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Goodness–of–Fit Tests for Bivariate Time Series of Counts

Author

Listed:
  • Šárka Hudecová

    (Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic)

  • Marie Hušková

    (Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic)

  • Simos G. Meintanis

    (Department of Economics, National and Kapodistrian University of Athens, 105 59 Athens, Greece
    Unit for Pure and Applied Analytics, North–West University, Potchefstroom 2531, South Africa)

Abstract

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

Suggested Citation

  • Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2021. "Goodness–of–Fit Tests for Bivariate Time Series of Counts," Econometrics, MDPI, vol. 9(1), pages 1-20, March.
    • Handle: RePEc:gam:jecnmx:v:9:y:2021:i:1:p:10-:d:510257
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    References listed on IDEAS

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