Stock markets and their relationship
with the real economy in Latin America
Samuel Brugger *and Edgar Ortiz **
Stock Market Activity and Development in Latin America

Unit Roots Analysis

To analyze the difference between two or more variables, it is important to establish if the stochastic processes that generate the time series are variable in time, i.e. if the processes are stationary (Eq. 1). They should not have unit roots and should be on the order of I (0). The series with an order of I(d) > 0 have at least one unit root. The test most frequently applied in financial economics to determine the presence or absence of unit roots is the Augmented Dickey-Fuller test along with the critical value of McKinnon (1996) (one-sided p-values). Table 1 shows the results of this test for GDP in Argentina, Brazil, Chile and Mexico in levels and with first differences. The tests are reported with tendency and intercept.

The Latin American stock market series in levels generally show unit roots, as confirmed by Brugger (2010). The GDP and stock market series in levels are analyzed in this study. The unit root tests for the first differences are shown in Tables 1 and 2. Table I shows that the series for GDP growth for countries shown is stationary. In each case the rejection of the null hypothesis is strong. The t statistic obtained exceeds all the critical values, indicating that there is no unit root to 1%. The one-sided p-values of MacKinnon confirm this result: in all cases it is less than 0.05%.

Table 2 shows similar results for stock market index growth (first differences) to those obtained from the Unit Root tests for national GDP growth. The series for emerging stock market profits in Latin America are stationary and do not have a unit root. The unit roots are absent in the case of all the stock markets analyzed: the ADF test t-statistic is greater than the critical values in all the markets for all the confidence levels. The one-sided p-values of MacKinnon, which in all cases have a value equal to zero, corroborates this finding, showing that there are no unit roots for all confidence levels in the series of returns in the four capital markets. Finally, it is important to note that the test of the series in the first difference was only applied with intercept and favorable results were obtained between 6 and 10 lags. It is important to highlight that most of the studies in these analyses do not go beyond 6 lags. The result obtained on the stationarity of the series is consistent with results in Peirs studies (1996) and Ortiz et al. (2007).