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

Box-Cox transformation, brownian motion, constant eElasticity of volatility, mean reversion, nonstandard distribution
Erasmus School of Economics
hdl.handle.net/1765/22150
Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Huang, J, Kobayashi, M, & McAleer, M.J. (2011). Testing the Box-Cox Parameter for an Integrated Process (No. EI 2010-77). Report / Econometric Institute, Erasmus University Rotterdam (pp. 1–21). Erasmus School of Economics. Retrieved from http://hdl.handle.net/1765/22150