Huang, Jian and Kobayashi, Masahito and McAleer, Michael (2011) Testing the Box-Cox Parameter for an Integrated Process. [Working Paper or Technical Report] (Unpublished)
Available under License Creative Commons Attribution Non-commercial.
Official URL: http://eprints.ucm.es/12815/
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.
|Item Type:||Working Paper or Technical Report|
|Uncontrolled Keywords:||Box-Cox transformation, Brownian Motion, Constant Elasticity of Volatility, Mean Reversion, Nonstandard distribution.|
|Subjects:||Social sciences > Economics > Econometrics|
|Series Name:||Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE)|
Adkins, L.C. and T. Krehbiel (1999), “Mean Reversion and Volatility of Short-term London Interbank Offer Rates: An Empirical Comparison of Competing Models”, International Review of Economics and Finance, 8, 45-54.
Bickel, P.J. and K.A. Doksum (1981), “An Analysis of Transformations Revisited”, Journal of the American Statistical Association, 76, 296-310.
Box, G.E.P. and D.R. Cox (1964), “An Analysis of Transformations”, Journal of the Royal Statistical Society B, 26, 211-243.
Brenner, R.J.R., H. Harjes and K.F. Kroner (1996), “Another Look at Models of the Short-term Interest Rate”, Journal of Financial and Quantitative Analysis, 31, 85-107.
Bliss, R.R. and D.C. Smith (1998), “The Elasticity of Interest Rate Volatility: Chan, Karolyi, Longstaff and Sanders Revisited”, Journal of Risk, 1, 21-46.
Chan, K.C., G.A. Karolyi, F.A. Longstaff and A.B. Sanders (1992), “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate”, Journal of Finance, 47, 1209-1227.
Cox, J.C., J.E. Ingersoll and S.A. Ross (1985), “A Theory of the Term Structure of Interest Rates”, Econometrica, 53, 385-407.
Dickey, D.A. and W.A. Fuller (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”, Journal of the American Statistical Association, 74, 427-431.
Jarque, C. and A. Bera (1980), “Efficient Tests for Normality, Homoskedasticity, and Serial Independence of Regression Residuals”, Economics Letters, 6, 255-259.
Kobayashi, M. and M. McAleer (1999), “Tests of Linear and Logarithmic Transformations for Integrated Processes”, Journal of the American Statistical Association, 94, 860-868.
Koedijk, K.G., F.G.J. Nissen, P.C. Schotman and C.C.P. Wolfe (1997), “The Dynamics of Short-Term Interest Rate Volatility Reconsidered”, European Finance Review, 1, 105-130.
McAleer, M. (2005), “Automated Inference and Learning in Modeling Financial Volatility”, Econometric Theory, 21, 232-261.
McAleer, M. and M.C. Medeiros (2008), “Realized Volatility: A Review”, Econometric Reviews, 27, 10-45.
Park, J.Y. and P.C.B. Phillips (1999), “Asymptotics for Nonlinear Transformations of Integrated Time Series”, Econometric Theory, 15, 269-298.
Park, J.Y. and P.C.B. Phillips (2001), “Nonlinear Regressions with Integrated Time Series”, Econometrica, 69, 117-161.
Rodrigues, P. and A. Rubia (2004), “Testing Non-stationarity in Short-term Interest Rates”, Technical Report, Faculty of Economics, University of Algarve.
Staiger, D. and J.H. Stock (1997), “Instrumental Variables Regression with Weak Instruments”, Econometrica, 65, 557-586.
Treepongkaruna, S. and S.F. Gray (2003), “On the Robustness of Short-rate Models”, Accounting and Finance, 43, 87-121.
Vasicek, O. (1977), “An Equilibrium Characterization of the Term Structure”, Journal of Financial Economics, 5, 177-158.
Yu, J. and P.C.B. Phillips (2001), “Gaussian Approach for Continuous Time Models of the Short Term Interest Rate”, Econometrics Journal, 4, 210-224.
|Deposited On:||02 Jun 2011 14:20|
|Last Modified:||14 Mar 2014 09:41|
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