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Testing the Box-Cox Parameter in an Integrated Process

Author

Listed:
  • 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

Suggested Citation

  • Jian Huang & Masahito Kobayashi & Michael McAleer, 2009. "Testing the Box-Cox Parameter in an Integrated Process," CIRJE F-Series CIRJE-F-661, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf661
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf661.pdf
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    References listed on IDEAS

    as
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