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

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  • Nelson, Daniel B.

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.

Suggested Citation

  • Nelson, Daniel B., 1996. "A Note on the Normalized Errors in ARCH and Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 12(1), pages 113-128, March.
    • Handle: RePEc:cup:etheor:v:12:y:1996:i:01:p:113-128_00
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    Cited by:

    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," Multinational Finance Journal, Multinational Finance Journal, vol. 4(3-4), pages 159-179, September.
    2. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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