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<p>The effects of temporal aggregation and systematic sampling on the integer-valued GARCH (INGARCH) processes have been studied. In this paper, we generalize these results to a periodic INGARCH (PINGARCH) process. First, we give definitions of strong and weak PINGARCH processes, and show that aggregated or sampled PINGARCH processes are weak. Second, we provide expressions of aggregated or sampled PINGARCH process, and find that a lower-period weak PINGARCH process can be obtained by aggregating or sampling the original process. Methods for estimating aggregated periodic processes are shown. Finally, from our simulation results, we find that estimates based on aggregated or sampled PINGARCH processes usually perform better than those based on the original process, in terms of mean square error. Actually, our results are different from those in past studies, which shows the superiority of using the original process, and related explanations are also given.</p>

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The effects of aggregation and sampling on periodic INGARCH processes

  • 期刊论文

  • 发表日期：

    2025年3月12日

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  • Bing Su,
  • Fukang Zhu

摘要

The effects of temporal aggregation and systematic sampling on the integer-valued GARCH (INGARCH) processes have been studied. In this paper, we generalize these results to a periodic INGARCH (PINGARCH) process. First, we give definitions of strong and weak PINGARCH processes, and show that aggregated or sampled PINGARCH processes are weak. Second, we provide expressions of aggregated or sampled PINGARCH process, and find that a lower-period weak PINGARCH process can be obtained by aggregating or sampling the original process. Methods for estimating aggregated periodic processes are shown. Finally, from our simulation results, we find that estimates based on aggregated or sampled PINGARCH processes usually perform better than those based on the original process, in terms of mean square error. Actually, our results are different from those in past studies, which shows the superiority of using the original process, and related explanations are also given.