Estimating moving average parameters in the presence of measurement error

Suppose that a moving average time series X t is not observed, but instead Y t = X t + ε t is observed, where ε t , is measurement error. Estimation of the parameters of X t has previously been considered under the assumption that X t and ε t are uncorrelated. The case where X t and ε t have known cross covariances is considered here, and a method is described for estimating the parameters of X t . A simulation compares four estimators for a MA(1) series parameter in the presence of measurement error.