics and Mathematics
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January 1994 - Volume 62 Issue 1 Page 1 - 41


Asymptotic Filtering Theory for Univariate Arch Models

Daniel B. Nelson
Dean P. Foster


Many researchers have employed ARCH models to estimate conditional variances and covariances. How successfully can ARCH models carry out this 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 models, (b) characterize the impact of different kinds of misspecification (e.g., "fat-tailed" errors, misspecified conditional means) on efficiency, and (c) characterize asymptotically optimal ARCH conditional variance estimates. We apply our results to derive optimal ARCH filters 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).

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