Comptes Rendus
no. 17-18
Statistics
Separability and window length in singular spectrum analysis
[Séparabilité et longueur de fenêtre dans lʼanalyse dʼun spectre singulier]

Présenté par : Paul Deheuvels

Hossein Hassani1, 2 ; Rahim Mahmoudvand3 ; Mohammad Zokaei3 
1 Statistics Group, School of Mathematics, Cardiff University, CF24 4AG, UK
2 Institute for International Studies (I.I.E.S), 1967743711, Tehran, IR, Iran
3 Faculty of Mathematical Sciences, Shahid Beheshti University, GC, Iran
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 987-990.

Pour déterminer la valeur optimale de la longueur de fenêtre dans lʼanalyse dʼun spectre singulier (SSA) on utilise le concept de séparabilité entre le signal et la composante du bruit. Les résultats théoriques confirment, que pour une classe importante de séries temporelles, la valeur la mieux adaptée de ce paramètre est la médiane de {1,…,N} pour des séries de longueur N. Les résultats théoriques obtenus dans cette Note coïncident avec ceux qui sont utilisés à partir de méthodes empiriques.

To find the optimal value of window length in singular spectrum analysis (SSA), we consider the concept of separability between the signal and noise component. The theoretical results confirm that for a wide class of time series, the suitable value of this parameter is median{1,…,T} with the series of length T. The theoretical results obtained here coincide with those obtained previously from the empirical point of view.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.012
Hossein Hassani 1, 2 ; Rahim Mahmoudvand 3 ; Mohammad Zokaei 3

1 Statistics Group, School of Mathematics, Cardiff University, CF24 4AG, UK
2 Institute for International Studies (I.I.E.S), 1967743711, Tehran, IR, Iran
3 Faculty of Mathematical Sciences, Shahid Beheshti University, GC, Iran 
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Hossein Hassani; Rahim Mahmoudvand; Mohammad Zokaei. Separability and window length in singular spectrum analysis. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 987-990. doi : 10.1016/j.crma.2011.07.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.012/

[1] N. Golyandina; V. Nekrutkin; A. Zhigljavsky Analysis of Time Series Structure: SSA and Related Techniques, Chapman & Hall/CRC, New York, London, 2001

[2] H. Hassani Singular spectrum analysis: Methodology and comparison, Journal of Data Science, Volume 5 (2007) no. 2, pp. 239-257

[3] H. Hassani; S. Heravi; A. Zhigljavsky Forecasting European industrial production with singular spectrum analysis, International Journal of Forecasting, Volume 25 (2009) no. 1, pp. 103-118

[4] A. Zhigljavsky Singular spectrum analysis for time series: Introduction to this special issue, Statistics and Its Interface, Volume 3 (2010) no. 3, pp. 255-258

[5] H. Hassani; D. Thomakos A review on singular spectrum analysis for economic and financial time series, Statistics and Its Interface, Volume 3 (2010) no. 3, pp. 377-397

[6] J.B. Elsner; A.A. Tsonis Singular Spectrum Analysis: A New Tool in Time Series Analysis, Plenum, 1996

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