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A Note on the Normalized Errors in ARCH and Stochastic Volatility Models

Published online by Cambridge University Press:  11 February 2009

Daniel B. Nelson
Daniel B. Nelson
Affiliation:
University of Chicago and National Bureau of Economic Research
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Abstract

It is well-known that conditional heteroskedasticity thickens the tails of the unconditional distribution of an error term relative to its conditional distribution. To what extent do imperfect forecasts of the conditional variance undo this tail thickening? This note considers the effect of changing the quality of the information embodied in a forecast of a conditional variance. Adding noise of a certain form thickens the tails of the normalized errors, but decreasing the amount of information used in the forecast may or may not thicken the tails. We also explore the relation between tail thickness and various notions of “optimal” volatility forecasts. The relationship is surprisingly complicated.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 1 , March 1996 , pp. 113 - 128
Copyright
Copyright © Cambridge University Press 1996

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