Mathematical Methods of Statistics

, Volume 23, Issue 2, pp 103–115 | Cite as

Asymptotic properties of the MLE for the autoregressive process coefficients under stationary Gaussian noise

  • A. Brouste
  • C. Cai
  • M. Kleptsyna


In this paper we study the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order p with regular stationary Gaussian noise. We prove the large sample asymptotic properties of the MLE under very mild conditions. We do simulations for fractional Gaussian noise (fGn), autoregressive noise (AR(1)) and moving average noise (MA(1)).


autoregressive process MLE fractional Gaussian noise 

2000 Mathematics Subject Classification

62J05 62F12 62M09 


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© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.Univ. du MaineLeMansFrance

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