IDEAS home Printed from https://ideas.repec.org/p/ris/smuesw/2018_020.html
   My bibliography  Save this paper

The Grid Bootstrap for Continuous Time Models

Author

Listed:
  • Lui, Yiu Lim

    (School of Economics, Singapore Management University)

  • Xiao, Weilin

    (School of Management, Zhejiang University)

  • Yu, Jun

    (School of Economics, Singapore Management University)

Abstract

This paper considers the grid bootstrap for constructing confidence intervals for the persistence parameter in a class of continuous time models driven by a Levy process. Its asymptotic validity is established by assuming the sampling interval (h) shrinks to zero. Its improvement over the in-fill asymptotic theory is achieved by expanding the coefficient-based statistic around its in fill asymptotic distribution which is non-pivotal and depends on the initial condition. Monte Carlo studies show that the gird bootstrap method performs better than the in-fill asymptotic theory and much better than the longspan theory. Empirical applications to U.S. interest rate data highlight differences between the bootstrap confidence intervals and the confidence intervals obtained from the in-fill and long-span asymptotic distributions.

Suggested Citation

  • Lui, Yiu Lim & Xiao, Weilin & Yu, Jun, 2018. "The Grid Bootstrap for Continuous Time Models," Economics and Statistics Working Papers 20-2018, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2018_020
    as

    Download full text from publisher

    File URL: https://ink.library.smu.edu.sg/soe_research/2210/
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
    3. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.
    4. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    5. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    6. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    7. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    8. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    9. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    10. Yong Bao & Aman Ullah & Yun Wang, 2017. "Distribution of the mean reversion estimator in the Ornstein–Uhlenbeck process," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1039-1056, October.
    11. Perron, Pierre, 1991. "A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept," Econometrica, Econometric Society, vol. 59(1), pages 211-236, January.
    12. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    13. Tanaka, Katsuto, 1983. "Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean," Econometrica, Econometric Society, vol. 51(4), pages 1221-1231, July.
    14. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    15. Zhou, Qiankun & Yu, Jun, 2015. "Asymptotic theory for linear diffusions under alternative sampling schemes," Economics Letters, Elsevier, vol. 128(C), pages 1-5.
    16. Peter C. B. Phillips, 2012. "Folklore Theorems, Implicit Maps, and Indirect Inference," Econometrica, Econometric Society, vol. 80(1), pages 425-454, January.
    17. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    18. Mikusheva, Anna, 2015. "Second Order Expansion Of The T-Statistic In Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 426-448, June.
    19. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    20. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    2. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, vol. 6(1), pages 1-28, March.
    3. Zhou, Qiankun & Yu, Jun, 2015. "Asymptotic theory for linear diffusions under alternative sampling schemes," Economics Letters, Elsevier, vol. 128(C), pages 1-5.
    4. John C. Chao & Peter C. B. Phillips, 2019. "Uniform Inference in Panel Autoregression," Econometrics, MDPI, vol. 7(4), pages 1-28, November.
    5. Jiang, Liang & Wang, Xiaohu & Yu, Jun, 2018. "New distribution theory for the estimation of structural break point in mean," Journal of Econometrics, Elsevier, vol. 205(1), pages 156-176.
    6. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    7. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    8. Aman Ullah & Yong Bao & Ru Zhang, 2014. "Moment Approximation for Unit Root Models with Nonnormal Errors," Working Papers 201401, University of California at Riverside, Department of Economics.
    9. Laurent, Sébastien & Shi, Shuping, 2020. "Volatility estimation and jump detection for drift–diffusion processes," Journal of Econometrics, Elsevier, vol. 217(2), pages 259-290.
    10. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    11. Mukhtar Ali, 2002. "Distribution Of The Least Squares Estimator In A First-Order Autoregressive Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 89-119.
    12. Sabzikar, Farzad & Wang, Qiying & Phillips, Peter C.B., 2020. "Asymptotic theory for near integrated processes driven by tempered linear processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 192-202.
    13. Christis Katsouris, 2023. "Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates," Papers 2302.05193, arXiv.org.
    14. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    15. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, University Library of Munich, Germany.
    16. Anna Bykhovskaya & James A. Duffy, 2022. "The Local to Unity Dynamic Tobit Model," Papers 2210.02599, arXiv.org, revised Feb 2023.
    17. Chambers, Marcus J. & Kyriacou, Maria, 2012. "Jackknife bias reduction in autoregressive models with a unit root," MPRA Paper 38255, University Library of Munich, Germany.
    18. Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    19. Marcet, Albert & Jarociński, Marek, 2010. "Autoregressions in small samples, priors about observables and initial conditions," Working Paper Series 1263, European Central Bank.
    20. Carlos A. Medel & Pablo M. Pincheira, 2016. "The out-of-sample performance of an exact median-unbiased estimator for the near-unity AR(1) model," Applied Economics Letters, Taylor & Francis Journals, vol. 23(2), pages 126-131, February.

    More about this item

    Keywords

    Grid bootstrap; In-fill asymptotics; Continuous time models; Long-span asymptotics.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ris:smuesw:2018_020. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Cheong Pei Qi (email available below). General contact details of provider: https://edirc.repec.org/data/sesmusg.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.