Consistent Model Selection Procedure for Random Coefficient INAR Models.

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Information criteria (AIC, BIC) are vital for time series lag order selection.
• Likelihood-based criteria are difficult to apply to random coefficient integer-valued time series models due to complex likelihood functions.
• Existing methods face challenges in accurately selecting models for these complex time series structures.

Purpose of the Study:

• To develop a novel penalized criterion for model selection in random coefficient integer-valued time series.
• To address the limitations of traditional information criteria (AIC, BIC) in this specific modeling context.
• To provide a robust and effective method for determining lag order and selecting variables.

Main Methods:

• Formulation of a penalized criterion using the estimation equation from conditional least squares estimation.
• Derivation of the asymptotic properties of the proposed penalized criterion.
• Numerical simulation studies and comparative analysis to evaluate performance.

Main Results:

• The novel penalized criterion is shown to have sound asymptotic properties.
• Simulation studies demonstrate the criterion's effectiveness in variable selection under relaxed conditions.
• Comparative analysis confirms the superiority of the new method over traditional approaches.

Conclusions:

• The proposed penalized criterion offers a viable and effective alternative for model selection in random coefficient integer-valued time series.
• The method demonstrates consistent variable selection performance, even with complex data structures.
• Successful application to infectious disease and seismic frequency data highlights its practical utility.