In this paper an expression for the bias implied by prediction error methods (weighted least squares methods) in both i.i.d. samples and time series models with heteroscedasticity is derived provided that explicit expression for the (conditional) mean and variance are available. It is shown that prediction error methods including weighted least squares methods fit within the general theory of estimating functions, which facilitates the derivation of optimal weights in the sense of (Heyde, 1997) such that the properties of estimators, in particular unbiasedness, optimality and efficiency, obtained by using these methods may be discussed. Four examples are provided.
Estimating theory; Optimal estimation; Maximum likelihood; Parameter estimation; Prediction error methods; Weighted least-squares.