Deviations from Normality in Autocorrelation Functions and Their Implications for MA(q) Modeling

20502 7 109429 2 331936 document 109429 stats-08-00019-v2.pdf application/pdf 983645d5d70f1db2475e6d0ea4f9376c MD5 14732652 2025-04-07 14:52:47 https://pure.iiasa.ac.at/id/eprint/20502/1/stats-08-00019-v2.pdf 20502 1 1 application/pdf text en public cc_by_4

stats-08-00019-v2.pdf

published 109431 2 331951 document 109431 lightbox.jpg image/png f4857459d2bebd81475c5e8e51657220 MD5 51256 2025-04-07 15:02:50 https://pure.iiasa.ac.at/id/eprint/20502/2/lightbox.jpg 20502 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/109429 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/109429 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/109429 archive 353 disk0/00/02/05/02 2025-04-07 14:53:52 2025-04-07 14:53:52 2025-04-07 14:53:52 article show Royer-Carenzi M. Hassani H. 9469 Deviations from Normality in Autocorrelation Functions and Their Implications for MA(q) Modeling pub ASA CAT time series analysis; autocorrelation function (ACF); white noise; moving average; normality tests The identification of the orders of time series models plays a crucial role in their accurate specification and forecasting. The Autocorrelation Function (ACF) is commonly used to identify the order q of Moving Average (MA(q)) models, as it theoretically vanishes for lags beyond q. This property is widely used in model selection, assuming the sample ACF follows an asymptotic normal distribution for robustness. However, our examination of the sum of the sample ACF reveals inconsistencies with these theoretical properties, highlighting a deviation from normality in the sample ACF for MA(q) processes. As a natural extension of the ACF, the Extended Autocorrelation Function (EACF) provides additional insights by facilitating the simultaneous identification of both autoregressive and moving average components. Using simulations, we evaluate the performance of q-order identification in MA(q) models, which is based on the properties of ACF. Similarly, for ARMA(p,q) models, we assess the (p,q)-order identification relying on EACF. Our findings indicate that both methods are effective for sufficiently long time series but may incorrectly favor an ARMA(p,q−1) model when the aq coefficient approaches zero. Additionally, if the cumulative sums of ACF (SACF) behave consistently and the Ljung–Box test validates the proposed model, it can serve as a strong candidate. The proposed models should then be compared based on their predictive performance. We illustrate our methodology with an application to wind speed data and sea surface temperature anomalies, providing practical insights into the relevance of our findings. 2025-02-20 published MDPI doi:10.3390/stats8010019 https://doi.org/10.3390/stats8010019 3410 public Stats 8 1 19 1 TRUE 2571-905X no info:eu-repo/semantics/article