Data-driven score test of fit for conditional distribution in the GARCH (1, 1) model

A data-driven score test for a conditional distribution in the GARCH (1, 1) model is proposed. Conditional distribution assumption is verified by a score test, obtained from nesting the null density into an exponential family and then choosing the dimension of this exponential family by a score-based selection rule. A simulation study, which is provided, shows good empirical behaviour of the proposed test, outperforming in most cases the behaviour of competitive tests.