On the test of the volatility proxy model

Abstract

Three common tests (Lagrange multiplier test, Likelihood ratio test and Wald test) are considered to test the GARCH effect of the volatility proxy model, proposed by Visser in 2011. Under reasonable assumptions, asymptotic distribution of the three test statistics and their asymptotic equivalence are established. The impact of different proxies to the test performance is also discussed. Numerous simulation studies are carried out to assess the performance of the three tests under different volatility proxies. An empirical study is given to show a potential application of the proposed tests.

Keywords:

• GARCH effect test
• GARCH model
• Volatility proxy

Mathematics Subject Classification:

• 62H15
• 62G20

Acknowledgments

The authors greatly appreciate the very helpful suggestions and comments of two anonymous referees and the Editor Prof. Narayanaswamy Balakrishnan that greatly improve this article.

Additional information

Funding

The work is partially supported by Young Innovative Talents Program for Colleges and Universities in Guangdong Province of China 2018KQNCX241, National Natural Science Foundation of China 11731015, 11571148, 11701116, and Guangzhou University Research Funding 69-6209254, 220030401.