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<p>Underdispersion and overdispersion in count time series data are frequently observed. In this paper, we introduce a first-order, non-negative integer-valued autoregressive process with intervened geometric innovations (INAR-IG(1)) based on the binomial thinning operator. It contains the zero-truncated geometric process as a submodel. This model can be used to describe zero-truncated count time series with all modes of dispersion. The main statistical and conditional properties of the proposed process are obtained. The model’s parameters are estimated using the conditional maximum likelihood, and conditional least squares methodologies. In order to evaluate the consistency and efficiency of the estimators under the two estimating methodologies, Monte Carlo simulation experiments are conducted.&#xa0;Also, the suggested model is fitted to a time series of the monthly counts of claimants collecting Short Term Wage Loss Benefits from the WCB and monthly counting burglary crime data sets to demonstrate its potential for challenging underdispersed and overdispersed count data. The INAR-IG(1) model is suitable for modeling claim and crime data, according to model adequacy verification with information criteria, Pearson residuals, predictive capability, etc. For the data sets, the INAR-IG(1) model takes into account a number of forecasting techniques, including the classical, round classical, and coherent median methods. To enable a comprehensive evaluation of its forecasting performance, some forecasting accuracy measures are applied&#xa0;to the mentioned data sets , allowing for meaningful comparison with other competing models. The proposed&#xa0;methodology is demonstrated using real data sets, specifically claim and crime data sets.</p>

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On Shifted INAR(1) Time Series with Intervened Geometric Innovations: Properties, Forecasting with Modeling Crime and Industry Data

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Hassan S. Bakouch,
  • M. M. Gabr,
  • B. S. El-Desouky,
  • Shimaa M. El-Hadidy

摘要

Underdispersion and overdispersion in count time series data are frequently observed. In this paper, we introduce a first-order, non-negative integer-valued autoregressive process with intervened geometric innovations (INAR-IG(1)) based on the binomial thinning operator. It contains the zero-truncated geometric process as a submodel. This model can be used to describe zero-truncated count time series with all modes of dispersion. The main statistical and conditional properties of the proposed process are obtained. The model’s parameters are estimated using the conditional maximum likelihood, and conditional least squares methodologies. In order to evaluate the consistency and efficiency of the estimators under the two estimating methodologies, Monte Carlo simulation experiments are conducted. Also, the suggested model is fitted to a time series of the monthly counts of claimants collecting Short Term Wage Loss Benefits from the WCB and monthly counting burglary crime data sets to demonstrate its potential for challenging underdispersed and overdispersed count data. The INAR-IG(1) model is suitable for modeling claim and crime data, according to model adequacy verification with information criteria, Pearson residuals, predictive capability, etc. For the data sets, the INAR-IG(1) model takes into account a number of forecasting techniques, including the classical, round classical, and coherent median methods. To enable a comprehensive evaluation of its forecasting performance, some forecasting accuracy measures are applied to the mentioned data sets , allowing for meaningful comparison with other competing models. The proposed methodology is demonstrated using real data sets, specifically claim and crime data sets.