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Article
Asymptotic Bias for Quasi-Maximum Likelihood Estimators in Models with Conditional Heteroskedasticity
Econometrica (1997)
  • Douglas G Steigerwald, University of California, Santa Barbara
  • Whitney Newey
Abstract
Virtually all applications of time-varying conditional variance models use a quasi-maximum likelihood estimator (QMLE). Consistency of a QMLE requires an identification condition that the quasi-log-likelihood have a unique maximum at the true conditional mean and relative scale parameters. We show that the identification condition holds for a non-Gaussian QMLE if the conditional mean is identically zero or if a symmetry condition is satisfied. Without symmetry an additional parameter, for the location of the innovation density, must be added for consistency. We calculate the efficiency loss from adding such a parameter under symmetry, when the parameter is not needed. We also show that there is no efficiency loss for the conditional variance parameters of a GARCH process.
Keywords
  • conditional heteroskedasticity,
  • consistency,
  • quasi-maximum likelihood
Publication Date
1997
Citation Information
Douglas G Steigerwald and Whitney Newey. "Asymptotic Bias for Quasi-Maximum Likelihood Estimators in Models with Conditional Heteroskedasticity" Econometrica Vol. 65 Iss. 3 (1997)
Available at: http://works.bepress.com/douglas_steigerwald/10/