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Testing the Box-Cox Parameter for an Integrated Process

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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.

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  • Jian Huang & Masahito Kobayashi & Michael McAleer, 2010. "Testing the Box-Cox Parameter for an Integrated Process," Working Papers in Economics 10/77, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:10/77
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    1. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
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    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Jun Yu & Peter C.B. Phillips, 2001. "Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate," Cowles Foundation Discussion Papers 1309, Cowles Foundation for Research in Economics, Yale University.
    8. Adkins, Lee C. & Krehbiel, Timothy, 1999. "Mean reversion and volatility of short-term London Interbank Offer Rates: An empirical comparison of competing models," International Review of Economics & Finance, Elsevier, vol. 8(1), pages 45-54, January.
    9. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(1), pages 232-261, February.
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    Keywords

    Box-Cox transformation; Brownian Motion; Constant Elasticity of Volatility; Mean Reversion; Nonstandard distribution;
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