NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Asypmtotic Filtering Theory for Univariate Arch Models

Daniel B. Nelson, Dean P. Foster

NBER Technical Working Paper No. 129
Issued in April 1994
NBER Program(s):   AP

This paper builds on this earlier work by deriving the asymptotic distribution of the measurement error. This allows us to approximate the measurement accuracy of ARCH conditional variance estimates and compare the efficiency achieved by different ARCH models. We are also able to characterize the relative importance of different kinds of misspecification; for example, we show that misspecifying conditional means adds only trivially (at least asymptotically) to measurement error, while other factors (for example, capturing the "leverage effect," accommodating thick tailed residuals, and correctly modelling the variability of the conditional variance process) are potentially much more important. Third, we are able to characterize a class of asymptotically optimal ARCH conditional variance estimates.

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Document Object Identifier (DOI): 10.3386/t0129

Published: Econometrica, Vol. 62, no. 1, pp. 1-41 (January 1994).

Users who downloaded this paper also downloaded these:
Nelson and Foster t0132 Filtering and Forecasting with Misspecified Arch Models II: Making the Right Forecast with the Wrong Model
Nelson t0162 Asymptotic Filtering Theory for Multivariate ARCH Models
 
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