Bayesian generalizations of the integer-valued autoregressive model.

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Integer-valued time series models are crucial for count data analysis.
• Standard Poisson models often fail with overdispersed count data, exhibiting more variability than expected.
• Existing models may not adequately capture complex heterogeneity in count data distributions.

Purpose of the Study:

• To develop advanced Bayesian generalized Poisson integer-valued autoregressive models.
• To address overdispersion and latent heterogeneity in count time series data.
• To evaluate the probabilistic forecasting performance of the proposed models.

Main Methods:

• Development of the AdINAR(1) model using finite mixture innovations for overdispersion.
• Development of the DP-INAR(1) model as a hierarchical extension with a Dirichlet process for heterogeneity.
• Application and evaluation of both models on Pittsburgh crime data for probabilistic forecasting.

Main Results:

• Both AdINAR(1) and DP-INAR(1) models successfully account for overdispersion in count data.
• The DP-INAR(1) model effectively captures latent heterogeneity in innovation rates.
• Favorable probabilistic forecasting results were achieved for crime data analysis using both models.

Conclusions:

• The proposed Bayesian generalized Poisson integer-valued autoregressive models offer robust alternatives for count time series analysis.
• These models provide improved handling of overdispersion and heterogeneity compared to traditional methods.
• The models demonstrate practical utility in real-world forecasting applications, such as crime data analysis.