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Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate

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Abstract

This paper proposes a Gaussian estimator for nonlinear continuous time models of the short term interest rate. The approach is based on a stopping time argument that produces a normalizing transformation facilitating the use of a Gaussian likelihood. A Monte Carlo study shows that the finite sample performance of the proposed procedure offers an improvement over the discrete approximation method proposed by Nowman (1997). An empirical application to U.S. and British interest rates is given.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:1309
    Note: CFP 1124 and CFP 1347, "Corrigendum," Econometrics Journal (February 2011), 14(4): 126-129
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    Cited by:

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    2. Baviera, Roberto & Santagostino Baldi, Tommaso, 2019. "Stop-loss and leverage in optimal statistical arbitrage with an application to energy market," Energy Economics, Elsevier, vol. 79(C), pages 130-143.
    3. Chang, Yoosoon, 2012. "Taking a new contour: A novel approach to panel unit root tests," Journal of Econometrics, Elsevier, vol. 169(1), pages 15-28.
    4. Roberto Baviera & Tommaso Santagostino Baldi, 2017. "Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market," Papers 1706.07021, arXiv.org.
    5. 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.
    6. K. Fergusson & E. Platen, 2015. "Application Of Maximum Likelihood Estimation To Stochastic Short Rate Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-26, December.
    7. Peter C. B. Phillips & Jun Yu, 2023. "Information loss in volatility measurement with flat price trading," Empirical Economics, Springer, vol. 64(6), pages 2957-2999, June.
    8. McCrorie, J. Roderick & Chambers, Marcus J., 2006. "Granger causality and the sampling of economic processes," Journal of Econometrics, Elsevier, vol. 132(2), pages 311-336, June.
    9. 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.
    10. Ali Ataullah & Andrew Higson & Mark Tippett, 2006. "Real (adaptation) options and the valuation of equity: some empirical evidence," Abacus, Accounting Foundation, University of Sydney, vol. 42(2), pages 236-265, June.
    11. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    12. Wymer Clifford R., 2012. "Continuous-Tme Econometrics of Structural Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-28, April.
    13. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    14. Ingrid Lo, 2005. "An Evaluation of MLE in a Model of the Nonlinear Continuous-Time Short-Term Interest Rate," Staff Working Papers 05-45, Bank of Canada.
    15. Alessandro De Gregorio & Stefano Iacus, 2010. "Adaptive LASSO-type estimation for ergodic diffusion processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1100, Universitá degli Studi di Milano.
    16. Terence D.Agbeyegbe & Elena Goldman, 2005. "Estimation of threshold time series models using efficient jump MCMC," Economics Working Paper Archive at Hunter College 406, Hunter College Department of Economics, revised 2005.
    17. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    18. Alessandro De Gregorio & Stefano Iacus, 2010. "Adaptive LASSO-type estimation for ergodic diffusion processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1100, Universitá degli Studi di Milano.
    19. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    20. Alejandra López-Pérez & Manuel Febrero-Bande & Wencesalo González-Manteiga, 2021. "Parametric Estimation of Diffusion Processes: A Review and Comparative Study," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    21. Huang, Jian & Kobayashi, Masahito & McAleer, Michael, 2012. "Testing for the Box–Cox parameter for an integrated process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 1-9.
    22. Emma M. Iglesias & Garry D. A. Phillips, 2020. "Further Results on Pseudo‐Maximum Likelihood Estimation and Testing in the Constant Elasticity of Variance Continuous Time Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 357-364, March.

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    More about this item

    Keywords

    Gaussian estimation; nonlinear diffusion; normalizing transformation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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