Bootstrap entropy test for general location-scale time series models with heteroscedasticity

ABSTRACT

This study considers a goodness-of-fit test for location-scale time series models with heteroscedasticity, including a broad class of generalized autoregressive conditional heteroscedastic-type models. In financial time series analysis, the correct identification of model innovations is crucial for further inferences in diverse applications such as risk management analysis. To implement a goodness-of-fit test, we employ the residual-based entropy test generated from the residual empirical process. Since this test often shows size distortions and is affected by parameter estimation, its bootstrap version is considered. It is shown that the bootstrap entropy test is weakly consistent, and thereby its usage is justified. A simulation study and data analysis are conducted by way of an illustration.

KEYWORDS:

• Location-scale models with heteroscedasticity
• GARCH-type models
• goodness-of-fit test
• entropy test
• residual empirical process
• bootstrap method

Acknowledgements

We thank an AE and referee for their careful reading and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Sangyeol Lee   http://orcid.org/0000-0003-1109-6768

Additional information

Funding

This work is is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and future Planning [grant number 2018R1A2A2A05019433].