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Summary
This summary is machine-generated.

This study introduces new tests for parameter change detection in random coefficient integer-valued autoregressive models, improving upon existing methods. Simulation results confirm the effectiveness of these novel estimating function-based and residual-based cumulative sum (CUSUM) tests.

Keywords:
RCINAR modelsconditional least squares estimatorinteger-valued time seriestest for parameter change

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Parameter change detection is crucial in time series analysis.
  • Existing cumulative sum (CUSUM) tests for random coefficient integer-valued autoregressive models can exhibit size distortions.
  • Accurate statistical testing is needed for reliable model inference.

Purpose of the Study:

  • To develop novel statistical tests for detecting parameter changes in random coefficient integer-valued autoregressive (AR) models.
  • To address and overcome the size distortions associated with traditional estimate-based CUSUM tests.
  • To provide robust methods for analyzing time series data with changing parameters.

Main Methods:

  • Proposed two new tests: an estimating function-based test and a residual-based CUSUM test.
  • Utilized the estimating function derived from the conditional least squares estimator.
  • Derived the limiting distributions of the proposed tests under regularity conditions and the null hypothesis.

Main Results:

  • Simulation studies demonstrated that the proposed tests possess good validity.
  • The new tests show improved performance compared to existing methods, mitigating size distortions.
  • The methods were successfully applied to real-world polio incidence data.

Conclusions:

  • The developed estimating function-based and residual-based CUSUM tests are effective for parameter change detection.
  • These novel approaches offer a more reliable alternative to existing methods for integer-valued time series models.
  • The study validates the practical applicability of the proposed tests in real data analysis.