Testing the Box-Cox Parameter for an Integrated Process
This paper analyses the constant elasticity of volatility (CEV) model suggested by Chan et al. (1992). The CEV model without mean reversion is shown to be the inverse Box-Cox transformation of integrated processes asymptotically. It is demonstrated that the maximum likelihood estimator of the power parameter has a nonstandard asymptotic distribution, which is expressed as an integral of Brownian motions, when the data generating process is not mean reverting. However, it is shown that the t-ratio follows a standard normal distribution asymptotically, so that the use of the conventional t-test in analyzing the power parameter of the CEV model is justified even if there is no mean reversion, as is often the case in empirical research. The model may applied to ultra high frequency data
|Date of creation:||2011|
|Date of revision:|
|Note:||The second author wishes to acknowledge the financial support of the Ministry of Education, Science, Culture and Sports of Japan, and the third author is most grateful for the financial support of the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science.|
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