This paper analyses the constant elasticity of volatility (CEV) model suggested by [6]. The
CEV model without mean reversion is shown to be the inverse BoxCox 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 tratio follows a standard normal
distribution asymptotically, so that the use of the conventional ttest 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.
