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<p>This paper addresses the coherent forecasting problem for integer-valued autoregressive (INAR) time series with a zero-modified geometric (ZMG) marginal distribution. Count time series often exhibit phenomenon of zero inflation or zero deflation which leads to overdispersion or underdispersion. To capture this phenomenon, an INAR model with ZMG marginal distribution and of order one (ZMGINAR(1)) can be used. This model is based on a negative binomial thinning operator. This model is suitable for count data having overdispersion and zero inflation or deflation, as seen in many epidemic time series. Some probabilistic and inferential properties of the model are studied. A coherent forecast methodology is suggested for this model and two real data sets have been analyzed using the proposed methodology.</p>

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Forecasting Zero Modified Geometric INAR(1) Process

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • Aishwarya Ghodake,
  • Manik Awale

摘要

This paper addresses the coherent forecasting problem for integer-valued autoregressive (INAR) time series with a zero-modified geometric (ZMG) marginal distribution. Count time series often exhibit phenomenon of zero inflation or zero deflation which leads to overdispersion or underdispersion. To capture this phenomenon, an INAR model with ZMG marginal distribution and of order one (ZMGINAR(1)) can be used. This model is based on a negative binomial thinning operator. This model is suitable for count data having overdispersion and zero inflation or deflation, as seen in many epidemic time series. Some probabilistic and inferential properties of the model are studied. A coherent forecast methodology is suggested for this model and two real data sets have been analyzed using the proposed methodology.