Estimating Conditional Expectations When Volatility Fluctuates

40 Pages Posted: 25 May 2006 Last revised: 10 Jun 2007

See all articles by Robert F. Stambaugh

Robert F. Stambaugh

University of Pennsylvania - The Wharton School; National Bureau of Economic Research (NBER)

Date Written: August 1993


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.

Suggested Citation

Stambaugh, Robert F., Estimating Conditional Expectations When Volatility Fluctuates (August 1993). NBER Working Paper No. t0140. Available at SSRN:

Robert F. Stambaugh (Contact Author)

University of Pennsylvania - The Wharton School ( email )

The Wharton School, Finance Department
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United States
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