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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.

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  • 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. 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.
    3. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
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    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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