Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models

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 t...

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Bibliographic Details
Published in:Econometrica 1997-05, Vol.65 (3), p.587-599
Main Authors: Newey, Whitney K., Steigerwald, Douglas G.
Format: Article
Language:English
Subjects:
Asymmetry
Consistent estimators
Density estimation
Econometrics
Economic models
Economic statistics
Efficiency
Efficiency loss
Empirical research
Estimators
Exact sciences and technology
Exchange rates
Foreign exchange rates
Heteroskedasticity
Identification
Mathematical economics
Mathematics
Non Gaussianity
Nonparametric inference
Parametric models
Probability and statistics
Rates of return
Regression analysis
Sciences and techniques of general use
Skewness
Statistical variance
Statistics
Stochastic models
Studies
Symmetry
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Summary: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 identification. 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.
ISSN:0012-9682
1468-0262
DOI:10.2307/2171754