Bayesian Forecasting of Bounded Poisson Distributed Time Series.

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Ordinal time series data, common in air quality index (AQI), economics, and credit ratings, are often bounded with probabilities concentrated on specific states (e.g., 0 and 1).
• Existing models may not adequately capture the unique characteristics of these zero-one-inflated bounded datasets.

Purpose of the Study:

• To develop and validate Bayesian zero-one-inflated bounded Poisson autoregressive (ZOBPAR) models for modeling and forecasting bounded ordinal time series.
• To extend ZOBPAR models to incorporate exogenous variables for enhanced predictive power.

Main Methods:

• Proposed Bayesian inference methods for ZOBPAR models.
• Incorporation of exogenous variables into the ZOBPAR framework.
• Simulation studies to assess parameter estimation accuracy and robustness.

Main Results:

• Simulation results confirm accurate parameter estimation, with posterior means converging to true values as sample size increases.
• Empirical application to daily AQI levels in Taiwan demonstrates the proposed method's effective forecasting capabilities.
• The ZOBPAR model showed particular strength in predicting AQI for the Miaoli station.

Conclusions:

• The proposed Bayesian ZOBPAR models provide a robust and accurate approach for modeling and forecasting bounded ordinal time series data.
• The inclusion of exogenous variables represents a significant advancement in Bayesian inference for these types of models.
• The method's practical utility is demonstrated through successful AQI forecasting, highlighting its potential in environmental monitoring and other fields.