On the asymptotic normality of instrumental variable and least squares estimators

Abstract

It is known [2],[3] that a large class of instrumental variable estimators for autoregressive moving average system parameters are strongly consistent. In this correspondence this class is described and is denoted by S . Then sufficient conditions are given for each member of the class S to be asymptotically normal. These conditions are as follows: 1) the unobserved noise process \upsilon disturbing the output measurements of the given system is a white noise process; and 2) \upsilon is independent of the observed input process u . It is further shown that under the same conditions the (strongly consistent) least squares estimator is asymptotically normal and possesses an (asymptotic) estimation error covariance matrix that bounds from below the set of covariance matrices of the class S .