Economic Models - Convex Optimization

34 Alexis Lazaridis
Nevertheless, the method proposed, produces better results than the ML
approach does.
Finally, we will consider the first of the two co-integration vectors
(since, it produces slightly better results), reported by Harris (1995, p. 102).
From this vector, which was obtained by the ML method, one gets the
following errors.
û i = (m − p) i + 7.325p i − 1.073y i + 6.808R i (23)
Also we obtain
standard deviation of û i ’s = 0.268 and
û i =−0.117378 − 0.178896
(0.068296) ûi−1 − 0.30095417û i−1
t =−2.619.
It is obvious that these additional results further support the previous
findings, which are due to some properties of SVD (Lazaridis, 1986).
6.1. A Note on Integration
It seems to be a common belief that differentiating a variable say n times,
we will always get a stationary series (Harris, 1995, p. 16). Hence, the
initial series is said to be I(n). But, this is not necessarily the case, as it is
verified that if we take into consideration the exports of goods and services
for Greece, as presented in Table 1. Besides if n is large enough, is it of
any good to obtain such a stationary series when economic variables are
considered?
Table 1. The series {x i }.
Exports of goods and services in bil. Eur. Greece 1956–2000.
X
2.4944974E-02 2.9053558E-02 2.9347029E-02 2.8760089E-02 2.8173149E-02
3.2575201E-02 3.5803374E-02 4.1379310E-02 4.2553190E-02 4.7248717E-02
6.6030815E-02 6.7498162E-02 6.6030815E-02 7.6008804E-02 8.8041089E-02
0.1000734 0.1300073 0.2022010 0.2664710 0.3325018
0.4258254 0.4763023 0.5998532 0.7325019 1.049743
1.239618 1.388114 1.788701 2.419956 2.868965
3.618782 4.510052 4.978430 5.818929 6.485106
7.690976 9.316215 9.847396 11.45708 14.08716
15.39428 18.87601 20.90506 22.56992 25.51577
Source: International Financial Statistics. (International Monetary Fund, Washington DC)