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A Systematic Review of INGARCH Models for Integer-Valued Time Series.

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  • 1School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.

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Summary

This review covers recent advances in integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models for various count time series data. It highlights innovations, methods, and applications for unbounded, bounded, Z-valued, and multivariate counts.

Keywords:
INGARCHconditional distributioncount time seriesdynamic structurerobust estimation

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Count time series data are prevalent across diverse scientific and economic fields.
  • There is a continuous need for advanced modeling techniques for count data.
  • Integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models are crucial for analyzing such data.

Purpose of the Study:

  • To provide a comprehensive review of recent developments in INGARCH models.
  • To cover advancements for different types of count data, including unbounded, bounded, Z-valued, and multivariate series.
  • To identify emerging research trends and potential future directions in INGARCH modeling.

Main Methods:

  • Systematic review of literature on INGARCH models published in the last five years.
  • Categorization of models based on data types: unbounded, bounded, Z-valued, and multivariate counts.
  • Analysis of model innovation, methodological advancements, and application expansions for each data type.

Main Results:

  • Significant progress has been made in INGARCH model development for various count data types.
  • Methodological innovations have enhanced the flexibility and applicability of these models.
  • New application areas have emerged, demonstrating the versatility of INGARCH models.

Conclusions:

  • The INGARCH modeling field has seen substantial growth and diversification.
  • Further research is warranted to integrate different INGARCH approaches and explore new frontiers.
  • Continued development is essential to meet the growing demand for count time series analysis.