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Prior Sensitivity Analysis in a Semi-Parametric Integer-Valued Time Series Model.

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Summary
This summary is machine-generated.

This study introduces a new statistical model for time series data, enhancing robustness and forecasting accuracy. A graphical criterion is presented to guide model parameter selection for improved inferential results.

Keywords:
Bayesian forecastingBayesian hierarchical modelingBayesian nonparametricsPitman–Yor processclusteringprior sensitivitytime series of counts

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Bayesian Inference

Background:

  • The Integer Autoregressive (INAR(p)) model is widely used for analyzing count time series data.
  • Prior sensitivity can affect the reliability of statistical inference in complex hierarchical models.
  • The Pitman-Yor process offers a flexible framework for modeling clustered data structures.

Purpose of the Study:

  • To develop a semi-parametric hierarchical extension of the INAR(p) model that addresses prior sensitivity.
  • To introduce a novel graphical criterion for specifying hyperparameters of the Pitman-Yor process base measure.
  • To enhance the robustness and forecasting performance of count time series models.

Main Methods:

  • A semi-parametric hierarchical extension of the INAR(p) model was developed.
  • The Pitman-Yor process was integrated into the model hierarchy to cluster innovation rates.
  • A graphical criterion was derived to guide the specification of hyperparameters for the Pitman-Yor base measure.

Main Results:

  • A graphical criterion was established to effectively guide the specification of Pitman-Yor process hyperparameters.
  • Demonstrated how discount and concentration parameters influence the base measure, enhancing inferential robustness.
  • The proposed model significantly outperformed the standard INAR(p) model in forecasting earthquake event data.

Conclusions:

  • The developed hierarchical INAR(p) model extension offers improved robustness against prior sensitivity.
  • The graphical criterion provides a practical tool for modelers to optimize hyperparameter choices.
  • The model shows superior forecasting capabilities, particularly for real-world count time series like seismic events.