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

Author

Listed:
  • Hossein Hassani

    (International Institute for Applied Systems Analysis (IIASA), 2361 Laxenburg, Austria)

  • Leila Marvian Mashhad

    (Big Data Lab, Imam Reza International University, Mashhad 178-436, Iran)

  • Manuela Royer-Carenzi

    (I2M, Aix-Marseille Univ, CNRS, UMR 7373, Centrale Marseille, 13007 Marseille, France)

  • Mohammad Reza Yeganegi

    (International Institute for Applied Systems Analysis (IIASA), 2361 Laxenburg, Austria)

  • Nadejda Komendantova

    (International Institute for Applied Systems Analysis (IIASA), 2361 Laxenburg, Austria)

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," Forecasting, MDPI, vol. 7(1), pages 1-14, February.
    • Handle: RePEc:gam:jforec:v:7:y:2025:i:1:p:8-:d:1584099
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    References listed on IDEAS

    as
    1. Hossein Hassani & Emmanuel Sirimal Silva, 2015. "A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts," Econometrics, MDPI, vol. 3(3), pages 1-20, August.
    2. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    3. Kirman Alan & Teyssière Gilles, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-23, January.
    4. M. Boutahar & M. Royer-Carenzi, 2024. "Identifying trend nature in time series using autocorrelation functions and stationarity tests," International Journal of Computational Economics and Econometrics, Inderscience Enterprises Ltd, vol. 14(1), pages 1-22.
    5. Hassani, Hossein & Yeganegi, Mohammad Reza, 2020. "Selecting optimal lag order in Ljung–Box test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    6. Hossein Hassani & Masoud Yarmohammadi & Leila Marvian Mashhad, 2023. "Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview," Risks, MDPI, vol. 11(6), pages 1-15, June.
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    Cited by:

    1. Manuela Royer-Carenzi & Hossein Hassani, 2025. "Deviations from Normality in Autocorrelation Functions and Their Implications for MA(q) Modeling," Stats, MDPI, vol. 8(1), pages 1-37, February.

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