DATA-DRIVEN SCORE TEST OF FIT FOR CONDITIONAL DISTRIBUTION
IN THE GARCH MODEL
Tadeusz Inglot
Bartosz Stawiarski
Abstract: A data-driven score test for a conditional distribution in the GARCH 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.
2000 AMS Mathematics Subject Classification: Primary: 62M10, 91B84; Secondary:
62G10, 62E20, 60F05, 65C05.
Key words and phrases: GARCH model, noise distribution, efficient score vector,
score test, BIC Schwarz selection rule, martingale difference array, central limit theorem,
ergodic theorem, Monte Carlo simulations.