Estimation of the mean of multivariate AR processes

In this paper, we show that for autoregressive processes the estimators of mean are consistent if the component of the process is ‘periodical’, and it is not the case if the component is a damping one. In the one-dimensional AR(1) case, the mean cannot be estimated well. In the complex AR(1), where the process behaves periodically, the mean can be estimated well. For an AR(2) process, the mean can be estimated well if the roots of the characteristic equation are complex.