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Computational approaches to estimation in the principal component analysis of a stochastic process

Author

Listed:
  • Ana M. Aguilera
  • Ramón Gutiérrez
  • Francisco A. Ocaña
  • Mariano J. Valderrama

Abstract

After performing a review of the classical procedures for estimation in the principal component analysis (PCA) of a second order stochastic process, two alternative procedures have been developed to approach such estimates. The first is based on the orthogonal projection method and uses cubic interpolating splines when the data are discrete. The second is based on the trapezoidal method. The accuracy of both procedures is tested by simulating approximated sample‐functions of the Brownian motion and the Brownian bridge. The real principal factors of these stochastic processes, which can be evaluated directly, are compared with those estimated by means of the two mentioned algorithms. An application for estimation in the PCA of tourism evolution in Spain from real data is also included.

Suggested Citation

  • Ana M. Aguilera & Ramón Gutiérrez & Francisco A. Ocaña & Mariano J. Valderrama, 1995. "Computational approaches to estimation in the principal component analysis of a stochastic process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(4), pages 279-299, December.
    • Handle: RePEc:wly:apsmda:v:11:y:1995:i:4:p:279-299
    DOI: 10.1002/asm.3150110402
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    Cited by:

    1. Paula R. Bouzas & Ana M. Aguilera & Nuria Ruiz-Fuentes, 2012. "Functional Estimation of the Random Rate of a Cox Process," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 57-69, March.
    2. Christian Acal & Ana M. Aguilera & Manuel Escabias, 2020. "New Modeling Approaches Based on Varimax Rotation of Functional Principal Components," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    3. Burghouwt, Guillaume & de Wit, Jaap G., 2015. "In the wake of liberalisation: long-term developments in the EU air transport market," Transport Policy, Elsevier, vol. 43(C), pages 104-113.

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