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Abstract:
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The focus of this talk is on modeling bivariate time series of counts. We consider a Poisson-based bivariate INGARCH model where the bivariate Poisson distribution is constructed by trivariate reduction of independent Poisson variables. We show that stability results previously obtained in the literature extend to the case where the Poisson distribution is replaced by a general distribution from the exponential family. Furthermore, we consider asymptotic properties of the maximum likelihood estimators. A limitation of the model is that it is not able to capture negative dependence between the two time series. We propose a new bivariate Poisson distribution to replace the distribution in the bivariate INGARCH model. It is constructed by use of copulas, which allows it to capture negative dependence between the two time series at a given point in time. We show that the aforementioned stability result also applies in this new setup. The two types of models are compared through a simulation study, and both models are applied to a real data example.
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