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

Hossein Hassani (hassani.stat@gmail.com), Leila Marvian Mashhad (leila.marveian@imamreza.ac.ir), Manuela Royer-Carenzi, Mohammad Reza Yeganegi (yeganegi@iiasa.ac.at) and Nadejda Komendantova
Additional contact information
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

Post-Print from HAL

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)
Date: 2025-02-05
New Economics Papers: this item is included in nep-for
Note: View the original document on HAL open archive server: https://hal.science/hal-04937317v1
References: Add references at CitEc
Citations:

Published in Forecasting, 2025, 7 (1), pp.8. ⟨10.3390/forecast7010008⟩

Downloads: (external link)
https://hal.science/hal-04937317v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04937317

DOI: 10.3390/forecast7010008

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD (hal@ccsd.cnrs.fr).