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INTEGER-VALUED SELF-EXCITING PERIODIC THRESHOLD AUTOREGRESSIVE PROCESSES
ISABEL PEREIRA, MANUEL SCOTTO, AND RAQUEL NICOLETTE
Dedicated to Maria de Nazar´e Lopes
Abstract. In this paper, the periodic self-exciting threshold integer- valued autoregressive model of order one with period T driven by a periodic sequence of independent Poisson-distributed random variables is introduced and analyzed in detail. Basic probabilistic and statistical properties of the model are discussed as well as parameter estimation and forecasting.
1. Introduction
Modeling the temporal dependence and evolution of integer-valued (and in particular low counts) time series is an area of research which is gaining im- portance in time series analysis. The problem of developing models for integer- valued time series is, indeed, very challenging because traditional approaches based on Gaussian autoregressive-moving average processes, are of little use to accurately describe time series defined over finite range of counts or exhibiting features such low counts, over dispersion, asymmetric marginal distributions, or excess of zeros. The need to analyze such data adequately led to a multi- plicity of approaches and a diversification of models that explicitly account for such features.
Recently, models for dealing with integer-valued time series exhibiting the so-called piecewise phenomenon have been proposed in the literature. The fun- damental reason for introducing such class of models is the need to model ran- dom cyclic behavior that exists in many time series. In the continuous-valued
Accepted: 14 March 2015.
2010 Mathematics Subject Classification. 62M10; 91B70; 60G10 .
Key words and phrases. Count processes, Binomial thinning, Threshold models.
This 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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