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A Conway-Maxwell-Poisson-Binomial AR(1) Model for Bounded Time Series Data.

Huaping Chen1, Jiayue Zhang2, Xiufang Liu3

  • 1School of Mathematics and Statistics, Henan University, Kaifeng 475004, China.

Entropy (Basel, Switzerland)
|January 21, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces the Conway-Maxwell-Poisson-binomial AR (CMPBAR) model for complex bounded time series counts. The new model demonstrates consistency and asymptotic normality, outperforming existing methods in real-world applications.

Keywords:
CMPB thinning operatorCMPBAR modelbounded time seriesequi-dispersionover-dispersionunder-dispersion

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Count Data Modeling

Background:

  • Traditional binomial autoregressive models are insufficient for complex bounded time series with dependent units.
  • Increasing prevalence of such complex count data necessitates advanced modeling techniques.

Purpose of the Study:

  • To develop a novel statistical model for analyzing complex bounded time series counts of exchangeable and dependent units.
  • Introduce the Conway-Maxwell-Poisson-binomial AR (CMPBAR) model and its associated estimation framework.

Main Methods:

  • Construction of an exchangeable Conway-Maxwell-Poisson-binomial (CMPB) thinning operator.
  • Establishment of the CMPBAR model, including its stationarity and ergodicity.
  • Development and asymptotic analysis of the conditional maximum likelihood (CML) estimator.

Main Results:

  • The CML estimator is shown to be consistent through simulation studies.
  • Asymptotic normality of the CML estimator is confirmed via quantile-quantile plots.
  • The proposed CMPBAR model achieved lower AIC and BIC values compared to competing models in a real data example.

Conclusions:

  • The CMPBAR model provides a robust and effective solution for complex bounded time series count data.
  • The CML estimation method is reliable, offering consistent and asymptotically normal parameter estimates.
  • The developed model offers superior performance over existing methods for specific count data applications.