Asymptotically Optimal Smoothing with ARCH Models

Daniel B Nelson

Econometrica, 1996, vol. 64, issue 3, 561-73

Abstract: Suppose an observed time series is generated by a stochastic volatility model. As shown by D. B. Nelson (1992) and D. B. Nelson and D. P. Foster (1994), a misspecified ARCH model will often be able to consistently (as a continuous time limit is approached) estimate the unobserved volatility process using information in the lagged residuals. This paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals. In particular, this paper expands the optimal filtering results of Nelson and Foster (1994) and Nelson (1994) to smoothing and to filtering with a random initial condition. Copyright 1996 by The Econometric Society.

Date: 1996
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