On the Criteria Functions used for the Estimation of Moving Average Processes
本文比较了可逆移动平均过程的无条件最小二乘、条件最小二乘和最大似然三种估计的准则函数，建立了它们之间以及相应扰动方差估计之间的简单不等式，并通过MA(1)案例分析了期望函数的性质。
Abstract It is well known that unconditional and conditional least squares estimators are asymptotically maximum likelihood for invertible moving average (MA) processes. By writing the criteria functions for these three estimators in comparable form, we establish simple inequalities between them and also between the corresponding disturbance variance estimates. Further analysis is carried out by examining the expected values of the criteria functions for given (true) coefficients in the MA(1) case. The properties of the expected functions are discussed in relation to the results of other studies of the moving average estimators.