The paper provides general matrix formulas for minimum mean squared error signal extraction for a finitely sampled time series whose signal and noise components are nonstationary autoregressive integrated moving average processes. These formulas are quite practical; in addition to being simple...

This paper considers the problem of variance estimation for the sample mean in the context of long memory and negative memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory generalizes the short memory results of...