Asymptotically Optimal Smoothing with ARCH Models
Daniel B. Nelson
NBER Technical Working Paper No. 161
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.
Published: Nelson, Daniel B. "Asymptotically Optimal Smoothing With ARCH Models," Econometrica, 1996, v64(3,May), 561-573.