Recent advancements in integer-valued autoregressive models for count data time series: A comprehensive review.

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Count data time series are prevalent in finance, health, economics, and environmental sciences.
• These series often display overdispersion, underdispersion, or zero-inflation, complicating analysis.
• Ignoring these features leads to biased estimates and flawed statistical inference.

Purpose of the Study:

• To provide a comprehensive review of recent methodological developments in integer-valued autoregressive (INAR) models.
• To focus on innovations in thinning operators, estimation techniques, and model extensions.
• To identify research gaps and future directions in count data time series modeling.

Main Methods:

• Systematic literature search of Scopus and Google Scholar (2010-2024).
• Review of methodological advancements in INAR models.
• Analysis of novel thinning operators and innovation distributions.

Main Results:

• Recent research emphasizes novel thinning operators and flexible innovation distributions.
• Development of unified modeling frameworks to simultaneously address multiple count data characteristics.
• Identification of key trends and gaps in current INAR model research.

Conclusions:

• Unified INAR models are crucial for accurately analyzing complex count data.
• Further research is needed to develop robust methods for over/underdispersion and zero-inflation.
• Future work should focus on flexible distributions and advanced estimation techniques.