Asymptotically Optimal Smoothing with ARCH Models

Daniel B. Nelson

No 161, NBER Technical Working Papers from National Bureau of Economic Research, Inc

Abstract: Suppose an observed time series is generated by a stochastic volatility model-i.e., there is an unobservable state variable controlling the volatility of the innovations in the series. As shown by Nelson (1992), and Nelson and 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.

JEL-codes: C32 (search for similar items in EconPapers)
Date: 1994-08
Note: AP
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Citations: View citations in EconPapers (76)

Published as Nelson, Daniel B. "Asymptotically Optimal Smoothing With ARCH Models," Econometrica, 1996, v64(3,May), 561-573.

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