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Partial Autocorrelation Diagnostics for Count Time Series.

Christian H Weiß1, Boris Aleksandrov1, Maxime Faymonville2

  • 1Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany.

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PubMed
Summary
This summary is machine-generated.

The partial autocorrelation function (PACF) test, useful for autoregressive (AR) models, struggles with AR-type count processes. This study introduces bootstrap PACF tests for improved performance with count time series data.

Keywords:
INAR bootstrapYule–Walker equationsautoregressive modelcount time seriespartial autocorrelation function

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Area of Science:

  • Time Series Analysis
  • Statistical Modeling
  • Econometrics

Background:

  • The partial autocorrelation function (PACF) is crucial for identifying and selecting orders in autoregressive (AR) models.
  • AR-type count processes, which satisfy Yule-Walker equations like AR models, are increasingly used.
  • Standard PACF tests rely on asymptotic results that often fail for AR-type count processes, hindering their performance.

Purpose of the Study:

  • To address the limitations of traditional PACF tests for AR-type count processes.
  • To develop and evaluate improved PACF testing methods for count time series.
  • To enhance the reliability of model identification for count data.

Main Methods:

  • Implementing various PACF test versions specifically designed for AR-type count processes.
  • Utilizing several bootstrap schemes tailored for count time series data.
  • Comparing the performance of bootstrap methods against standard asymptotic results via simulations.

Main Results:

  • Bootstrap-based PACF tests demonstrate superior performance compared to asymptotic methods for AR-type count processes.
  • The proposed bootstrap schemes provide more reliable order selection for count time series.
  • Simulation results highlight the practical advantages of the new implementations.

Conclusions:

  • Bootstrap methods offer a robust alternative for PACF testing in AR-type count processes.
  • The developed PACF test implementations improve model identification accuracy for count time series.
  • The study provides practical tools for analyzing real-world count time series data.