Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis Ltd in Econometric Reviews
- Vol. 11 (2), 143-172
- https://doi.org/10.1080/07474939208800229
Abstract
We study the properties of the quasi-maximum likelihood estimator (QMLE) and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood os maximized but the assumption of normality is violated. Because the score of the normal log-likelihood has the martingale difference property when the forst two conditional moments are correctly specified, the QMLE is generally Consistent and has a limiting normal destribution. We provide easily computable formulas for asymptotic standard errors that are valid under nonnormality. Further, we show how robust LM tests for the adequacy of the jointly parameterized mean and variance can be computed from simple auxiliary regressions. An appealing feature of these robyst inference procedures is that only first derivatives of the conditional mean and variance functions are needed. A monte Carlo study indicates that the asymptotic results carry over to finite samples. Estimation of several AR and AR-GARCH time series models reveals that in most sotuations the robust test statistics compare favorably to the two standard (nonrobust) formulations of the Wald and IM tests. Also, for the GARCH models and the sample sizes analyzed here, the bias in the QMLE appears to be relatively small. An empirical application to stock return volatility illustrates the potential imprtance of computing robust statistics in practice.Keywords
This publication has 36 references indexed in Scilit:
- Matrix Differential Calculus with Applications in Statistics and Econometrics.Biometrics, 1988
- ON THE FIRST–ORDER EFFICIENCY AND ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS OBTAINED FROM DEPENDENT OBSERVATIONSStatistica Neerlandica, 1986
- Generalized autoregressive conditional heteroskedasticityJournal of Econometrics, 1986
- Asymptotic Theory for ARCH Models: Estimation and TestingEconometric Theory, 1986
- Modelling the persistence of conditional variancesEconometric Reviews, 1986
- A Unified Theory of Consistent Estimation for Parametric ModelsEconometric Theory, 1985
- Small-Sample Properties of ARCH Estimators and TestsCanadian Journal of Economics/Revue canadienne d'économique, 1985
- ARMA MODELS WITH ARCH ERRORSJournal of Time Series Analysis, 1984
- More Efficient Estimation in the Presence of Heteroscedasticity of Unknown FormEconometrica, 1983
- Regression Analysis when the Variance of the Dependent Variable is Proportional to the Square of its ExpectationJournal of the American Statistical Association, 1973