Inference for regression models with errors from a non-invertible MA(1) process

摘要

This paper considers maximum likelihood estimation in a regression model when the errors follow a first-order moving average model which is non-invertible or nearly non-invertible. The latter corresponds to a moving average parameter θ that is equal to or close to 1. The joint limiting distribution of the maximum likelihood estimators b? and θ of the regression parameter vector b and the moving average parameter θ is described. Unlike the case with standard time series models, the limiting distribution of b? depends on whether or not θ is being estimated. Specifically, the limit distribution of b? is non-normal if θ is also being estimated and is normal if θ is unestimated and equal to 1. The asymptotic behavior of the generalized likelihood ratio statistic for testing θ = 1 vs. θ < 1 is also studied and shown to perform well compared to the locally best invariant unbiased test of Tanaka (1990). We also indicate extensions to seasonal moving average models with a unit root.