Economic Models - Convex Optimization

A Novel Method of Estimation Under Co-Integration 31
It is obvious from these findings, the super consistency of the OLS.
However, the method we introduce here, produces almost minimum variance
errors, which is a quite desirable property, as suggested by Engle and
Granger (Dickey et al., 1994, p. 27). Hence, we will mainly focus on this
property in our next section.
6. Case Study 2: Further Evidence Regarding the Minimum
Variance Property
With the same set of data, the co-integration vector without an intercept
obtained by applying the ML method is:
1 − 0.9422994 − 0.058564
The errors corresponding to this vector are obtained from:
û i = C i − 0.9422994I i − 0.058564W i (18)
Again these errors will be denoted by uml i .
Next, we apply SVD to in Eq. (12) to obtain matrix C, which is:
⎡
⎤
1 −0.9192042 −0.066081211
⎢
⎥
C = ⎣ 1 1.160720 −1.012970 ⎦
1 0.9395341 2.063768
and
⎛ ⎞
1.359891
⎜ ⎟
Euclidean norm = ⎝ 1.836676 ⎠
2.47828
The singular values of are:
f 1 = 0.89514, f 2 = 0.0403121 and f 3 = 0.0026218249
Again, all f i ’s are less than 1. We consider the first row of C, so that
the errors corresponding to this vector are obtained from:
û i = C i − 0.9192042I i − 0.066081211W i (19)
These errors will be also denoted by usvd i .
The co-integrating vector reported by the authors (p. 109), which is
obtained from the VAR(2), including the dummies mentioned previously,