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Testing the Box-Cox Parameter in an Integrated Process

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  • Jian Huang

    (Guangdong University of Finance)

  • Masahito Kobayashi

    (Faculty of Economics, Yokohama National University)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo)

Abstract

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 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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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf661.pdf
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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-661.

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Length: 22 pages
Date of creation: Sep 2009
Date of revision:
Handle: RePEc:tky:fseres:2009cf661

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  1. Michael McAleer & Marcelo Cunha Medeiros, 2006. "Realized volatility: a review," Textos para discussão 531 Publication status: F, Department of Economics PUC-Rio (Brazil).
  2. 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.
  3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  4. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  5. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
  6. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  7. 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 1209-27, July.
  8. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  10. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
  11. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  12. Koedijk, C.G. & Nissen, F. & Schotman, P.C. & Wolff, C.C.P., 1997. "The dynamics of short-term interest rate volatility reconsidered," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3108628, Tilburg University.
  13. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
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