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A note on compatibility of conditional autoregressive models

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  • Dreassi, Emanuela
  • Rigo, Pietro

Abstract

Suppose that, to assess the joint distribution of a random vector (X1,…,Xn), one selects the kernels Q1,…,Qn with Qi to be regarded as a possible conditional distribution for Xi given (Xj:j≠i); Q1,…,Qn are compatible if there exists a joint distribution for (X1,…,Xn) with conditionals Q1,…,Qn. Similarly, Q1,…,Qn are improperly compatible if they can be obtained, according to the usual rule, with an improper distribution in place of a probability distribution. In this paper, compatibility and improper compatibility of Q1,…,Qn are characterized under some assumptions on their functional form. The characterization applies, in particular, if each Qi belongs to a one parameter exponential family. Special attention is paid to Gaussian conditional autoregressive models.

Suggested Citation

  • Dreassi, Emanuela & Rigo, Pietro, 2017. "A note on compatibility of conditional autoregressive models," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 9-16.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:9-16
    DOI: 10.1016/j.spl.2017.01.008
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    References listed on IDEAS

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    1. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
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