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Prediction of functional ARMA processes with an application to traffic data

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  • Klepsch, J.
  • Klüppelberg, C.
  • Wei, T.

Abstract

For a functional ARMA(p, q) process an approximating vector model, based on functional PCA, is presented. Sufficient conditions are given for the existence of a stationary solution to both the functional and the vector model equations, and the structure of the approximating vector model is investigated. The stationary vector process is used to predict the functional process, where bounds for the difference between vector and functional best linear predictor are given. Finally, functional ARMA processes are applied for the modeling and prediction of highway traffic data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecosta:v:1:y:2017:i:c:p:128-149
    DOI: 10.1016/j.ecosta.2016.10.009
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    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. 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.
    3. Spangenberg, Felix, 2013. "Strictly stationary solutions of ARMA equations in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 127-138.
    4. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    5. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    6. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
    7. Gabrys, Robertas & Kokoszka, Piotr, 2007. "Portmanteau Test of Independence for Functional Observations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1338-1348, December.
    8. Chrobok, R. & Kaumann, O. & Wahle, J. & Schreckenberg, M., 2004. "Different methods of traffic forecast based on real data," European Journal of Operational Research, Elsevier, vol. 155(3), pages 558-568, June.
    9. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
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