Bootstrap for Maximum Likelihood Estimates of PARMA Coefficients

  • Anna E. DudekEmail author
  • Harry Hurd
  • Wioletta Wójtowicz
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


In this chapter we use bootstrap techniques to estimate empirical distributions of parameter estimates for PAR sequences determined by maximum likelihood techniques. The parameters are not the periodic autoregression parameters, but are the coefficients in the Fourier series representing the parameters. We compare two different bootstrap techniques, IID and GSBB, applied to the residuals of the maximum likelihood estimation. The IID method seems a little better, which is not a surprise since the conditions for the GSBB are not completely satisfied. We expect these method to also work satisfactorily for full PARMA estimations, where both PMA and PAR terms are present in the model.



Research of Anna Dudek was partially supported by the Polish Ministry of Science and Higher Education and AGH local grant.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Anna E. Dudek
    • 1
    Email author
  • Harry Hurd
    • 2
  • Wioletta Wójtowicz
    • 1
  1. 1.AGH University of Science and TechnologyKrakowPoland
  2. 2.Department of Statistics and Operations ResearchUniversity of North Carolina at Chapel HillChapel HillUSA

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