50
0
-50
Value
100
Independent random walks X and Y have “common trends”;
this may lead to substantial problems when building regression
models, as first shown by Granger and Newbold (1974)
0
2000
4000
6000
Time
8000
10000
Regression model (Y on X)
Yt  0   X t   t
R suggests that the model is highly significant!
Regression model (Y on X and a lagged value of Y)
Yt  0  1 X t   2Yt 1   t
R CLEARLY shows that the processes are independent!