Bias reduction of the maximum-likelihood estimator for a conditional Gaussian MA(1) model

In this paper, we consider an estimation for the unknown parameters of a conditional Gaussian MA(1) model. In the majority of cases, a maximum-likelihood estimator is chosen because the estimator is consistent. However, for small sample sizes the error is large, because the estimator has a bias of O(n(-1)). Therefore, we provide a bias of O(n(-1)) for the maximum-likelihood estimator for the conditional Gaussian MA(1) model. Moreover, we propose new estimators for the unknown parameters of the conditional Gaussian MA(1) model based on the bias of O(n(-1)). We investigate the properties of the bias, as well as the asymptotical variance of the maximum-likelihood estimators for the unknown parameters, by performing some simulations. Finally, we demonstrate the validity of the new estimators through this simulation study.