Page 104 - Textos de Matemática Vol. 47

94 I. PEREIRA, M. SCOTTO, AND R. NICOLETTE
5. Concluding Remarks
This paper has presented 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. Basic probabilistic and statistical properties of the model are established as well as parameter estima- tion and forecasting.
We would like to stress here that an important issue when fitting PINAR models lies with parsimony. Even every simple PINAR model can have an in- ordinately large number of parameters. This is also true when dealing with PSETINAR models. Therefore, the development of procedures for dimensionality reduction is an impeding problem. This remains a topic of future research.
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(I. Pereira and M. Scotto) Departamento de Matema´tica and CIDMA, Universidade de Aveiro, Portugal
E-mail address: isabel.pereira@ua.pt; mscotto@ua.pt
(R. Nicolette) CIDMA
E-mail address: raquel.nicolette@gmail.com