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Weighted portmanteau statistics for testing for zero autocorrelation in dependent data.

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  • 1Departamento de Física y Matemáticas, Universidad Iberoamericana, CDMX.

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Summary

This study introduces robust portmanteau test statistics for time series analysis. These new methods maintain accurate test sizes and improve power, especially in financial modeling applications.

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Robust portmanteauasymptotic testsdependent time seriesfinancial time seriesspurious correlation

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Portmanteau test statistics are crucial for time series model diagnostics.
  • Traditional tests can exhibit size distortions under dependent data.
  • Autocorrelation and partial autocorrelation functions are key components of these tests.

Purpose of the Study:

  • To develop and evaluate robust portmanteau test statistics under dependence.
  • To analyze the asymptotic distribution and accuracy of weighted autocorrelation-based statistics.
  • To demonstrate the practical benefits of robust statistics in financial time series modeling.

Main Methods:

  • Theoretical derivation of asymptotic distributions for weighted autocorrelation statistics.
  • Monte Carlo simulations to assess test size and power.
  • Empirical application to financial time series data.

Main Results:

  • Proposed statistics show sizes close to nominal levels, indicating good accuracy.
  • The tests exhibit high power, effectively detecting deviations from the null hypothesis.
  • Accuracy and precision of the tests improve with increasing sample size.
  • Robust tests significantly outperform traditional tests in financial applications, avoiding size deviations.

Conclusions:

  • The developed robust portmanteau statistics offer reliable diagnostic tools for time series models, particularly under dependence.
  • These robust methods are essential for accurate statistical inference in financial econometrics.
  • The study highlights the limitations of traditional tests and the advantages of robust alternatives.