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Wenjie Dang1, Fukang Zhu1, Nuo Xu1

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This study introduces local influence analysis for mixed Poisson integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models. The methods effectively identify influential points in count time series data.

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Area of Science:

  • Statistical modeling
  • Time series analysis
  • Econometrics

Background:

  • Local influence analysis is vital for statistical diagnosis.
  • Mixed Poisson distributions offer flexibility for count data.
  • Integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models handle count time series.

Purpose of the Study:

  • To apply local influence analysis to mixed Poisson INGARCH models.
  • To identify influential observations in count time series.
  • To assess the performance of proposed diagnostic methods.

Main Methods:

  • Utilized the Expectation-Maximization algorithm for parameter estimation.
  • Applied local influence analysis with generalized Cook distance and Q-distance.
  • Investigated four perturbation schemes: case weights, data, additive, and scale.

Main Results:

  • Demonstrated the identification of influential points using the proposed framework.
  • Validated the effectiveness of local influence methods in mixed Poisson INGARCH models.
  • Showcased the practical utility through simulations and real-world data analysis.

Conclusions:

  • The local influence method is a valuable tool for mixed Poisson INGARCH models.
  • The proposed diagnostic techniques are feasible and effective for count time series.
  • This approach enhances the reliability of statistical inference in count data analysis.