Abstract
The aim of this paper is to develop a probabilistic study of a wide class of conditionally heteroscedastic models recently introduced in the literature, the compound Poisson INGARCH processes [7]. This class includes, in particular, some well-known models like the Poisson INGARCH of Ferland, Latour, and Oraichi [4] or the negative binomial and generalized Poisson INGARCH introduced by Zhu in 2011 and 2012, respectively.
Within this class, we analyze the existence and ergodicity of a strictly and weakly stationary solution. For a new particular model of that class, the Neyman type-A INGARCH model, we derive the autocorrelation function, analyze the existence of higher-order moments, and obtain an explicit form of their first four cumulants, from which we deduce the corresponding skewness and kurtosis.
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*This work is supported by the Centro de Matemática da Universidade de Coimbra (funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT – Fundação para a Ciência e Tecnologia under the project PEst-C/MAT/UI0324/2013). The work of the third author was supported by a grant from the FCT with reference SFRH/BD/85336/2012.
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Gonçalves, E., Lopes, N.M. & Silva, F. A New Approach to Integer-Valued Time Series Modeling: The Neyman Type-A INGARCH Model* . Lith Math J 55, 231–242 (2015). https://doi.org/10.1007/s10986-015-9276-x
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DOI: https://doi.org/10.1007/s10986-015-9276-x