Titre : Some analytical properties of moving averages. Application to the detection of trends in a signal 

Auteurs : Jacques Padet,  

Revue : Entropy: Thermodynamics – Energy – Environment – Economy  

Numéro : Issue 2 

Volume : 5 

Date : 2024/02/19 

DOI : 10.21494/ISTE.OP.2024.1079 

ISSN : 2634-1476 

Résumé : The analysis of very irregular processes is often based on the search for a trend, an average curve representing the general course of the observed phenomenon. If each people is more or less capable of drawing such a curve freehand, in an intuitive way, its objective determination is very delicate. The method of moving averages being one of the most used in the search for trends, we propose here to study some properties of these moving averages (essentially mean and variance, or standard deviation). We then show that they can be used to detect characteristic observation windows, leading to structural trends of the analyzed signal. The notion of tau-average (trend obtained by a moving average with a variable window) is also re-examined. 

Éditeur : ISTE OpenScience