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A Systematic Review of INGARCH Models for Integer-Valued Time Series
Mengya Liu1, Fukang Zhu2, Jianfeng Li1
1School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.
Entropy (Basel, Switzerland)
|June 28, 2023
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.
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.
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