Statistics Papers

Document Type

Journal Article

Date of this Version

4-1992

Publication Source

Journal of Econometrics

Volume

52

Issue

1-2

Start Page

61

Last Page

90

DOI

10.1016/0304-4076(92)90065-Y

Abstract

A companion paper (Nelson (1992)) showed that in data observed at high frequencies, an ARCH model may do a good job at estimating conditional variances, even when the ARCH model is severely misspecified. While such models may perform reasonably well at filtering (i.e., at estimating unobserved instantaneous conditional variances) they may perform disastrously at medium and long term forecasting. In this paper, we develop conditions under which a misspecified ARCH model successfully performs both tasks, filtering and forecasting. The key requirement (in addition to the conditions for consistent filtering) is that the ARCH model correctly specifies the functional form of the first two conditional moments of all state variables. We apply these results to a diffusion model employed in the options pricing literature, the stochastic volatility model of Hull and White (1987), Scott (1987), and Wiggins (1987).

Copyright/Permission Statement

© 1992. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

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Date Posted: 27 November 2017

This document has been peer reviewed.