Page 117 - Textos de Matemática Vol. 47

MODELLING TIME SERIES OF COUNTS: AN INAR APPROACH
MARIA EDUARDA SILVA
Not everything that counts can be counted, and not everything that can be counted counts Thank you, Nazar´e
Abstract. Timeseriesofcountsarisewhentheinterestliesonthenum- ber of certain events occurring during a specified time interval. Many of these data sets are characterized by low counts, asymmetric distributions, excess zeros, over dispersion, ruling out normal approximations. Several approaches and diversified models that explicitly account for the dis- creteness of the data have been considered in the literature, among which are the INteger-valued AutoRegressive, INAR, models. These models are based on random operations which, operating on discrete variables ensure an integer-valued result. The INAR models are attractive since they are linear-like models for discrete time series and exhibit recognizable corre- lation structures. This paper considers INAR models for analyzing time series of counts and discusses associated statistical inference, comprising estimation, diagnostics and model assessment.
1. Introduction
The problem of modelling time series of low counts has attracted many researchers over the last few decades. In fact time series of counts arise in many di↵erent contexts, usually as counts of certain events or objects in specified time intervals as for example: social science [31, 37], queueing systems [1], experimental biology [54], environmental processes [48, 11, 24], economics and finance [6, 39, 15, 28, 27], epidemiology [10, 53], international tourism demand [8, 17, 7], statistical control processes [50, 52], telecommunications [30], optimal alarm systems [34], and in the biopharmaceutical industry [3].
Accepted: 23 February 2015.
2010 Mathematics Subject Classification. 60G10, 62M10. Key words and phrases. Time Series, Count Data, INAR.
The work was supported by Portuguese funds through the CIDMA - Center for Re- search and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT Fundac¸˜ao para a Ciˆencia e a Tecnologia), within project UID/MAT/04106/2013.
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