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Inference for bivariate integer-valued moving average models based on binomial thinning operation

Author

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  • Isabel Silva
  • Maria Eduarda Silva
  • Cristina Torres

Abstract

Time series of (small) counts are common in practice and appear in a wide variety of fields. In the last three decades, several models that explicitly account for the discreteness of the data have been proposed in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so detailed. This work considers Bivariate INteger-valued Moving Average, BINMA, models based on the binomial thinning operation. The main probabilistic and statistical properties of BINMA models are studied. Two parametric cases are analysed, one with the cross-correlation generated through a Bivariate Poisson innovation process and another with a Bivariate Negative Binomial innovation process. Moreover, parameter estimation is carried out by the Generalized Method of Moments. The performance of the model is illustrated with synthetic data as well as with real datasets.

Suggested Citation

  • Isabel Silva & Maria Eduarda Silva & Cristina Torres, 2020. "Inference for bivariate integer-valued moving average models based on binomial thinning operation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2546-2564, November.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:13-15:p:2546-2564
    DOI: 10.1080/02664763.2020.1747411
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    Cited by:

    1. J. Hüsler & M. G. Temido & A. Valente-Freitas, 2022. "On the Maximum of a Bivariate INMA Model with Integer Innovations," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2373-2402, December.
    2. Robert C. Jung & Andrew R. Tremayne, 2020. "Maximum-Likelihood Estimation in a Special Integer Autoregressive Model," Econometrics, MDPI, vol. 8(2), pages 1-15, June.

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