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On mixed AR(1) time series model with approximated beta marginal

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  • Popovic, Bozidar V.
  • Pogány, Tibor K.
  • Nadarajah, Saralees

Abstract

We consider the mixed AR(1) time series model when Xt has the two parameter beta distribution , p[set membership, variant](0,1],q>1. Special attention is given to the case p=1 when the marginal distribution is approximated by the power law distribution closely connected with the two parameter Kumaraswamy distribution . Using the Laplace transform technique, we prove that for p=1 the distribution of the innovation process is uniform discrete. For p[set membership, variant](0,1), the innovation process has a continuous distribution. We also consider estimation issues of the model.

Suggested Citation

  • Popovic, Bozidar V. & Pogány, Tibor K. & Nadarajah, Saralees, 2010. "On mixed AR(1) time series model with approximated beta marginal," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1551-1558, October.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:19-20:p:1551-1558
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    References listed on IDEAS

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    1. Ed McKenzie, 1985. "An Autoregressive Process for Beta Random Variables," Management Science, INFORMS, vol. 31(8), pages 988-997, August.
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    1. Božidar Popović & Saralees Nadarajah & Miroslav Ristić, 2013. "A new non-linear AR(1) time series model having approximate beta marginals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 71-92, January.

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