Exact Likelihood Function Forms for an ARFIMA Process

  • Jeffrey S. Pai
  • Nalini Ravishanker
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


We present four closed form expressions for the exact likelihood function for a Gaussian ARFIMA process, which is useful in modeling time series with long memory and short memory behavior. Use is made of the relationship between the ARFIMA process and the corresponding fractional Gaussian noise process. Application to the simpler short memory ARMA process is illustrated.


Closed Form Expression Markov Chain Monte Carlo Method Multivariate Normal Distribution Partial Regression Coefficient ARMA Process 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • Jeffrey S. Pai
    • 1
  • Nalini Ravishanker
    • 2
  1. 1.Institut für Statistik und Ökonometrie, WWZUniversität BaselBaselSwitzerland
  2. 2.Department of StatisticsUniversity of ConnecticutStorrsUSA

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