Test for parameter change in the presence of outliers: the density power divergence-based approach

ABSTRACT

This study considers the problem of testing for parameter change, particularly in the presence of outliers. To lessen the impact of outliers, we propose a robust test based on the density power divergence introduced by Basu et al. (Biometrika, 1998), and then derive its limiting null distribution. Our test procedure can be naturally extended to any parametric model to which MDPDE can be applied. To illustrate this, we apply our test procedure to GARCH models. We demonstrate the validity and robustness of the proposed test through a simulation study. In a real data application to the Hang Seng index, our test locates some change-points that are not detected by the existing tests such as the score test and the residual-based CUSUM test.

Keywords:

• Test for parameter change
• robust test
• outliers
• density power divergence
• GARCH models

2010 Mathematics Subject Classifications:

• 62M10
• 62F03
• 62F35

Acknowledgements

We would like to thank the associate editor and the referee for carefully examining the paper and providing valuable comments. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean government (MSIT)(NRF-2016R1C1B1015963), (ME)(NRF-2019R1I1A3A01056924)(J.Song) and (MSIT)(NRF-2019R1G1A1099809)(J.Kang).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Research Foundation of Korea [NRF-2016R1C1B1015963, NRF-2019R1G1A1099809, NRF-2019R1I1A3A01056924].