Residual variance estimation in moving average models

We consider time series models of the MA (moving average) family, and deal with the estimation of the residual valiance. Results are known for maximum likelihood estimates under normality, both for known or unknown mean, in which case the asymptotic biases depend on the number of parameters (including the mean), and do not depend on the values of the parameters. For moment estimates the situation is different, because we find that the asymptotic biases depend on the values of the parameters, and become large as they approach the boundary of the region of invertibility. Our approach is to use Taylor series expansions, and the objective is to obtain asymptotic biases with error of o(1/T), where T is the sample size. Simulation results are presented, and corrections for bias suggested.