The use of bias correction versus the Jackknife when testing the mean reversion and long term mean parameters in continuous time models
-
and
Abstract
In this paper we extend the results in [5] in two directions: First, we show that by bias correcting the estimated mean reversion parameter we can also have better finite sample properties of the testing procedure using a t-statistic in the near unit root situation when the mean reversion parameter is approaching its lower bound versus using the Jackknife estimator of Phillips and Yu [8]. Second, we show that although Tang and Chen [10] demonstrate that the variance of the maximum likelihood estimator of the long term mean parameter is of an order equal to the reciprocal of the sample size (the same order as that of the bias and variance of the mean reversion parameter estimator and so it does not converge very fast to its true value), the t-statistic related to that parameter does not exhibit large empirical size distortions and so does not need to be bias corrected in practice.
Funding source: Ministry of Science and Technology
Award Identifier / Grant number: ECO2015-63845-P
Funding statement: The first author is very grateful for the financial support from the Ministry of Science and Technology, project ECO2015-63845-P.
Acknowledgements
We wish to thank the Editorial Board for very helpful comments.
References
[1] Y. Bao, A. Ullah, Y. Wang and J. Yu, Bias in the estimation of mean reversion in continuous-time Lévy processes, Econom. Lett. 134 (2015), 16–19. 10.1016/j.econlet.2015.06.002Search in Google Scholar
[2] S. B. Bull, W. W. Hauck and C. M. T. Greenwood, Two-step jackknife bias reduction for logistic regression MlEs, Comm. Statist. Simulation Comput. 23 (1994), no. 1, 59–88. 10.1080/03610919408813156Search in Google Scholar
[3] R. Gibson and E. S. Schwartz, Stochastic convenienceyield and the pricing of oil contingent claims, J. Finance 45 (1990), no. 3, 959–976. 10.1111/j.1540-6261.1990.tb05114.xSearch in Google Scholar
[4] K. Hayes, Finite-sample bias-correction factors for the median absolute deviation, Comm. Statist. Simulation Comput. 43 (2014), no. 10, 2205–2212. 10.1080/03610918.2012.748913Search in Google Scholar
[5] E. M. Iglesias, Testing of the mean reversion parameter in continuous time models, Econom. Lett. 120 (2014), 146–148. 10.1016/j.econlet.2013.11.022Search in Google Scholar
[6] J. Janczura, S. Orzeł and A. Wyłomańska, Subordinated α-stable Ornstein–Uhlenbeck process as a tool for financial data description, Phys. A 390 (2011), 4379–4387. 10.1016/j.physa.2011.07.007Search in Google Scholar
[7] R. C. Merton, Continuous-Time Finance, Wiley-Blackwell, Massachusetts, 1990. Search in Google Scholar
[8] P. C. B. Phillips and J. Yu, Jackknifing bond option prices, Rev. Financial Stud. 18 (2005), 707–742. 10.1093/rfs/hhi018Search in Google Scholar
[9] Y. Román-Montoya, M. Rueda and A. Arcos, Confidence intervals for quantile estimation using jackknife techniques, Comput. Statist. 23 (2008), 573–585. 10.1007/s00180-007-0099-zSearch in Google Scholar
[10] C. Y. Tang and S. X. Chen, Parameter estimation and bias correction for diffusion processes, J. Econometrics 149 (2009), 65–81. 10.1016/j.jeconom.2008.11.001Search in Google Scholar
[11] K. L. P. Vasconcellos, A. C. Frery and L. B. Silva, Improving estimation in speckled imagery, Comput. Statist. 20 (2005), 503–519. 10.1007/BF02741311Search in Google Scholar
[12] O. Vasicek, An equilibrium characterization of the term structure, J. Financial Econ. 5 (1977), 177–188. 10.1002/9781119186229.ch6Search in Google Scholar
[13] J. Yu, Bias in the estimation of the mean reversion parameter in continuous time models, J. Econometrics 169 (2012), 114–122. 10.1016/j.jeconom.2012.01.004Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A method for the calculation of characteristics for the solution to stochastic differential equations
- The use of bias correction versus the Jackknife when testing the mean reversion and long term mean parameters in continuous time models
- Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies
- Random walk on spheres algorithm for solving transient drift-diffusion-reaction problems
Articles in the same Issue
- Frontmatter
- A method for the calculation of characteristics for the solution to stochastic differential equations
- The use of bias correction versus the Jackknife when testing the mean reversion and long term mean parameters in continuous time models
- Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies
- Random walk on spheres algorithm for solving transient drift-diffusion-reaction problems
