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Empirical Likelihood for a First-Order Generalized Random Coefficient Integer-Valued Autoregressive Process.

Jianhua Cheng1, Xu Wang1, Dehui Wang2

  • 1School of Mathematics, Jilin University, Changchun, 130012 China.

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|April 25, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces the empirical likelihood method for generalized integer-valued autoregressive processes. It provides tools for parameter estimation, confidence regions, and hypothesis testing, validated by simulations and real data.

Keywords:
Empirical likelihoodgeneralized random coefficientinteger-valued time seriesthinning operator

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Generalized random coefficient integer-valued autoregressive (GINAR) models are crucial for analyzing count time series data.
  • Existing statistical inference methods for GINAR processes have limitations.
  • The empirical likelihood method offers a non-parametric approach to statistical inference.

Purpose of the Study:

  • To develop and analyze the empirical likelihood method for a first-order GINAR process.
  • To establish the asymptotic properties of the log empirical likelihood ratio statistic.
  • To provide methods for parameter estimation, confidence regions, and hypothesis testing for GINAR models.

Main Methods:

  • Derivation of the log empirical likelihood ratio statistic.
  • Asymptotic distribution theory for the statistic.
  • Application of the empirical likelihood method for point estimation, confidence intervals, and hypothesis tests.
  • Simulation studies and real data analysis for performance evaluation.

Main Results:

  • The log empirical likelihood ratio statistic is established for the first-order GINAR process.
  • The limiting distribution of the statistic is obtained.
  • The empirical likelihood method provides a viable approach for inference on GINAR model parameters.

Conclusions:

  • The empirical likelihood method is a powerful tool for statistical inference in GINAR models.
  • The proposed methods are effective, as demonstrated by simulation and real data.
  • This work contributes to the statistical methodology for analyzing integer-valued time series data.