IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i1p93-108.html
   My bibliography  Save this article

Sieves estimator of the operator of a functional autoregressive process

Author

Listed:
  • Mourid, Tahar
  • Bensmain, Nawel

Abstract

We consider the estimation of the operator of one-order functional autoregressive process by the sieves method of Grenander in the case of dependent random variables framework. We show the almost sure convergence in Hilbert-Schmidt norm when the operator is of kernel type in Gaussian case afterwards we generalize the results to the Hilbert-Schmidt operator. In the kernel operator type the a.s. convergence is obtained under polynomial growth size improving the logaritmic growth size obtained early. Prediction of continuous time stochastic process is also examined.

Suggested Citation

  • Mourid, Tahar & Bensmain, Nawel, 2006. "Sieves estimator of the operator of a functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 93-108, January.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:1:p:93-108
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00273-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    2. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(2), pages 260-284, April.
    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. Berhoune, Kamila & Bensmain, Nawel, 2018. "Sieves estimator of functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 60-69.
    2. Chang, Chih-Hao & Chen, Zih-Bing & Huang, Shih-Feng, 2022. "Forecasting of high-resolution electricity consumption with stochastic climatic covariates via a functional time series approach," Applied Energy, Elsevier, vol. 309(C).
    3. Ying Chen & Wee Song Chua & Wolfgang Karl Härdle, 2019. "Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1473-1489, September.
    4. Chen, Ying & Chua, Wee Song & Koch, Thorsten, 2018. "Forecasting day-ahead high-resolution natural-gas demand and supply in Germany," Applied Energy, Elsevier, vol. 228(C), pages 1091-1110.
    5. Chen, Ying & Xu, Xiuqin & Koch, Thorsten, 2020. "Day-ahead high-resolution forecasting of natural gas demand and supply in Germany with a hybrid model," Applied Energy, Elsevier, vol. 262(C).
    6. Ying Chen & Bo Li, 2017. "An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 371-388, July.
    7. Boukhiar, Souad & Mourid, Tahar, 2022. "Resolvent estimators for functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    8. Xu, Meng & Li, Jialiang & Chen, Ying, 2017. "Varying coefficient functional autoregressive model with application to the U.S. treasuries," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 168-183.

    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. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
    2. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    3. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
    4. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
    5. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    6. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    7. Brendstrup, Bjarne & Paarsch, Harry J., 2007. "Semiparametric identification and estimation in multi-object, English auctions," Journal of Econometrics, Elsevier, vol. 141(1), pages 84-108, November.
    8. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    9. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    10. Chen, Liang & Dolado, Juan José & Gonzalo, Jesús & Pan, Haozi, 2023. "Estimation of characteristics-based quantile factor models," UC3M Working papers. Economics 37095, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Xiaohong Chen & James J. Heckman & Edward Vytlacil, 2000. "Identification and SQRT N Efficient Estimation of Semiparametric Panel Data Models with Binary Dependent Variables and a Latent Factor," Econometric Society World Congress 2000 Contributed Papers 1567, Econometric Society.
    12. Coppejans, Mark, 2001. "Estimation of the binary response model using a mixture of distributions estimator (MOD)," Journal of Econometrics, Elsevier, vol. 102(2), pages 231-269, June.
    13. Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
    14. Hall, George & Rust, John, 2021. "Estimation of endogenously sampled time series: The case of commodity price speculation in the steel market," Journal of Econometrics, Elsevier, vol. 222(1), pages 219-243.
    15. Demian Pouzo, 2015. "On the Non-Asymptotic Properties of Regularized M-estimators," Papers 1512.06290, arXiv.org, revised Oct 2016.
    16. Xiaohong Chen & Zhipeng Liao & Yixiao Sun, 2012. "Sieve Inference on Semi-nonparametric Time Series Models," Cowles Foundation Discussion Papers 1849, Cowles Foundation for Research in Economics, Yale University.
    17. Kapetanios, G. & Mitchell, J. & Price, S. & Fawcett, N., 2015. "Generalised density forecast combinations," Journal of Econometrics, Elsevier, vol. 188(1), pages 150-165.
    18. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    19. Michael McAleer & Marcelo C. Medeiros, 2009. "Forecasting Realized Volatility with Linear and Nonlinear Models," CARF F-Series CARF-F-189, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    20. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, 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:stapro:v:76:y:2006:i:1:p:93-108. 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.