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Computing the best linear predictor in a Hilbert space. Applications to general ARMAH processes

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  • Bosq, D.

Abstract

This article deals with linear prediction in large dimensions. One obtains various explicit forms of the best linear predictor in a Hilbert space. The difficulty comes from the fact that the associated linear operator is, in general, not continuous. Applications to ARMAH processes, models with noise and Bayesian estimators are considered.

Suggested Citation

  • Bosq, D., 2014. "Computing the best linear predictor in a Hilbert space. Applications to general ARMAH processes," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 436-450.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:436-450
    DOI: 10.1016/j.jmva.2013.11.013
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    References listed on IDEAS

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    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    2. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    3. Ruiz-Medina, M.D. & Salmeron, R. & Angulo, J.M., 2007. "Kalman filtering from POP-based diagonalization of ARH(1)," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4994-5008, June.
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    Cited by:

    1. Atefeh Zamani & Hossein Haghbin & Maryam Hashemi & Rob J. Hyndman, 2022. "Seasonal functional autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 197-218, March.
    2. Klepsch, J. & Klüppelberg, C. & Wei, T., 2017. "Prediction of functional ARMA processes with an application to traffic data," Econometrics and Statistics, Elsevier, vol. 1(C), pages 128-149.
    3. Kada Kloucha, Meryem & Mourid, Tahar, 2019. "Best linear predictor of a C[0,1]-valued functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 114-120.
    4. Klepsch, J. & Klüppelberg, C., 2017. "An innovations algorithm for the prediction of functional linear processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 252-271.

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