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Asymptotically Optimal Smoothing with ARCH Models

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  • Nelson, Daniel B

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.

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  • Nelson, Daniel B, 1996. "Asymptotically Optimal Smoothing with ARCH Models," Econometrica, Econometric Society, vol. 64(3), pages 561-573, May.
    • Handle: RePEc:ecm:emetrp:v:64:y:1996:i:3:p:561-73
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    Cited by:

    1. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    2. Hwang, Soosung & Satchell, Stephen E., 2000. "Market risk and the concept of fundamental volatility: Measuring volatility across asset and derivative markets and testing for the impact of derivatives markets on financial markets," Journal of Banking & Finance, Elsevier, vol. 24(5), pages 759-785, May.
    3. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
    4. Gopal Basak & Mrinal Ghosh & Diganta Mukherjee, 2011. "Influence of Big Traders on the Stock Market: Theory and Simulation," Dynamic Games and Applications, Springer, vol. 1(2), pages 220-252, June.
    5. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    6. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    7. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    8. Eduardo Rossi, 2010. "Univariate GARCH models: a survey (in Russian)," Quantile, Quantile, issue 8, pages 1-67, July.
    9. Tu, Anthony H. & Wang, Ming-Chun, 2007. "The innovations of e-mini contracts and futures price volatility components: The empirical investigation of S&P 500 stock index futures," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 17(2), pages 198-211, April.
    10. F. Campigli & G. Bormetti & F. Lillo, 2022. "Measuring price impact and information content of trades in a time-varying setting," Papers 2212.12687, arXiv.org, revised Dec 2023.

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