Stock markets and their relationship
with the real economy in Latin America
Samuel Brugger *and Edgar Ortiz **
Self-Regression Vector Analysis

VAR analyses (Eq. 8, 9, 10) have become increasingly popular in recent years, mainly as a result of the restrictions of traditions models and the criticism they have received. Sims VAR methodology (1980), (Eq. 9, 10 and 11) is closely related to the cointegration analysis examined in the previous section by the Granger Representation Theorem, which shows that if cointegration exists, there should be a representation of this relationship long and short term that corrects the error and prevents the cointegrated series being dispersed in time. The theorem also considers cointegration a necessary condition for estimating an error correction model. In this way, the idea of finding a long term stable relationship is combined with the short term statistical adjustment of imbalances. In fact, cointegration analysis efficiently solves the original problem of imbalance in VARs, and the lack of a theoretical basis.

To estimate the VAR, the level of integration between the variables must be identified. If the variables have the same integration order, relevant historical information can be gathered. In the present example, the series in levels are I (1) and are not cointegrated so only the primary differences in the series are analyzed. Another important factor in VAR analysis is the number of lags employed and for this each lag must be evaluated one by one to find the optimum number. To this end, it is important to compare the criteria of the statistical information for the results of each specification. The majority of econometric packages calculate a large number of statistical criteria: LR testing, Final Prediction Error (FPE), Hannan-Quinn, Akaike and Schwarz. In the present study, the last two criteria will be used, the most frequently used in financial literature. They generally show very similar, even identical results, but occasionally can give very different results. In this case the criterion with the fewest lags will be used. This is owing to the fact that an increase in lags reduces R2, as Lora demonstrates (2007).

Another important characteristic is the dynamic stability of VAR, which can be observed in the value of its characteristic roots. This ensures that the variables return to long term equilibrium in the face of short term shocks. If this did not occur, the model would not make economic sense. To check stability therefore, the root characteristics λn need to be examined and their absolute value should be less than 1: As seen in Table 6, the optimum for the four VAR is 11 lags, which is not surprising given what was discussed in the previous section.

Once the VAR model is defined it must be ascertained if the model passes basic tests such as normality, heteroscedasticity and stability. Table 7 shows the results obtained for the most representative countries in Latin America.