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Autoregressive representations of multivariate stationary stochastic processes
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  • Published: December 1988

Autoregressive representations of multivariate stationary stochastic processes

  • Mohsen Pourahmadi1 

Probability Theory and Related Fields volume 80, pages 315–322 (1988)Cite this article

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Abstract

Consider a q-variate weakly stationary stochastic process {X n } with the spectral density W. The problem of autoregressive representation of {X n } or equivalently the autoregressive representation of the linear least squares predictor of X n , based on the infinite past is studied. It is shown that for every W in a large class of densities, the corresponding process has a mean convergent autoregressive representation. This class includes as special subclasses, the densities studied by Masani (1960) and Pourahmadi (1985). As a consequence it is shown that the condition W -1∈L 1qxq or minimality of {X n } is dispensable for this problem. When W is not in this class or when W has zeros of order 2 or more, it is shown that {X n } has a mean Abel summable or mean compounded Cesáro summable autoregressive representation.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, 60115, DeKalb, IL, USA

    Mohsen Pourahmadi

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  1. Mohsen Pourahmadi
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Additional information

Research supported by the NSF Grant MCS-8301240 and the AFOSR, Grant F49620 82 C0009. This work was done while the author was visiting Center for Stochastic Processes, University of North Carolina, Chapel Hill

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Pourahmadi, M. Autoregressive representations of multivariate stationary stochastic processes. Probab. Th. Rel. Fields 80, 315–322 (1988). https://doi.org/10.1007/BF00356109

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  • Received: 30 January 1985

  • Revised: 09 March 1988

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00356109

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Keywords

  • Stochastic Process
  • Probability Theory
  • Spectral Density
  • Large Class
  • Mathematical Biology
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