IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v134y2019icp110-122.html
   My bibliography  Save this article

A novel partial-linear single-index model for time series data

Author

Listed:
  • Huang, Lei
  • Jiang, Hui
  • Wang, Huixia

Abstract

Partial-linear single-index models have been widely studied and applied, but their current applications to time series modeling still need some strong and inappropriate assumptions. A novel method which relaxes those assumptions is proposed. It extends the applicability of partial-linear single-index models to time series modeling, taking both lag variables and autocorrelated errors into consideration. An estimation procedure based on Whittle likelihood is proposed and some asymptotical properties of the corresponding estimators are derived. In addition, some simulation studies are conducted to elaborate that the proposed model is necessary in certain situations. The proposed models are also shown to be useful and reasonable in real data analysis, indicating the feasibility and practicability of the proposed estimation method.

Suggested Citation

  • Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.
  • Handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:110-122
    DOI: 10.1016/j.csda.2018.12.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302913
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2018.12.012?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. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.
    3. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    4. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    5. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," LSE Research Online Documents on Economics 28868, London School of Economics and Political Science, LSE Library.
    6. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 928-955, November.
    7. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," Journal of Econometrics, Elsevier, vol. 157(1), pages 151-164, July.
    8. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    9. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    10. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    11. Tianhao Wang & Yingcun Xia, 2015. "Whittle Likelihood Estimation of Nonlinear Autoregressive Models With Moving Average Residuals," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1083-1099, September.
    12. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models. I. Time series," LSE Research Online Documents on Economics 57580, London School of Economics and Political Science, LSE Library.
    13. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    14. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    15. Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 857-875, November.
    16. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    17. Yao, Qiwei & Brockwell, Peter J., 2006. "Gaussian maximum likelihood estimation for ARMA models I: time series," LSE Research Online Documents on Economics 5825, London School of Economics and Political Science, LSE Library.
    18. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    19. 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.
    20. Jun Zhang & Yao Yu & Li-Xing Zhu & Hua Liang, 2013. "Partial linear single index models with distortion measurement errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 237-267, April.
    21. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    22. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, 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. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    2. 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).
    3. Ke, Rui & Lu, Wanbo & Jia, Jing, 2021. "Evaluating multiplicative error models: A residual-based approach," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    4. Rodrigo A. Oliveira & Gilberto A. Paula, 2021. "Additive models with autoregressive symmetric errors based on penalized regression splines," Computational Statistics, Springer, vol. 36(4), pages 2435-2466, December.

    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. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.
    2. Michael Wegener & Göran Kauermann, 2017. "Forecasting in nonlinear univariate time series using penalized splines," Statistical Papers, Springer, vol. 58(3), pages 557-576, September.
    3. Jia Chen & Degui Li & Jiti Gao, 2013. "Non- and Semi-Parametric Panel Data Models: A Selective Review," Monash Econometrics and Business Statistics Working Papers 18/13, Monash University, Department of Econometrics and Business Statistics.
    4. 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).
    5. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 928-955, November.
    6. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    7. 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.
    8. Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
    9. Timothy K.M. Beatty & Erling Røed Larsen, 2005. "Using Engel curves to estimate bias in the Canadian CPI as a cost of living index," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 482-499, May.
    10. Yong Bao, 2018. "The asymptotic covariance matrix of the QMLE in ARMA models," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 309-324, April.
    11. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    13. repec:esx:essedp:767 is not listed on IDEAS
    14. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    15. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    16. Li, Jinqing & Ma, Jun, 2019. "Maximum penalized likelihood estimation of additive hazards models with partly interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 170-180.
    17. Tianhao Wang & Yingcun Xia, 2015. "Whittle Likelihood Estimation of Nonlinear Autoregressive Models With Moving Average Residuals," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1083-1099, September.
    18. Robinson, Peter M., 2011. "Inference on power law spatial trends (Running Title: Power Law Trends)," LSE Research Online Documents on Economics 58100, London School of Economics and Political Science, LSE Library.
    19. Norkutė, Milda & Westerlund, Joakim, 2019. "The factor analytical method for interactive effects dynamic panel models with moving average errors," Econometrics and Statistics, Elsevier, vol. 11(C), pages 83-104.
    20. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Mélard, 2017. "Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 617-635, September.
    21. Zheng, Tingguo & Chen, Rong, 2017. "Dirichlet ARMA models for compositional time series," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 31-46.

    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:134:y:2019:i:c:p:110-122. 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.