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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 25, Fasc. 2,
pages 331 - 362
 

DATA-DRIVEN SCORE TEST OF FIT FOR CONDITIONAL DISTRIBUTION IN THE GARCH(1,1) MODEL

Tadeusz Inglot
Bartosz Stawiarski

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 62M10, 91B84; Secondary: 62G10, 62E20, 60F05, 65C05.

Key words and phrases: GARCH(1,1) model, noise distribution, efficient score vector, score test, BIC Schwarz selection rule, martingale difference array, central limit theorem, ergodic theorem, Monte Carlo simulations.

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