On the Test of the Volatility Proxy Model.

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.