IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v114y2013icp40-53.html
   My bibliography  Save this article

Efficient inference for autoregressive coefficients in the presence of trends

Author

Listed:
  • Qiu, D.
  • Shao, Q.
  • Yang, L.

Abstract

Time series often contain unknown trend functions and unobservable error terms. As is known, Yule–Walker estimators are asymptotically efficient for autoregressive time series. The focus of this article is the Yule–Walker estimators for time series with trends. A nonparametric detrending procedure is proposed. It is concluded that the asymptotic properties of the Yule–Walker estimators of autoregressive coefficients are not altered by the detrending procedure. The results of the simulation studies and real data application corroborate the asymptotic theory.

Suggested Citation

  • Qiu, D. & Shao, Q. & Yang, L., 2013. "Efficient inference for autoregressive coefficients in the presence of trends," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 40-53.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:40-53
    DOI: 10.1016/j.jmva.2012.07.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12001844
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.07.016?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. L. Yang & R. Tschernig, 1999. "Multivariate bandwidth selection for local linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 793-815.
    2. Peter Hall & Ingrid Van Keilegom, 2003. "Using difference‐based methods for inference in nonparametric regression with time series errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 443-456, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. L. Tang & Q. Shao, 2014. "Efficient Estimation For Periodic Autoregressive Coefficients Via Residuals," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 378-389, July.
    2. Benny Ren & Ian Barnett, 2022. "Autoregressive mixture models for clustering time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 918-937, November.
    3. Qin Shao & Lijian Yang, 2017. "Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 507-524, March.

    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. Rong Liu & Lijian Yang, 2008. "Kernel estimation of multivariate cumulative distribution function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 661-677.
    2. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Estimation of Generalized Impulse Response Functions," Econometric Society World Congress 2000 Contributed Papers 1417, Econometric Society.
    3. Yuejin Zhou & Yebin Cheng & Wenlin Dai & Tiejun Tong, 2018. "Optimal difference-based estimation for partially linear models," Computational Statistics, Springer, vol. 33(2), pages 863-885, June.
    4. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871.
    5. Max Köhler & Anja Schindler & Stefan Sperlich, 2014. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," International Statistical Review, International Statistical Institute, vol. 82(2), pages 243-274, August.
    6. Cheng, Ming-Yen & Peng, Liang, 2006. "Simple and efficient improvements of multivariate local linear regression," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1501-1524, August.
    7. Biqing Cai & Dag Tjøstheim, 2015. "Nonparametric Regression Estimation for Multivariate Null Recurrent Processes," Econometrics, MDPI, vol. 3(2), pages 1-24, April.
    8. Sébastien Laurent & Jean‐Pierre Urbain, 2005. "Bridging the gap between Ox and Gauss using OxGauss," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 131-139, January.
    9. Dalla, Violetta & Giraitis, Liudas & Robinson, Peter M., 2020. "Asymptotic theory for time series with changing mean and variance," Journal of Econometrics, Elsevier, vol. 219(2), pages 281-313.
    10. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    11. Qin Shao & Lijian Yang, 2017. "Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 507-524, March.
    12. Naito, Kanta & Yoshizaki, Masahiro, 2009. "Bandwidth selection for a data sharpening estimator in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1465-1486, August.
    13. Wolfgang Härdle & Torsten Kleinow & Rolf Tschernig, 2001. "Web Quantlets for Time Series Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 179-188, March.
    14. Hupfeld, Stefan, 2009. "Rich and healthy--better than poor and sick?: An empirical analysis of income, health, and the duration of the pension benefit spell," Journal of Health Economics, Elsevier, vol. 28(2), pages 427-443, March.
    15. Mohamed Chikhi & Claude Diebolt, 2010. "Nonparametric analysis of financial time series by the Kernel methodology," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 865-880, August.
    16. Inder Tecuapetla-Gómez & Axel Munk, 2017. "Autocovariance Estimation in Regression with a Discontinuous Signal and m-Dependent Errors: A Difference-Based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 346-368, June.
    17. Vidaurre, Diego & Bielza, Concha & Larrañaga, Pedro, 2013. "Sparse regularized local regression," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 122-135.
    18. Wei, Honglei & Zhang, Hongfan & Jiang, Hui & Huang, Lei, 2022. "On the semi-varying coefficient dynamic panel data model with autocorrelated errors," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    19. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.
    20. Jan Koláček & Ivana Horová, 2017. "Bandwidth matrix selectors for kernel regression," Computational Statistics, Springer, vol. 32(3), pages 1027-1046, September.

    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:jmvana:v:114:y:2013:i:c:p:40-53. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.