Abstract
Count data appears in many research fields and exhibits certain features that make modeling difficult. Most popular approaches to modeling count data can be classified into observation and parameter-driven models. In this paper, we review two models from these classes: the log-linear multivariate conditional intensity model (also referred to as an integer-valued generalized autoregressive conditional heteroskedastic model) and the non-linear state-space model for count data. We compare these models in terms of forecasting performance on simulated data and two real datasets. In simulations, we consider the case of model misspecification. We find that both models have advantages in different situations, and we discuss the pros and cons of inference for both models in detail.
Highlights
Modeling time series of counts is relevant in a range of application areas, including the dynamics of the number of infectious diseases, number of road accidents or number of bank failures
We present a comparative study of two families of multivariate count data models, namely
We first summarize the use of Poisson distribution for count data, analyze both models under an independence assumption in the Poisson random variables, and at the end of this section, we discuss the extension of modeling multiple count time series with multivariate Poisson distribution
Summary
Modeling time series of counts is relevant in a range of application areas, including the dynamics of the number of infectious diseases, number of road accidents or number of bank failures. The problem of calculating confidence sets for the parameters that are close to or on the boundary rises and has not been yet solved in the literature Another observation driven model that has been proposed as an alternative to ACI framework is log-linear model, see Fokianos and Tjøstheim [17], a multivariate extension of which has been considered in Doukhan et al [10]. Even though the problem of modeling joint distribution remains, the advantage of this approach is that no restrictions on the parameter space are required due to the log-transform of the data Another class of models that can be considered for modeling count data, but is rarely used in the literature, is parameter driven models and, in particular, non-linear state-space models.
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