Testing of the mean reversion parameter in continuous time models
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.
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- Chambers, Marcus J., 2013.
"Jackknife estimation of stationary autoregressive models,"
Journal of Econometrics,
Elsevier, vol. 172(1), pages 142-157.
- Marcus J Chambers, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 684, University of Essex, Department of Economics.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Jun Yu, 2009.
"Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models,"
Microeconomics Working Papers
23045, East Asian Bureau of Economic Research.
- 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.
- Jun Yu, 2007. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers CoFie-06-2008, Sim Kee Boon Institute for Financial Economics, revised Oct 2008.
- Jun Yu, 2009. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers 16-2009, Singapore Management University, School of Economics.
- 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.
- 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(06), pages 1058-1086, December.
- 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.
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