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Related Experiment Videos

Locally asymptotically rank-based procedures for testing autoregressive moving average dependence.

M Hallin1, M L Puri

  • 1Institut de Statistique, Université Libre de Bruxelles, Campus Plaine C.P. 210, B-1050 Brussels, Belgium.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1988
PubMed
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This study introduces novel distribution-free tests for Autoregressive Moving Average (ARMA) models with unspecified noise densities. These rank-based statistics offer powerful alternatives for model comparison, even with unknown coefficients.

Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Autoregressive Moving Average (ARMA) models are widely used for time series analysis.
  • Testing ARMA models often relies on assumptions about the underlying noise distribution.
  • Existing methods may lack power or applicability when noise characteristics are unknown.

Purpose of the Study:

  • To develop distribution-free statistical tests for comparing ARMA models.
  • To address the challenge of unspecified white noise densities in ARMA model testing.
  • To provide robust methods for ARMA model selection and validation.

Main Methods:

  • Development of a generalized linear serial rank statistic for distribution-free testing.
  • Establishment of asymptotic sufficiency of rank statistics for ARMA models with unspecified coefficients.

Related Experiment Videos

  • Derivation of an asymptotically maximin most powerful test using a generalized quadratic serial rank statistic.

    • Main Results:

    • A distribution-free, asymptotically most powerful test is proposed against specified ARMA alternatives.
    • Asymptotic sufficiency is demonstrated for rank statistics, enabling tests with unspecified coefficients.
    • The derived test statistic is a rank-based, weighted version of the Box-Pierce statistic.

    Conclusions:

    • The proposed rank-based tests offer robust and powerful methods for ARMA model evaluation without assuming noise distribution.
    • These methods extend the applicability of model testing in scenarios with unknown or complex noise structures.
    • The findings contribute to more reliable time series modeling and analysis in various scientific fields.