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Estimating Conditional Expectations when Volatility Fluctuates

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Robert F. Stambaugh

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Abstract

Asymptotic variance of estimated parameters in models of conditional expectations are calculated analytically assuming a GARCH process for conditional volatility. Under such heteroskedasticity, OLS estimators or parameters in single-period models can posses substantially larger asymptotic variances the GMM estimators employing additional multiperiod moment conditions - an approach yielding no efficiency gain under homoskedasticity. In estimating models of long- horizon expectations, the VAR approach provides an efficiency advantage over long-horizon regressions under homoskedasticity, but that ordering can reverse under heteroskedasticity, especially when the conditional mean and variance are both persistent. In such cases, the VAR approach maintains a slight efficiency advantage if the OLS estimator is replaced by an alternative GMM estimator. Heteroskedasticity can increase dramatically the apparent asymptotic power advantages of long-horizon regressions to reject constant expectations against persistent alternatives.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0140.

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Date of creation: Aug 1993
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Handle: RePEc:nbr:nberte:0140

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C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General

References listed on IDEAS
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  1. Hansen, Lars Peter & Singleton, Kenneth J, 1996. "Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 53-68, January.
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  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. 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)
  4. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October. [Downloadable!] (restricted)
  5. Geweke, John, 1981. "The Approximate Slopes of Econometric Tests," Econometrica, Econometric Society, vol. 49(6), pages 1427-42, November. [Downloadable!] (restricted)
  6. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 5(3), pages 357-86. [Downloadable!] (restricted)
  7. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113. [Downloadable!] (restricted)
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  8. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December. [Downloadable!] (restricted)
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  9. Frederic S. Mishkin, 1991. "Does Correcting for Heteroskedasticity Help?," NBER Technical Working Papers 0088, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-79, March. [Downloadable!] (restricted)
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  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  12. Richardson, Matthew & Smith, Tom, 1991. "Tests of Financial Models in the Presence of Overlapping Observations," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(2), pages 227-54. [Downloadable!] (restricted)
  13. Shmuel Kandel & Robert F. Stambaugh, . "Modeling Expected Stock Returns for Long and Short Horizons," Rodney L. White Center for Financial Research Working Papers 42-88, Wharton School Rodney L. White Center for Financial Research.
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  1. Stanislav Anatolyev, 2005. "Optimal Instruments in Time Series: A Survey," Working Papers w0069, Center for Economic and Financial Research (CEFIR). [Downloadable!]
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  2. James D. Hamilton, 2008. "Macroeconomics and ARCH," NBER Working Papers 14151, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Jacob Boudoukh & Matthew Richardson & Robert Whitelaw, 2005. "The Myth of Long-Horizon Predictability," NBER Working Papers 11841, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Paul Harrison & Harold H. Zhang, . "Cyclical Variation in the Risk and Return Relation," Computing in Economics and Finance 1997 175, Society for Computational Economics. [Downloadable!]
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