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A non-parametric statistic for testing conditional heteroscedasticity for unobserved component models.

Alejandro Rodriguez1, Gabriel Pino2, Rodrigo Herrera2

  • 1Departamento de Ingeniería Industrial, Universidad de Talca, Curico, Chile.

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|June 16, 2022
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Summary
This summary is machine-generated.

This study introduces a new nonparametric test for heteroscedasticity in unobserved component models (UCM). The proposed Wilcoxon rank-based statistic improves test accuracy and identifies heteroscedastic components more reliably than existing methods.

Keywords:
62G1062G30Auxiliary residualsKalman filterbootstrap proceduressquared autocorrelationsstate smoothingstate-space models

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Area of Science:

  • Econometrics
  • Statistical Modeling
  • Time Series Analysis

Background:

  • Unobserved Component Models (UCM) are susceptible to heteroscedasticity, complicating accurate prediction intervals.
  • Existing methods for testing heteroscedasticity in UCM often fail due to serial correlation affecting test statistic distributions.
  • Correctly identifying heteroscedastic components is crucial for reliable statistical inference.

Purpose of the Study:

  • To develop a robust nonparametric statistic for testing conditional heteroscedasticity in UCM.
  • To address the limitations of existing tests affected by serial correlation.
  • To improve the accuracy and reliability of heteroscedasticity detection in time series models.

Main Methods:

  • A novel nonparametric test statistic based on Wilcoxon's rank statistic is proposed.
  • Asymptotic validation of the new statistic is performed.
  • Bootstrap procedures are employed to approximate the finite sample distribution of the test statistic.

Main Results:

  • The proposed test demonstrates improved size control for homoscedasticity tests.
  • The power of the new test is comparable to the best existing alternatives.
  • Simulations show superior performance in identifying heteroscedastic components.

Conclusions:

  • The nonparametric Wilcoxon rank-based test offers a more reliable approach to detecting heteroscedasticity in UCM.
  • Application to inflation data yields different conclusions than alternative methods, highlighting the test's distinct findings.
  • The developed method enhances the accuracy of prediction intervals by correctly identifying sources of error term heteroscedasticity.