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Sieves estimator of the operator of a functional autoregressive process

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.
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    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. repec:hum:wpaper:sfb649dp2016-025 is not listed on IDEAS
    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. 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.
    8. Boukhiar, Souad & Mourid, Tahar, 2022. "Resolvent estimators for functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    9. 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.

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