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A Bivariate First-Order Autoregressive Time Series Model in Exponential Variables (BEAR(1))

Author

Listed:
  • Lee S. Dewald

    (United States Military Academy, West Point, New York 10996-1786)

  • Peter A. W. Lewis

    (Department of Operations Research, Naval Postgraduate School, Monterey, California 93942-5000)

  • Ed McKenzie

    (Department of Mathematics, University of Strathclyde, Glasgow, Scotland)

Abstract

A simple time series model for bivariate exponential variables having first-order autoregressive structure is presented, the BEAR(1) model. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR(2)). The process is Markovian in the bivariate sense and has correlation structure analogous to that of the Gaussian AR(1) bivariate time series model. The model exhibits a full range of positive correlations and cross-correlations. With some modification in either the innovation or the random coefficients, the model admits some negative values for the cross-correlations. The marginal processes are shown to have correlation structure of ARMA(2, 1) models.

Suggested Citation

  • Lee S. Dewald & Peter A. W. Lewis & Ed McKenzie, 1989. "A Bivariate First-Order Autoregressive Time Series Model in Exponential Variables (BEAR(1))," Management Science, INFORMS, vol. 35(10), pages 1236-1246, October.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:10:p:1236-1246
    DOI: 10.1287/mnsc.35.10.1236
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    Citations

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    Cited by:

    1. Miroslav Ristić & Biljana Popović, 2003. "A bivariate uniform autoregressive process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 797-802, December.
    2. Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    3. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.

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