The BDS statistics strongly reject the null of no nonlinearity in the [AR(i),S] errors for the JEI and KLEI series.
It is apparent from the BDS statistics presented in Table 4, that the Asymmetric GARCH model may explain the nonlinearities in the KLEI values.
Table 5 reports the maximum likelihood results for the KLEI and JEI series.
The overall significance of the model coefficients shows that an Asymmetric Component GARCH(1,1) may successfully explain the returns-generating process in the case of KLEI series.
For instance, if a nonlinear model that is based on historic data is successful in predicting near term KLEI movements and volatility, the weak form of market efficiency may be violated.
The JEI and KLEI series are subjected to Correlation Dimension and BDS tests.
For the KLEI returns series, we isolate an appropriate ARCH-type model.