Under-reported time-varying MINAR(1) process for modeling multivariate count series.

Area of Science:

• Statistics, Time Series Analysis, Econometrics, Biostatistics

Background:

• Non-stationary count time series often exhibit under-reporting, complicating accurate modeling.
• Existing models may not adequately capture cross-correlations in multivariate count data, especially with under-reporting.

Purpose of the Study:

• To introduce a novel time-varying multivariate integer-valued autoregressive model of order one (tvMINAR(1)) for non-stationary, correlated count data with potential under-reporting.
• To develop a method that preserves cross-correlations and facilitates model fitting using the Viterbi algorithm.

Main Methods:

• Development of a tvMINAR(1) model with a non-diagonal autoregression probability network to maintain multivariate series cross-correlation.
• Utilization of the Viterbi algorithm for deriving the full likelihood, accommodating random thinning operators for under-reported counts.
• Conducting simulation studies to validate the proposed model's performance.

Main Results:

• The proposed tvMINAR(1) model effectively handles non-stationary and correlated count data, even with under-reporting.
• Simulation studies demonstrate the model's ability to accurately capture the underlying data generating process.
• Application to COVID-19 daily case data showcases the model's practical utility in real-world scenarios.

Conclusions:

• The tvMINAR(1) model provides a robust framework for analyzing complex count time series data with under-reporting.
• The Viterbi algorithm and random thinning operator integration enhance the model's applicability and computational efficiency.
• Model comparison via posterior predictive checking confirms the proposed method's effectiveness.