Nongaussian autoregressive sequences and random fields

  • Keh-Shin Lii
  • Murray Rosenblatt
Part of the Progress in Probability book series (PRPR, volume 39)


In this paper we discuss estimation procedures for the parameters of autoregressive schemes. There is a large literature concerned with estimation in the one-dimensional Gaussian case. Much of our discussion will however be dedicated to the nonGaussian context, some aspects of which have been considered only in recent years. Results have also at times been obtained in the broader context of autoregressive moving average schemes. We restrict ourselves to the case of autoregressive schemes for the sake of simplicity. Also they are the discrete analogue of simple versions of stochastic differential equations with constant coefficients. It is also apparent that nonGaussian autoregressive stationary sequences have a richer and more complicated structure than that of the Gaussian autoregressive stationary sequences.


Minimum Entropy Gaussian Case Unique Stationary Solution Rational Spectral Density Autoregressive Scheme 
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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Keh-Shin Lii
    • 1
  • Murray Rosenblatt
    • 1
  1. 1.Mathematics DepartmentUniversity of CaliforniaSan Diego La JollaUSA

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