Walsh spectral analysis of multiple dyadic stationary processes and its applications

In this paper, we investigate some properties of multiple dyadic stationary processes from the viewpoint of their Walsh spectral analysis. It is shown that under certain conditions a dyadic autoregressive and moving average process of finite order is expressed as a dyadic autoregressive process of finite order and also as a dyadic moving average process of finite order. We can see that the principal component process of such a dyadic stationary process has a simple finite structure in the sense that a dyadic filter which generates the principal component process has only one-side finite lags.