Linear Processes

Abstract

We consider stationary sequences generated through independent identically distributed $(\xi _n)_{n\in \mathbb {Z}}$. A reference is Brockwell and Davis (Time series: theory and methods. Springer, New York, 1991). Such models are natural in signal theory since they appear through linear filtering of a white noise. The usual setting is that $(\xi _n)_{n\in \mathbb {Z}}$ is only a $\mathbb {L}^2$-stationary white noise sequence and not an independent identically distributed sequence.