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<p>Long memory and zero inflation are widely observed in time series, but there are few studies for modeling integer-valued time series with these two common properties. In this paper, we introduce a new long memory zero-inflated geometric INAR(1) model and its <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation>-valued version. Some basic properties of the models are discussed. The method of moments is used for estimating the parameters without observing the modulating process. In addition, a zero inflation test based on the model is established. As an illustration, some simulation results are presented to evaluate the performance of parameter estimation and testing methods. Finally, we apply the models to liquor offense and exchange rate data, effectively identifying the zero inflation phenomenon in datasets with long memory.</p>

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Modeling long memory with zero-inflated geometric INAR(1) process and its \(\mathbb {Z}\)-valued version

  • 期刊论文

  • 发表日期：

    2026年4月11日

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  • Yixuan Niu,
  • Fukang Zhu,
  • Yanqiu Yang

摘要

Long memory and zero inflation are widely observed in time series, but there are few studies for modeling integer-valued time series with these two common properties. In this paper, we introduce a new long memory zero-inflated geometric INAR(1) model and its \(\mathbb {Z}\) Z -valued version. Some basic properties of the models are discussed. The method of moments is used for estimating the parameters without observing the modulating process. In addition, a zero inflation test based on the model is established. As an illustration, some simulation results are presented to evaluate the performance of parameter estimation and testing methods. Finally, we apply the models to liquor offense and exchange rate data, effectively identifying the zero inflation phenomenon in datasets with long memory.