Asymptotic Filtering Theory for Univariate Arch Models

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...

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Bibliographic Details
Published in:Econometrica 1994-01, Vol.62 (1), p.1-41
Main Authors: Nelson, Daniel B., Foster, Dean P.
Format: Article
Language:English
Subjects:
Approximation
Brownian motion
Econometric models
Econometrics
Economic models
Economic theory
Efficiency
Estimates
Estimating techniques
Exact sciences and technology
Forecasting models
Inference from stochastic processes
time series analysis
Mathematical moments
Mathematics
Modeling
Parametric models
Perceptron convergence procedure
Probability and statistics
Random variables
Sciences and techniques of general use
Standard deviation
Statistical discrepancies
Statistics
Stochastic models
Studies
Working papers
Citations: Items that cite this one
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Summary: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).
ISSN:0012-9682
1468-0262
DOI:10.2307/2951474