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Estimating Conditional Expectations When Volatility Fluctuates

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  • Robert F. Stambaugh

Abstract

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.

Suggested Citation

  • Robert F. Stambaugh, "undated". "Estimating Conditional Expectations When Volatility Fluctuates," Rodney L. White Center for Financial Research Working Papers 17-93, Wharton School Rodney L. White Center for Financial Research.
  • Handle: RePEc:fth:pennfi:17-93
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    References listed on IDEAS

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    10. Shmuel Kandel & Robert F. Stambaugh, "undated". "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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    Cited by:

    1. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    2. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    3. Paul Harrison & Harold H. Zhang, "undated". "Cyclical Variation in the Risk and Return Relation," Computing in Economics and Finance 1997 175, Society for Computational Economics.
    4. 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.
    5. James D. Hamilton, 2008. "Macroeconomics and ARCH," NBER Working Papers 14151, National Bureau of Economic Research, Inc.
    6. 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.
    7. Jacob Boudoukh & Matthew Richardson & Robert Whitelaw, 2005. "The Myth of Long-Horizon Predictability," NBER Working Papers 11841, National Bureau of Economic Research, Inc.
    8. 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.
    9. Jacob Boudouk & Matthew Richardson, 1994. "The Statistics Of Long‐Horizon Regressions Revisited1," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 103-119, April.
    10. 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.

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    JEL classification:

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

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