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

Hossein Hassani, Leila Marvian Mashhad, Manuela Royer-Carenzi, Mohammad Reza Yeganegi and Nadejda Komendantova ()
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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

Forecasting, 2025, vol. 7, issue 1, 1-14

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.

Keywords: time series analysis; model selection; Hassani ?1/2 theorem; white noise; ARMA; Gaussian; Ljung–Box test (search for similar items in EconPapers)
JEL-codes: A1 B4 C0 C1 C2 C3 C4 C5 C8 M0 Q2 Q3 Q4 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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