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A Residual Based Method for Fitting PAR Models Using Fourier Representation of Periodic Coefficients

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Cyclostationarity: Theory and Methods III

Part of the book series: Applied Condition Monitoring ((ACM,volume 6))

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Abstract

In this paper we present a preliminary simulation study of a method for estimating the Fourier coefficients of the periodic parameters of a periodic autoregressive (PAR) sequence. For motivational and comparative purposes, we first examine the estimation of Fourier coefficients of a periodic function added to white noise. The method is based on the numerical minimization of mean squared residuals, and permits the fitting of PAR models when the period T equals the observation size N. For this paper, algorithms and simulations were coded in MATLAB, but an implementation will be available in the R package, perARMA.

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References

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Acknowledgements

The author would like to acknowledge the efforts of Dr. Wioletta Wójtowicz for assistance in the simulations described here.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-3260, USA

    Harry Hurd

Authors
  1. Harry Hurd
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Corresponding author

Correspondence to Harry Hurd .

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Editors and Affiliations

  1. National School of Engineers of Sfax , Sfax, Tunisia

    Fakher Chaari

  2. Institute of Mathematics, Cracow University of Technology, Cracow, Poland

    Jacek Leskow

  3. Department of Engineering, University of Napoli “Parthenope” , Napoli, Italy

    Antonio Napolitano

  4. Institute of Mining Engineering, Wrocław University of Technology, Wroclaw, Poland

    Radoslaw Zimroz

  5. Institute of Mathematics and computer Science, Wroclaw University of Technology, Wroclaw, Poland

    Agnieszka Wylomanska

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Hurd, H. (2017). A Residual Based Method for Fitting PAR Models Using Fourier Representation of Periodic Coefficients. In: Chaari, F., Leskow, J., Napolitano, A., Zimroz, R., Wylomanska, A. (eds) Cyclostationarity: Theory and Methods III. Applied Condition Monitoring, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-51445-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-51445-1_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51444-4

  • Online ISBN: 978-3-319-51445-1

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