Abstract
The temporal aggregation (TA) and systematic sampling (SS) in continuous-valued time series were widely studied, while the TA and SS in integer-valued time series obtain very little attention. In this paper, we thoroughly discuss them based on the integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) process. On one hand, the TA and SS for INGARCH processes are studied, and related predictors are discussed. We also illustrate that the TA or SS provides approaches to estimate INGARCH processes with different frequencies. On the other hand, definitions of the strong and weak INGARCH processes are given. The aggregated INGARCH and sampled INGARCH processes are shown to be weak, that is, they satisfy a weak characterization of INGARCH processes in terms of linear projection. Quasi maximum likelihood and nonlinear least squares estimation methods are considered for the weak INGARCH processes. Related asymptotic properties and simulation results are discussed. Finally, an empirical example illustrates the applicability of our results.
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