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White Noise and Its Misapplications: Impacts on Time Series Model Adequacy and Forecasting

Author

Listed:
  • Hossein Hassani
  • Leila Marvian Mashhad
  • Manuela Royer-Carenzi

    (I2M - Institut de Mathématiques de Marseille - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Mohammad Reza Yeganegi
  • Nadejda Komendantova

Abstract

This paper contributes significantly to time series analysis by discussing the empirical properties of white noise and their implications for model selection. This paper illustrates the ways in which the standard assumptions about white noise typically fail in practice, with a special emphasis on striking differences in sample ACF and PACF. Such findings prove particularly important when assessing model adequacy and discerning between residuals of different models, especially ARMA processes. This study addresses issues involving testing procedures, for instance, the Ljung–Box test, to select the correct time series model determined in the review. With the improvement in understanding the features of white noise, this work enhances the accuracy of modeling diagnostics toward real forecasting practice, which gives it applied value in time series analysis and signal processing.

Suggested Citation

  • Hossein Hassani & Leila Marvian Mashhad & Manuela Royer-Carenzi & Mohammad Reza Yeganegi & Nadejda Komendantova, 2025. "White Noise and Its Misapplications: Impacts on Time Series Model Adequacy and Forecasting," Post-Print hal-04937317, HAL.
    • Handle: RePEc:hal:journl:hal-04937317
    DOI: 10.3390/forecast7010008
    Note: View the original document on HAL open archive server: https://hal.science/hal-04937317v1
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    Keywords

    time series analysis; model selection; Hassani -1/2 theorem; white noise; ARMA; Gaussian; Ljung-Box test;
    All these keywords.

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