Nonparametric Verification of GARCH-Class Models for Selected Polish Exchange Rates and Stock Indices

The iid property of the model’s residuals is a crucial criterion for assessing the fit of the model to the data. GARCH-class models are the most commonly used nonlinear models in financial econometrics. In this paper various uni- and multivariate GARCH-class models were applied to selected Polish financial series. In the research the iid property of the residuals and their absolute values was verified. To this end, the BDS test, the mutual information measure, and, for comparison, the Ljung-Box and Engle tests were used. To calculate p-values the bootstrap procedure was applied in each test. The results indicate that ARMA-GARCH models are generally able to capture the dependencies in the time series analyzed. However, this does not mean that every specified ARMA-GARCH model describes the existing dependencies well enough. The study shows that different parameterizations of the GARCH-class models analyzed have different abilities to describe the dynamics of financial processes. Furthermore, the research indicates that the application of higher lags in a GARCH model may have a crucial impact on the removal of the ARCH effect and, in consequence, on the nonlinearity identification.