Brazilian Journal of Probability and Statistics

Time series of count data: A review, empirical comparisons and data analysis

Glaura C. Franco, Helio S. Migon, and Marcos O. Prates

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Observation and parameter driven models are commonly used in the literature to analyse time series of counts. In this paper, we study the characteristics of a variety of models and point out the main differences and similarities among these procedures, concerning parameter estimation, model fitting and forecasting. Alternatively to the literature, all inference was performed under the Bayesian paradigm. The models are fitted with a latent AR($p$) process in the mean, which accounts for autocorrelation in the data. An extensive simulation study shows that the estimates for the covariate parameters are remarkably similar across the different models. However, estimates for autoregressive coefficients and forecasts of future values depend heavily on the underlying process which generates the data. A real data set of bankruptcy in the United States is also analysed.

Article information

Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 756-781.

Received: May 2018
Accepted: March 2019
First available in Project Euclid: 26 August 2019

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Zentralblatt MATH identifier

Observation driven model parameter driven model autoregressive processes Bayesian inference


Franco, Glaura C.; Migon, Helio S.; Prates, Marcos O. Time series of count data: A review, empirical comparisons and data analysis. Braz. J. Probab. Stat. 33 (2019), no. 4, 756--781. doi:10.1214/19-BJPS437.

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