Economic Models - Convex Optimization

Credit and Income 211
Table 2.
Eigen values.
No. Real part Coefficient of imaginary part Length
1 0.94 0 0.94
2 0.8567 0.0579 0.8586
3 0.8567 −0.0579 0.8586
4 0.3807 0.0 0.3807
5 0.0367 0.3655 0.3674
6 0.0367 −0.3677 0.3674
7 −0.3581 0.0 0.3581
8 −0.1142 0.0 0.1142
To decide whether the dynamic system described by Eq. (8a) is stable, we
compute the eigenvalues of matrix Ã, presented in Table 2.
Since the greater length (0.94) is less then 1, the dynamic system as
given in Eq. (8a) is stable and can be used for forecasting purposes. A side
verification of this stability test, is that once the system is stable, then the
elements of the state vector x in the initial VAR(4), which in this case are the
series {Y i }, {W i }, are either difference stationary series (DSS), or in some
cases, stationary series. In fact, we show that these series are DSS and in
particular, they are I(1).
4.3. The Estimated Co-Integrating Vectors
We applied the ML method, to compute matrices C and A, which have the
following form:
Y W t
[ ]
1 −0.289613 −0.003621
C =
,
1 −0.653108 −0.000292
[ ]
−0.087991 −0.004980
A =
−0.038535 0.054745
(9)
satisfying AC = ˜. We can easily verify that only the first row of matrix
C is a promising candidate, verified from the computed value of the t-
statistic (−0.23), which corresponds to the (1, 2) element of matrix A, that
corresponds to the second row of matrix C. Thus, we have the co-integrating