Count Data Time Series Modelling in Julia-The CountTimeSeries.jl Package and Applications

Area of Science:

• Computational Statistics
• Time Series Analysis
• Statistical Software

Background:

• Integer-valued time series data present unique modeling challenges.
• Existing statistical software may lack specialized methods for count time series.
• The Julia programming language offers a high-performance environment for statistical computing.

Purpose of the Study:

• Introduce the CountTimeSeries.jl software package for Julia.
• Demonstrate the utility of likelihood-based methods for integer-valued time series.
• Provide practical examples of time series analysis for real-world data.

Main Methods:

• Development of the CountTimeSeries.jl package in Julia.
• Simulation studies evaluating Maximum Likelihood (ML) estimation.
• Application of models to COVID-19 infection data, animal submission data, and corporate insolvency data.

Main Results:

• The CountTimeSeries.jl package provides efficient tools for count time series analysis.
• Simulation results offer insights into the finite sample properties of ML estimation.
• The package successfully models diverse real-world count time series phenomena, including overdispersion and zero inflation.

Conclusions:

• CountTimeSeries.jl is a valuable new resource for researchers and practitioners in time series analysis.
• Likelihood-based methods are effective for modeling integer-valued time series.
• The package facilitates reproducible research through readily available code and documentation.