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Economic Models - Convex Optimization

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206 Athanasios Athanasenas<br />

I end up by applying a dynamic forecasting technique with the estimated<br />

ECVAR. The very low value of Theil’s inequality coefficient U, provides<br />

a concrete evidence that I have formulated the suitable ECVAR obtaining,<br />

thus, robust results. Our particular emphasis on the system stability is<br />

evident and it is clarified in detail in the following section.<br />

4. Co-Integration<br />

Considering the series {Y i }, {W i } and applying the Dickey–Fuller<br />

(DA/ADF) tests (Dickey and Fuller, 1979; 1981; Harris, 1995, pp. 28–47),<br />

I found that both series are not stationary, but they are integrated of order<br />

1, that is I(1). This implies that by differentiating the initial series, we<br />

get stationary ones. In other words, the series Y i = Y i − Y i−1 and<br />

W i = W i − W i−1 are stationary, that is I(0). This can be easily verified<br />

from Fig. 1, where the non-stationary series {Y i }, {W i } are also presented.<br />

Y i<br />

W i<br />

∆Y i<br />

∆W i<br />

Figure 1. The I(1) series {Y i }, {W i } and the stationary ones {Y i }, {W i }.

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