Abstract
To avoid the risk of misspecification between homoscedastic and heteroscedastic models, we propose a combination method based on ordinary least-squares (OLS) and generalized least-squares (GLS) model-averaging estimators. To select optimal weights for the combination, we suggest two information criteria and propose feasible versions that work even when the variance-covariance matrix is unknown. The optimality of the method is proven under some regularity conditions. The results of a Monte Carlo simulation demonstrate that the method is adaptive in the sense that it achieves almost the same estimation accuracy as if the homoscedasticity or heteroscedasticity of the error term were known.
Highlights
Model averaging has been developed as an alternative to model selection
(2012), Liu and Okui (2013) and Zhang et al (2013, 2015) proposed model averaging methods that are still based on the ordinary least-squares (OLS) estimator, while Liu et al (2016) proposed a method based on the generalized least squares estimator (GLS)
We propose a combination method based on OLS and generalized least-squares (GLS) estimators to reduce the risk of misspecification between homoscedastic and heteroscedastic linear models
Summary
Model averaging has been developed as an alternative to model selection. In many situations, model-averaging methods perform better than alternative model-selection methods. For linear regression models with heteroscedastic errors, Hansen and Racine (2012), Liu and Okui (2013) and Zhang et al (2013, 2015) proposed model averaging methods that are still based on the OLS estimator, while Liu et al (2016) proposed a method based on the generalized least squares estimator (GLS). They demonstrated that their methods are optimal in the sense of. We propose a combination method based on OLS and GLS estimators to reduce the risk of misspecification between homoscedastic and heteroscedastic linear models.
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