Table 1: Approximate bias, variance, and Mean Squared Error of the Method of Moments and the Maximum Likelihood Estimator for the MA(1) parameter from 1000 replications.


Bias Var MSE Bias Var MSE
MME −0.403345 0.00020972 0.162897 0.0931052 0.00097912 0.00964771
MLE 0.01795 0.00015984 0.00048204 0.020949 0.00062347 0.00104331

Bias Var MSE Bias Var MSE
MME −0.123812 0.00021444 0.0155439 0.0217928 0.00097912 0.00145404
MLE 0.00521 0.00031329 0.00034043 0.00599 0.00063936 0.00067524

Bias Var MSE Bias Var MSE
MME −0.0422653 0.00021173 0.00199808 0.0123275 0.00097912 0.00113109
MLE −0.00116 0.00022068 0.00022202 0.00275 0.00062348 0.00063104

Bias Var MSE Bias Var MSE
MME −0.00708814 0.00023768 0.00028792 −0.00166597 0.00097912 0.00098189
MLE 0.00313 0.00029131 0.00036115 0.00386 0.00065544 0.00067034