Empirical characteristic function tests for GARCH innovation distribution using multipliers

ABSTRACT

Goodness-of-fit tests for the innovation distribution in GARCH models based on measuring deviations between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis have been proposed in the literature. The asymptotic distributions of these test statistics depend on unknown quantities, so their null distributions are usually estimated through parametric bootstrap (PB). Although easy to implement, the PB can become very computationally expensive for large sample sizes, which is typically the case in applications of these models. This work proposes to approximate the null distribution through a weighted bootstrap. The procedure is studied both theoretically and numerically. Its asymptotic properties are similar to those of the PB, but, from a computational point of view, it is more efficient.

KEYWORDS:

• Characteristic function
• consistency
• GARCH model
• goodness-of-fit
• integral transformation
• weighted bootstrap

Acknowledgments

The authors thank the anonymous referee for their constructive comments and suggestions which helped to improve the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research in this manuscript has been financially supported by grant MTM2014-55966-P of the Spanish Ministry of Economy and Competitiveness