[Une nouvelle approche dans l'extraction de signal pour le filtrage et la prévision par des séries exponentielles avec bruit]
Les coefficients des relations récurrentes linéaires (RRL) jouent un rôle central dans beaucoup de techniques de prévision. Une formule exacte et close des coefficients d'une RRL permet d'obtenir des prévisions plus précises. Prenant en compte le fait que, dans la réalité, une suite temporelle de données est contaminée par du bruit, il est très important de pouvoir en extraire la série sans bruit. Ce texte vise à obtenir une forme close, avec un niveau de bruit moindre, des coefficients d'une RRL, pour les suites en temps exponentiel avec bruit. Une autre nouveauté de notre approche est l'amélioration de l'efficacité du filtrage par l'utilisation de vecteurs propres sans bruit de la matrice de covariance. Les résultats des simulations confirment que l'approche proposée améliore le filtrage et les prévisions.
The coefficients of Linear Recurrent Relations (LRR) play a pivotal role in many forecasting techniques. Precise and closed form of the LRR coefficients enables one to achieve more accurate forecasts. On account to the fact that, in real-world situations, a time series data is contaminated with noise, extracting the noiseless series is of great importance. This paper seeks to obtain a closed form, with less noise level, of LRR coefficients for noisy exponential time series. Improving the filtering performance through employing noiseless eigenvectors of the covariance matrix is another novelty of this study. Our simulation results confirm that the proposed approach enhances filtering and forecasting results.
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@article{CRMATH_2018__356_5_563_0,
author = {Hassani, Hossein and Kalantari, Mahdi},
title = {A novel signal extraction approach for filtering and forecasting noisy exponential series},
journal = {Comptes Rendus. Math\'ematique},
pages = {563--570},
publisher = {Elsevier},
volume = {356},
number = {5},
year = {2018},
doi = {10.1016/j.crma.2018.03.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.03.006/}
}
TY - JOUR AU - Hassani, Hossein AU - Kalantari, Mahdi TI - A novel signal extraction approach for filtering and forecasting noisy exponential series JO - Comptes Rendus. Mathématique PY - 2018 SP - 563 EP - 570 VL - 356 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.03.006/ DO - 10.1016/j.crma.2018.03.006 LA - en ID - CRMATH_2018__356_5_563_0 ER -
%0 Journal Article %A Hassani, Hossein %A Kalantari, Mahdi %T A novel signal extraction approach for filtering and forecasting noisy exponential series %J Comptes Rendus. Mathématique %D 2018 %P 563-570 %V 356 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.03.006/ %R 10.1016/j.crma.2018.03.006 %G en %F CRMATH_2018__356_5_563_0
Hassani, Hossein; Kalantari, Mahdi. A novel signal extraction approach for filtering and forecasting noisy exponential series. Comptes Rendus. Mathématique, Tome 356 (2018) no. 5, pp. 563-570. doi : 10.1016/j.crma.2018.03.006. http://www.numdam.org/articles/10.1016/j.crma.2018.03.006/
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