FILTERING AND FORECASTING WITH MISSPECIFIED ARCH MODELS .2. MAKING THE RIGHT FORECAST WITH THE WRONG MODEL

A companion paper (Nelson, 1992) showed that in data observed at high frequencies, an ARCH model may perform well in estimating the conditio nal variance of a process, even when the ARCH model is severely misspe cified, While such models may perform reasonably well at filtering (i. e., at estimating unobserved instantaneous conditional variances), the y may perform disastrously at medium- and long-term forecasting of the process and its volatility. In this paper, we develop conditions unde r which a misspecified ARCH model successfully performs both tasks, fi ltering and forecasting. The key requirement (in addition to the condi tions for consistent filtering) is that the ARCH model correctly speci fies the functional form of the first two conditional moments of all s tate variables. We apply these results to a diffusion model employed i n the options pricing literature, the stochastic volatility model of H ull and White (1987), Scott (1987), and Wiggins (1987).