Stationarity on Finite Strings and Shift Register Sequences

Abstract

Stationarity is a property of infinite sequences of random variables. An appropriate extension of this definition is made, to cover finite sequences. The set of finite stationary sequences is shown to be a convex set and its extreme points are related to shift register sequences (which are paths on a graph known as the shift net, or the de Bruijn graph). The set of finite stationary sequences as defined here is simply the set of finite dimensional projections of infinite stationary sequences.