Optimal Instrumental Variables Estimation for Arma Models

Abstract

In this paper a new class of Instrumental Variables estimator 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 those 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 parts is developed. One consequence of these results is that Gaussian estimators for linear time series models are inefficient members of this IV class. A leading example of an inefficient member is the OLS estimator for AR(p) models which is known to be efficient under homoskedasticity.

Keywords: ARMA, conditional heteroskedasticity, insgtrumental variables, efficiency lower-bound, frequency domain

JEL Classification: C13, C22