Copula-based Markov zero-inflated count time series models with application.

Area of Science:

• Statistics
• Time Series Analysis
• Statistical Modeling

Background:

• Count time series data frequently exhibit excess zeros and serial dependence.
• Ignoring these features can lead to inaccurate statistical analyses.
• Existing models may not adequately capture both zero-inflation and temporal correlation.

Purpose of the Study:

• To propose novel Markov zero-inflated count time series models.
• To address the challenges of excess zeros and serial dependence in count data.
• To provide a flexible framework using copula functions for joint distributions.

Main Methods:

• Development of Markov models incorporating univariate margins like zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP).
• Construction of joint distributions for consecutive observations using bivariate and trivariate copula functions (Gaussian, Frank, Gumbel, max-infinitely divisible).
• Application of likelihood-based inference and study of asymptotic properties.

Main Results:

• The proposed models effectively handle both zero-inflation and serial dependence in count time series.
• Simulated examples demonstrate the validity of the estimation methods and asymptotic results.
• The models show advantages over existing methods when applied to real-world data, such as sandstorm counts.

Conclusions:

• The proposed Markov zero-inflated count time series models provide a robust and flexible approach.
• These models offer improved performance for analyzing complex count time series data with excess zeros and serial dependence.
• The findings suggest practical benefits for applied disciplines dealing with such data.