Statistical Modelling 15 (6) (2015), 590–618

Thinning-based models in the analysis of integer-valued time series: a review

Manuel G. Scotto
CIDMA and Department of Mathematics,
University of Aveiro,
Portugal
e-mail: mscotto@ua.pt

Christian H. Weiß
2Department of Mathematics and Statistics,
Helmut Schmidt University Hamburg,
Germany


Sónia Gouveia
IEETA,
CIDMA and Department of Mathematics,
University of Aveiro,
Portugal


Abstract:

This article aims at providing a comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning. Such models have proven to be useful in the analysis of many real-world applications ranging from economy and finance to medicine. We review the literature of the most relevant thinning operators proposed in the analysis of univariate and multivariate integer-valued time series with either finite or infinite support. Finally, we also outline and discuss possible directions of future research.

Keywords:

time series; autocorrelation function(ACF); counts; thinning operators.

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