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Testing the Box-Cox Parameter for an Integrated Process

Huang, Jian and Kobayashi, Masahito and McAleer, Michael (2011) Testing the Box-Cox Parameter for an Integrated Process. [ Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 19, 2011, ] (Unpublished)

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Abstract

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.


Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Box-Cox transformation, Brownian Motion, Constant Elasticity of Volatility, Mean Reversion, Nonstandard distribution.
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2011
Number:19
ID Code:12815
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Deposited On:02 Jun 2011 14:20
Last Modified:14 Mar 2014 09:41

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