Linear least squares estimation of the first order moving average parameter

Abstract

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the rst order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed.nonlinear optimization, monte carlo simulation in time series, invertible models, moving average processes, consistent estimator