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Asymptotic Filtering Theory for Univariate ARCH Models

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  • Nelson, Daniel B
  • Foster, Dean P

Abstract

Researchers often employ ARCH models to estimate conditional variances and covariances. How successfully can misspecified ARCH models carry out this estimation? This paper employs continuous record asymptotics to approximate the distribution of the measurement error. This allows the authors to (1) compare the efficiency of various ARCH models, (2) characterize the impact of different kinds of misspecification on efficiency, and (3) characterize asymptotically optimal ARCH conditional variance estimates. They apply their 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 S. Taylor (1986) and G. W. Schwert (1989). Copyright 1994 by The Econometric Society.

Suggested Citation

  • Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
  • Handle: RePEc:ecm:emetrp:v:62:y:1994:i:1:p:1-41
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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