Alternatives to the Generalized Autoregressive Conditional Heteroskedasticity Model in case of Identification Loss

This study shows the consequences of identification loss within the generalized autoregressive conditional heteroskedasticity (GARCH) model. It shows that identification loss leads to incorrect inferences on the significance of the parameter estimates. Parameter estimates follow nonstandard distributions in case of identification loss, ranging from uniform to bimodal distributions. The t-values associated to the parameter estimates explode for the GARCH model with error specification following the normal distribution (GARCH-N). This shows the challenge in recognizing identification loss. Therefore, the robust t-values are higher than the expected 1.98. Especially for the GARCH-N model the robust t-value is excessive: the t-value associated to the identifying parameter β should be higher than 55.7 to guarantee an identified GARCH model. For the GARCH model with error specification following the t-distribution (GARCH-t) the t-values of the identifying parameter _ are often imaginary in case of nonidentification and the t-values in general are not as high as for the GARCH-N model. The robust t-value should exceed 2.9 for identification purposes. However, an added issue for the GARCH-t model is the trade-off between identification loss and nonstationarity. If the GARCH-t model is better identified, the GARCH model is dangerously close to nonstationarity. Therefore, the t-distribution should not be preferred as assumption for the error specification. In case of identification loss, the autoregressive conditional heteroskedasticity (ARCH) model outperforms the GARCH-N model. However, this is not the case for the GARCH-t model. In general, the stochastic volatility model (SVM) outperforms the GARCH model, based on the Diebold-Mariano test. This has to do with the lower volatility estimated by the SVM with respect to the GARCH model. Therefore, the value at risk does not contain the true value of the return in more cases for the SVM than for the GARCH. For predictive purposes, based on the Diebold-Mariano test, the SVM should be preferred.