Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle
单位圆上或附近根的 MA(1) 过程极大似然估计
This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θ LM , defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle.…