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Estimating Conditional Expectations when Volatility Fluctuates

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  • Robert F. Stambaugh

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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  1. Geweke, John, 1981. "The Approximate Slopes of Econometric Tests," Econometrica, Econometric Society, vol. 49(6), pages 1427-42, November.
  2. 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.
  3. Baillie, R.T. & Bollerslev, R.T., 1990. "Prediction In Dynamic Models With Time Dependent Conditional Variances," Papers 8815, Michigan State - Econometrics and Economic Theory.
  4. 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.
  5. 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.
  6. John Y. Campbell, 1990. "A Variance Decomposition for Stock Returns," NBER Working Papers 3246, National Bureau of Economic Research, Inc.
  7. Mishkin, Frederic S., 1990. "Does correcting for heteroscedasticity help?," Economics Letters, Elsevier, vol. 34(4), pages 351-356, December.
  8. 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.
  9. 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.
  10. 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.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. 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.
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Cited by:
  1. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, 02.
  2. Edmonds, Radcliffe Jr. & So, Jacky Y. C., 2004. "Is exchange rate volatility excessive? An ARCH and AR approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(1), pages 122-154, February.
  3. Jacob Boudoukh & Matthew Richardson & Robert F. Whitelaw, 2008. "The Myth of Long-Horizon Predictability," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1577-1605, July.
  4. Jacob Boudoukh & Matthew Richardson & Robert Whitelaw, 2005. "The Myth of Long-Horizon Predictability," NBER Working Papers 11841, National Bureau of Economic Research, Inc.
  5. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 459-491, December.
  6. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  7. James D. Hamilton, 2008. "Macroeconomics and ARCH," NBER Working Papers 14151, National Bureau of Economic Research, Inc.
  8. Paul Harrison & Harold H. Zhang, . "Cyclical Variation in the Risk and Return Relation," Computing in Economics and Finance 1997 175, Society for Computational Economics.

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