NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Filtering and Forecasting with Misspecified Arch Models II: Making the Right Forecast with the Wrong Model

Daniel B. Nelson, Dean P. Foster

NBER Technical Working Paper No. 132
Issued in December 1992
NBER Program(s):   AP

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).

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Document Object Identifier (DOI): 10.3386/t0132

Published: Nelson, Daniel B. and Dean P. Foster. "Filtering And Forecasting With Misspecified ARCH Models: Making The Right Forecast With The Wrong Model," Journal of Econometrics, 1995, v67(2), 303-335.

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