Testing the Box-Cox Parameter for an Integrated Process
AbstractThis 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.
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Bibliographic InfoPaper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/77.
Length: 22 pages
Date of creation: 01 Dec 2010
Date of revision:
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Box-Cox transformation; Brownian Motion; Constant Elasticity of Volatility; Mean Reversion; Nonstandard distribution;
Other versions of this item:
- Jian Huang & Masahito Kobayashi & Michael McAleer, 2010. "Testing the Box-Cox Parameter for an Integrated Process," KIER Working Papers 750, Kyoto University, Institute of Economic Research.
- Jian Huang & Masahito Kobayashi & Michael McAleer, 2011. "Testing the Box-Cox Parameter for an Integrated Process," Documentos del Instituto Complutense de AnÃ¡lisis EconÃ³mico 2011-19, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
- Huang, J. & Kobayashi, M. & McAleer, M.J., 2011. "Testing the Box-Cox Parameter for an Integrated Process," Econometric Institute Report EI 2010-77, Erasmus University Rotterdam, Econometric Institute.
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