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Hassani, H., Royer-Carenzi, M., Mashhad, L.M., Yarmohammadi, M., & Yeganegi, R. (2024). Exploring the Depths of the Autocorrelation Function: Its Departure from Normality. Information 15 (8) e449. 10.3390/info15080449.
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Abstract
In this article, we study the autocorrelation function (ACF), which is a crucial element in time series analysis. We compare the distribution of the ACF, both from a theoretical and empirical point of view. We focus on white noise processes (WN), i.e., uncorrelated, centered, and identically distributed variables, whose ACFs are supposed to be asymptotically independent and converge towards the same normal distribution. But, the study of the sum of the sample ACF contradicts this property. Thus, our findings reveal a deviation of the sample ACF from normality beyond a specific lag. Note that this phenomenon is observed for white noise of varying lengths, and evenforn the residuals of an ARMA(
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | autocorrelation function (ACF); time series analysis; white noise; normality tests; Ljung–Box test; Box–Pierce test; ARMA(p,q); residuals |
| Research Programs: | Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Cooperation and Transformative Governance (CAT) |
| Depositing User: | Luke Kirwan |
| Date Deposited: | 04 Sep 2024 07:47 |
| Last Modified: | 04 Sep 2024 07:47 |
| URI: | https://pure.iiasa.ac.at/19971 |
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