Yule-Walker Estimation for the Moving-Average Model

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.

	𝜃=0.5			𝜃=−0.8
𝑁=30	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
𝑁=100	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
𝑁=200	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
𝑁=300	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