Asymptotically Optimal Smoothing with ARCH Models
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.
|Date of creation:||Aug 1994|
|Publication status:||published as Nelson, Daniel B. "Asymptotically Optimal Smoothing With ARCH Models," Econometrica, 1996, v64(3,May), 561-573.|
|Contact details of provider:|| Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.|
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- Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
- Daniel B. Nelson, 1994. "Asymptotic Filtering Theory for Multivariate ARCH Models," NBER Technical Working Papers 0162, National Bureau of Economic Research, Inc.
- Ghysels, E. & Harvey, A. & Renault, E., 1996.
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
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NBER Technical Working Papers
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"Asymptotic Filtering Theory for Univariate ARCH Models,"
Econometric Society, vol. 62(1), pages 1-41, January.
- Daniel B. Nelson & Dean P. Foster, 1994. "Asypmtotic Filtering Theory for Univariate Arch Models," NBER Technical Working Papers 0129, National Bureau of Economic Research, Inc.
- Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
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