Optimal instrumental variables estimation for ARMA models

In this paper a new class of instrumental variables (IV) estimators for linear processes and in particular ARMA models is developed. Previously, IV estimators based on lagged observations as instruments have been used to account for unmodelled MA(q) errors in the estimation of the AR parameters. Here it is shown that these IV methods can be used to improve efficiency of linear time series estimators in the presence of unmodelled conditional heteroskedasticity. Moreover, an IV estimator for both the AR and MA part is developed. Estimators based on a Gaussian likelihood are inefficient members of the class of IV estimators analyzed here when the innovations are conditionally heteroskedastic.