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Estimating Conditional Expectations When Volatility Fluctuates

  • Robert F. Stambaugh

Asymptotic variances of estimated parameters in models of conditional expectations are calculated analytically assuming a GARCH process for conditional volatility. Under such heteroskedasticity, OLS estimators of parameters in single-period models can possess substantially larger asymptotic variances than 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 Wharton School Rodney L. White Center for Financial Research in its series Rodney L. White Center for Financial Research Working Papers with number 17-93.

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Handle: RePEc:fth:pennfi:17-93
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  1. Frederic S. Mishkin, 1991. "Does Correcting for Heteroskedasticity Help?," NBER Technical Working Papers 0088, National Bureau of Economic Research, Inc.
  2. John Y. Campbell, 1990. "A Variance Decomposition for Stock Returns," NBER Working Papers 3246, National Bureau of Economic Research, Inc.
  3. 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.
  4. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
  5. 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.
  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.
  7. Donald B. Keim & Robert F. Stambaugh, . "Predicting Returns in the Stock and Bond Markets," Rodney L. White Center for Financial Research Working Papers 15-85, Wharton School Rodney L. White Center for Financial Research.
  8. Lars Peter Hansen & Kenneth J. Singleton, 1997. "Efficient Estimation of Linear Asset Pricing Models with Moving-Average Errors," NBER Technical Working Papers 0086, National Bureau of Economic Research, Inc.
  9. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-63, May.
  10. Geweke, John, 1981. "The Approximate Slopes of Econometric Tests," Econometrica, Econometric Society, vol. 49(6), pages 1427-42, November.
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  12. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  14. 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.
  15. Richardson, Matthew & Smith, Tom, 1991. "Tests of Financial Models in the Presence of Overlapping Observations," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 227-54.
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