Template-type: ReDIF-Paper 1.0
Author-Name: Jian Huang
Author-Workplace-Name: Guangdong University of Finance PRC
Author-Name: Masahito Kobayashi
Author-Email: mkoba@ynu.ac.jp.
Author-Workplace-Name: Faculty of Economics Yokohama National University, Japan.
Author-Name: Michael McAleer
Author-Person: pmc90 
Author-Workplace-Name: Econometrisch Instituut (Econometric Institute), Faculteit der Economische 
	Wetenschappen (Erasmus School of Economics), Erasmus Universiteit, Tinbergen Instituut (Tinbergen Institute).
Title: Testing the Box-Cox Parameter for an Integrated Process
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
Keywords: Box-Cox transformation, Brownian Motion, Constant Elasticity of Volatility, Mean Reversion, Nonstandard distribution.
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.
Length: 21 pages 
Creation-Date: 2011 
Number: 2011-19 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1119.txt
File-URL: https://eprints.ucm.es/id/eprint/12815/1/1119.pdf
File-Format: Application/pdf
File-Function: Revised May 2011
Handle: RePEc:ucm:doicae:1119