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A State Space Model for Non-Stationary Functional Data1

  • Conference paper
Compstat

  • 1145 Accesses

Abstract

A time dependent state space model with minimal dimension is introduced in this paper by approximating the stochastic process of continuous time nature by means of spline interpolation of its sample paths and then by differentiating its Karhunen-Loève expansion. A comparative study of forecasting, using the Kalman-Bucy filter, with simulated data is presented from a well known non-stationary process, the Brownian motion, discussing its advantages.

1This research was supported in part by Project No. BFM2000-1466 of Dirección General de Investigación, Ministerio de Ciencia y Tecnología.

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References

  • Ruiz, J.C., Valderrama, M.J., and Gutiérrez, R. (1995). Kalman Filtering on Approximative State Space Models. Journal of Optimization Theory and Applications, 84(2), 415–431.

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  • Valderrama, M.J., Aguilera, A.M. and Ocaña, F.A. (2000). Predicción Dinámica mediante Análisis de Datos Funcionales. Hespérides-La Muralla, Madrid.

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  • Valderrama, M.J., Aguilera, A.M. and Ruiz, J.C. (1998). Time Series Forecasting by Principal Component Methods. In: COMPSTAT98 Proceedings in Computational Statistics, 137–146. Heidelberg: Physica-Verlag.

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Author information

Authors and Affiliations

  1. Department of General Economics and Statistics, Faculty of Economics Sciences, University of Huelva, Huelva, 21071, Spain

    Mónica Ortega-Moreno

  2. Department of Statistics and Operations Research, Faculty of Pharmacy, University of Granada, Granada, 18071, Spain

    Mariano J. Valderrama

  3. Department of Statistics and Operations Research, Faculty of Social Sciences, University of Jaén, 23071, Jaén, Spain

    Juan Carlos Ruiz-Molina

Authors
  1. Mónica Ortega-Moreno
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  2. Mariano J. Valderrama
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  3. Juan Carlos Ruiz-Molina
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Editor information

Editors and Affiliations

  1. CASE — Centre of Applied Statistics and Economics, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178, Berlin, Germany

    Wolfgang Härdle

  2. Wirtschaftswissenschaftliche Fakultät, Institut für Statistik und Ökonometrie, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178, Berlin, Germany

    Bernd Rönz

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© 2002 Springer-Verlag Berlin Heidelberg

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Ortega-Moreno, M., Valderrama, M.J., Ruiz-Molina, J.C. (2002). A State Space Model for Non-Stationary Functional Data1 . In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-57489-4_15

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1517-7

  • Online ISBN: 978-3-642-57489-4

  • eBook Packages: Springer Book Archive

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