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A dependent counting INAR model with serially dependent innovation.

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Summary
This summary is machine-generated.

This study introduces a flexible integer-valued autoregressive model for count data, enhancing predictions for dependent random events like disease spread and crime rates.

Keywords:
62G0562M0562M1062M2062P25Alternative dependent thinning operatorINAR modelmodified conditional least squareoverdispersion

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Traditional count data models often lack flexibility for serially dependent events.
  • Integer-valued autoregressive (INAR) models provide a framework for count time series.
  • Existing INAR models may not fully capture complex dependencies in real-world count data.

Purpose of the Study:

  • To extend the first-order integer-valued autoregressive (INAR(1)) model.
  • To incorporate serially dependent innovations using a dependent thinning operator.
  • To develop a more flexible model for count data exhibiting interdependencies.

Main Methods:

  • Development of a novel INAR(1) model with dependent innovations.
  • Derivation and analysis of key statistical properties of the proposed model.
  • Parameter estimation using established statistical methods.
  • Simulation studies to evaluate parameter estimation properties.
  • Application to real-world count data sets.

Main Results:

  • The proposed model demonstrates flexibility in capturing serial dependence in count data.
  • Statistical properties of the new model were theoretically determined.
  • Simulation results indicate satisfactory performance of the estimation methods.
  • The model's efficiency was validated using contagious disease and robbery data.

Conclusions:

  • The extended INAR(1) model with dependent innovations offers a more flexible approach to modeling count data.
  • The model is suitable for analyzing time series data where events are serially dependent.
  • Empirical applications confirm the model's practical utility for real-world count phenomena.