A novel signal extraction approach for filtering and forecasting noisy exponential series

Hossein Hassani; Mahdi Kalantari

doi:10.1016/j.crma.2018.03.006

Statistics

A novel signal extraction approach for filtering and forecasting noisy exponential series

Presented by: Paul Deheuvels

Hossein Hassani ¹; Mahdi Kalantari ²

¹ Research Institute for Energy Management and Planning, University of Tehran, Tehran, Iran
² Department of Statistics, Payame Noor University, 19395-4697, Tehran, Iran

Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 563-570.

Abstract
Résumé

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.

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.

Received: 2018-01-27
Accepted: 2018-03-12
Published online: 2018-04-05

DOI: 10.1016/j.crma.2018.03.006

Author's affiliations:

Hossein Hassani ¹; Mahdi Kalantari ²

¹ Research Institute for Energy Management and Planning, University of Tehran, Tehran, Iran
² Department of Statistics, Payame Noor University, 19395-4697, Tehran, Iran

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     author = {Hossein Hassani and Mahdi Kalantari},
     title = {A novel signal extraction approach for filtering and forecasting noisy exponential series},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {563--570},
     publisher = {Elsevier},
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     number = {5},
     year = {2018},
     doi = {10.1016/j.crma.2018.03.006},
     language = {en},
}

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Hossein Hassani; Mahdi Kalantari. A novel signal extraction approach for filtering and forecasting noisy exponential series. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 563-570. doi : 10.1016/j.crma.2018.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.03.006/

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