The First Difference Method

Introduction

Since ρ lies between 0 and ± 1, one could start from two extreme positions. At one extreme, one could assume that ρ = 0, that is, no (first-order) serial correlation, and at the other extreme we could let ρ = ± 1, that is, perfect positive or negative correlation. As a matter of fact, when a regression is run, one generally assumes that there is no autocorrelation and then lets the Durbin–Watson or other test show whether this assumption is justified.
If, however, ρ = + 1, the generalized difference equation reduces to the first difference equation (Gujarati, 2013 : 443):
Yt − Yt−1 = β2(Xt − Xt−1) + (ut − ut−1)