ABSTRACT
In this chapter we study the regression model https://www.w3.org/1998/Math/MathML">yt=∑j=1kxtjβj+εt (t=1,2,…,n)https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/c73c8eaa-6e2d-45b3-bd8b-866a06ca944e/content/math_751_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where the xij are considered to be “fixed variates” and the residuals follow a first-order stationary Markov process (called an “AR(1) process” by Box and Jenkins 1986, pp. 51-54) defined by https://www.w3.org/1998/Math/MathML">εt=ρεt−1+ηt; |ρ|<1 (t=−N+1,−N+2,…,0,1,2,…,n),https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/c73c8eaa-6e2d-45b3-bd8b-866a06ca944e/content/math_752_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where -N is a remote initial period. The following was shown by Gurland (1954):
