IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v192y2024ics0167947323001974.html
   My bibliography  Save this article

Burn-in selection in simulating stationary time series

Author

Listed:
  • Li, Yuanbo
  • Chan, Chu Kin
  • Yau, Chun Yip
  • Ng, Wai Leong
  • Lam, Henry

Abstract

Many time series models are defined in a recursive manner, which prohibits exact simulations. In practice, one appeals to simulating a long time series and discarding a large number of initial simulated observations, known as the burn-in. For autoregressive models where the dependence decays exponentially fast, the choice of the burn-in is not critical. However, for long-memory time series where the dependence from the remote past is strong, it is not clear how to select the burn-in number. By combining several samplers with randomized burn-in numbers, a method for exactly simulating the expectation of a statistic computed from a time series is developed. Moreover, with some suitably chosen statistics, the exact simulation method can be applied to quantify the effect of burn-in numbers on the simulated sample. Simulation studies are conducted to provide some practical guidances for burn-in selections.

Suggested Citation

  • Li, Yuanbo & Chan, Chu Kin & Yau, Chun Yip & Ng, Wai Leong & Lam, Henry, 2024. "Burn-in selection in simulating stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323001974
    DOI: 10.1016/j.csda.2023.107886
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323001974
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107886?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pierre E. Jacob & Fredrik Lindsten & Thomas B. Schön, 2020. "Smoothing With Couplings of Conditional Particle Filters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 721-729, April.
    2. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    3. Piotr S. Kokoszka & Murad S. Taqqu, 2001. "Can One Use the Durbin–Levinson Algorithm to Generate Infinite Variance Fractional ARIMA Time Series?," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 317-337, May.
    4. Andreas Noack Jensen & Morten Ørregaard Nielsen, 2014. "A Fast Fractional Difference Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 428-436, August.
    5. McLeish, Don, 2011. "A general method for debiasing a Monte Carlo estimator," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 301-315, December.
    6. Chang-han Rhee & Peter W. Glynn, 2012. "A new approach to unbiased estimation for SDE's," Papers 1207.2452, arXiv.org.
    7. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    8. Morten Ørregaard Nielsen & Antoine L. Noël, 2021. "To infinity and beyond: Efficient computation of ARCH(∞) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 338-354, May.
    9. Pierre E. Jacob & John O’Leary & Yves F. Atchadé, 2020. "Unbiased Markov chain Monte Carlo methods with couplings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 543-600, July.
    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. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    2. Zhou, Zhengqing & Wang, Guanyang & Blanchet, Jose H. & Glynn, Peter W., 2023. "Unbiased Optimal Stopping via the MUSE," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    3. Zhengqing Zhou & Guanyang Wang & Jose Blanchet & Peter W. Glynn, 2021. "Unbiased Optimal Stopping via the MUSE," Papers 2106.02263, arXiv.org, revised Dec 2022.
    4. Yasa Syed & Guanyang Wang, 2023. "Optimal randomized multilevel Monte Carlo for repeatedly nested expectations," Papers 2301.04095, arXiv.org, revised May 2023.
    5. Cui, Zhenyu & Fu, Michael C. & Peng, Yijie & Zhu, Lingjiong, 2020. "Optimal unbiased estimation for expected cumulative discounted cost," European Journal of Operational Research, Elsevier, vol. 286(2), pages 604-618.
    6. Ruzayqat Hamza M. & Jasra Ajay, 2020. "Unbiased estimation of the solution to Zakai’s equation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 113-129, June.
    7. Pierre E. Jacob & John O’Leary & Yves F. Atchadé, 2020. "Unbiased Markov chain Monte Carlo methods with couplings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 543-600, July.
    8. Goda, Takashi & Kitade, Wataru, 2023. "Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 743-763.
    9. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    10. Dereich, Steffen, 2021. "General multilevel adaptations for stochastic approximation algorithms II: CLTs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 226-260.
    11. Imry Rosenbaum & Jeremy Staum, 2017. "Multilevel Monte Carlo Metamodeling," Operations Research, INFORMS, vol. 65(4), pages 1062-1077, August.
    12. Polala Arun Kumar & Ökten Giray, 2020. "Implementing de-biased estimators using mixed sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 26(4), pages 293-301, December.
    13. Sepideh Dolatabadi & Paresh Kumar Narayan & Morten Ørregaard Nielsen & Ke Xu, 2018. "Economic significance of commodity return forecasts from the fractionally cointegrated VAR model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(2), pages 219-242, February.
    14. Hsuan-Hao Lu & Karthik V. Myilswamy & Ryan S. Bennink & Suparna Seshadri & Mohammed S. Alshaykh & Junqiu Liu & Tobias J. Kippenberg & Daniel E. Leaird & Andrew M. Weiner & Joseph M. Lukens, 2022. "Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    15. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    16. Piotr Kokoszka & Michael Wolf, 2002. "Subsampling the mean of heavy-tailed dependent observations," Economics Working Papers 600, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Wei Fang & Zhenru Wang & Michael B. Giles & Chris H. Jackson & Nicky J. Welton & Christophe Andrieu & Howard Thom, 2022. "Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information," Medical Decision Making, , vol. 42(2), pages 168-181, February.
    18. Baillie, Richard T. & Cho, Dooyeon & Rho, Seunghwa, 2024. "Combining Long and Short Memory in Time Series Models: the Role of Asymptotic Correlations of the MLEs," Econometrics and Statistics, Elsevier, vol. 29(C), pages 88-112.
    19. Guay, François & Schwenkler, Gustavo, 2021. "Efficient estimation and filtering for multivariate jump–diffusions," Journal of Econometrics, Elsevier, vol. 223(1), pages 251-275.
    20. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business 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:eee:csdana:v:192:y:2024:i:c:s0167947323001974. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.