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Testing of the mean reversion parameter in continuous time models

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  • Iglesias, Emma M.

Abstract

In this paper we use the approximate bias expressions developed in Yu (2012) and Bao et al. (2013) to improve the testing of the ordinary least squares or quasi-maximum likelihood estimator of the mean reversion parameter in continuous time models. We follow the approach given in Iglesias and Phillips (2005) and Chambers (2013), where if we bias correct the estimated mean reversion parameter, we can improve on the small sample properties of the testing procedure. Simulation results confirm the usefulness of this approach using a t-statistic in this setting in the near unit root situation when the mean reversion parameter is approaching its lower bound. Therefore we always recommend bias correcting when applying a t-statistic in practice in this context.

Suggested Citation

  • Iglesias, Emma M., 2014. "Testing of the mean reversion parameter in continuous time models," Economics Letters, Elsevier, vol. 122(2), pages 187-189.
    • Handle: RePEc:eee:ecolet:v:122:y:2014:i:2:p:187-189
    DOI: 10.1016/j.econlet.2013.11.022
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    References listed on IDEAS

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    1. Yong Bao & Aman Ullah & Yun Wang & Jun Yu, 2013. "Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Lévy Processes," Working Papers 02-2013, Singapore Management University, School of Economics.
    2. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    3. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. 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.
    6. Iglesias, Emma M. & Phillips, Garry D.A., 2005. "Bivariate Arch Models: Finite-Sample Properties Of Qml Estimators And An Application To An Lm-Type Test," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1058-1086, December.
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    Cited by:

    1. Ardian, Aldin & Kumral, Mustafa, 2020. "Incorporating stochastic correlations into mining project evaluation using the Jacobi process," Resources Policy, Elsevier, vol. 65(C).
    2. Iglesias Emma M. & Phillips Garry D. A., 2017. "The use of bias correction versus the Jackknife when testing the mean reversion and long term mean parameters in continuous time models," Monte Carlo Methods and Applications, De Gruyter, vol. 23(3), pages 159-164, September.
    3. 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

    Least squares; Quasi-maximum likelihood; Continuous record; Estimation; Testing; Bias correction;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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