Estimation Bias and Feasible Conditional Forecasts from the First-Order Moving Average Model

The quasi-maximum likelihood estimator (QMLE) of parameters in the first-order moving average model can be biased in finite samples. We develop the second-order analytical bias of the QMLE and investigate whether this estimation bias can lead to biased feasible optimal forecasts conditional on the available sample observations. We find that the feasible multiple-step-ahead forecasts are unbiased under any nonnormal distribution, and the one-step-ahead forecast is unbiased under symmetric distributions.