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Filtering and Forecasting with Misspecified Arch Models II: Making the Right Forecast with the Wrong Model

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Author Info
Daniel B. Nelson
Dean P. Foster

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Abstract

A companion paper (Nelson (1992)) showed that in data observed at high frequencies, an ARCH model may do a good job at estimating conditional variances, even when the ARCH model is severely misspecified. While such models may perform reasonably well at filtering (i.e., at estimating unobserved instantaneous conditional variances) they may perform disastrously at medium and long term forecasting. In this paper, we develop conditions under which a misspecified ARCH model successfully performs both tasks, filtering and forecasting. The key requirement (in addition to the conditions for consistent filtering) is that the ARCH model correctly specifies the functional form of the first two conditional moments of all state variables. We apply these results to a diffusion model employed in the options pricing literature, the stochastic volatility model of Hull and White (1987), Scott (1987), and Wiggins (1987).

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0132.

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Date of creation: Dec 1992
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Handle: RePEc:nbr:nberte:0132

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237. [Downloadable!] (restricted)
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  2. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265. [Downloadable!] (restricted)
  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  4. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  7. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December. [Downloadable!] (restricted)
  8. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January. [Downloadable!] (restricted)
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  9. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 61-90. [Downloadable!] (restricted)
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  1. Torben G. Andersen & Tim Bollerslev, 1997. "Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts," NBER Working Papers 6023, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Anders Tolver Jensen & Theis Lange, 2009. "On IGARCH and convergence of the QMLE for misspecified GARCH models," CREATES Research Papers 2009-06, School of Economics and Management, University of Aarhus. [Downloadable!]
  3. K.C. Chan & G. Andrew Karolyi & Rene M. Stulz, 1992. "Global Financial Markets and the Risk Premium on U.S. Equity," NBER Working Papers 4074, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Daniel B. Nelson, 1994. "Asymptotic Filtering Theory for Multivariate ARCH Models," NBER Technical Working Papers 0162, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. John W. Galbraith & Victoria Zinde-Walsh, 2000. "Properties of Estimates of Daily GARCH Parameters Based on Intra-Day Observations," Econometric Society World Congress 2000 Contributed Papers 1800, Econometric Society. [Downloadable!]
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  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  7. Torben G. Andersen & Tim Bollerslev, 1996. "DM-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies," NBER Working Papers 5783, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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