Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
Asymptotic Information Measures Discrimination of Non-Stationary Time Series Based on Wavelet Domain
Discriminacion de medidas de información asintótica de series de tiempo no estacionarias basadas en dominio wavelet
DOI:
https://doi.org/10.15446/rce.v39n1.55141Keywords:
Chernoff information, discrimination, evolutionary wavelet spectrum, Kullback - Leibler information, locally stationary wavelet processes, seismic data (en)Datos sísmicos, Discriminación, Espectros wavelet evolucionarios, Información de Chernoff, Información de Kullback-Leibler, Procesos wavelet estacionarios locales. (es)
This article is concerned with the problem of discrimination between two classes of locally stationary time series based on minimum discrimination information. We view the observed signals as realizations of Gaussian locally stationary wavelet (LSW) processes. The asymptotic Kullback - Leibler discrimination information and Chernoff discrimination information are developed as discriminant criteria for LSW processes. The simulation study showed that our procedure performs as well as other procedures and in some cases better than some other classification methods. Applications to classifying real data show the usefulness of our discriminant criteria.
Este artículo se refiere al problema de discriminación entre dos clases de series de tiempo estacionarias locales basadas en información de discriminación mínima. Se consideran las señales observadas como realizaciones de procesos wavelet estacionarios locales (LSW, por sus siglas en inglés) gausianos. La información de discriminación Kullback - Leibler asintótica y la información de discriminación de Chernoff se desarrollan como criterios discriminantes para procesos LSW. El estudio de simulación mostró que el procedimiento propuesto se desempeña tan bien como otros procedimientos y en algunos casos mejor que otros métodos de clasificación. Aplicaciones a la clasificación de datos sísmicos muestran la utilidad de los criterios discriminantes propuestos.
1University of Shahid Chamran, Faculty of Mathematics and Computer Science, Department of Statistics, Ahvaz, Iran. Assistant Professor. Email: b.mansouri@scu.ac.ir
2University of Shahid Chamran, Faculty of Mathematics and Computer Science, Department of Statistics, Ahvaz, Iran. Professor. Email: chinipardaz_r@scu.ac.ir
This article is concerned with the problem of discrimination between two classes of locally stationary time series based on minimum discrimination information. We view the observed signals as realizations of Gaussian locally stationary wavelet (LSW) processes. The asymptotic Kullback - Leibler discrimination information and Chernoff discrimination information are developed as discriminant criteria for LSW processes. The simulation study showed that our procedure performs as well as other procedures and in some cases better than some other classification methods. Applications to classifying real data show the usefulness of our discriminant criteria.
Key words: Chernoff information, discrimination, evolutionary wavelet spectrum, Kullback - Leibler information, locally stationary wavelet processes, seismic data.
Este artículo se refiere al problema de discriminación entre dos clases de series de tiempo estacionarias locales basadas en información de discriminación mínima. Se consideran las señales observadas como realizaciones de procesos wavelet estacionarios locales (LSW, por sus siglas en inglés) gausianos. La información de discriminación Kullback - Leibler asintótica y la información de discriminación de Chernoff se desarrollan como criterios discriminantes para procesos LSW. El estudio de simulación mostró que el procedimiento propuesto se desempeña tan bien como otros procedimientos y en algunos casos mejor que otros métodos de clasificación. Aplicaciones a la clasificación de datos sísmicos muestran la utilidad de los criterios discriminantes propuestos.
Palabras clave: LaTeX Datos sísmicos, discriminación, espectros wavelet evolucionariosinformación de Chernoff, información de Kullback-Leibler, procesos wavelet estacionarios locales.
Texto completo disponible en PDF
References
1. Blandford, R. (1993), Discrimination of earthquakes and explosions. AFTAC-TR-93-044 HQ, Air Force Technical Applications Center, Patrick Air Force Base, Florida.
2. Chernoff, H. (1952), 'A measure of asymptotic efficiency for tests of a hypothesis based on the sum of the observations', The Annals of Mathematical Statistics 23(4), 573-578.
3. Dahlhaus, R. (1997), 'Fitting time series models to non stationary processes', The Annals of Statistics 25, 1-37.
4. Dargahi-Noubary, G. R. & Laycock, P. J. (1981), 'Spectral ratio discriminants and information theory', Journal of Time Series Analysis 2, 71-86.
5. Daubechies, I. (1992), Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia.
6. Fryzlewicz, P. (2003), Wavelet Techniques for Time Series and Poisson Data, PhD thesis, University of Bristol.
7. Fryzlewicz, P. & Ombao, H. (2009), 'Consistent classification of non stationary time series using stochastic wavelet representations', Journl of American Statistical Association 104, 299-312.
8. Gersch, W., Yeager, C. L., Diamond, S. L., Spire, J. P., Gerry, Z. M. & Gevins, A. H. (1975), Automated analysis of the electrical activity of the human brain (eeg), Proceedings of the IEEE 63, University of California Medical Center.
9. Gersch, W. & Yonemoto, J. (1977), 'Automatic classification of multivariate eeg, using an amount of information measure and the eigenvalues of parametric time series model features', Compute. Biomed. Reserch 10, 297-316.
10. Huang, H. S., Ombao, H. & Stoffer, D. (2004), 'Discrimination and classification of non-stationary time series using the slex model', Journl of American Statistical Association 99, 763-774.
11. Kakizawa, Y., Shumway, R. & Taniguchi, M. (1998), 'Discrimination and clustering for multivariate time series', Journl of American Statistical Association 93, 328-340.
12. Kalpakis, K., Gada, D. & Puttagunta, V. (2001), Distance measures for effective clustering of arima time-series, 'Proceedings of the IEEE International Conference on Data Mining', San Jose, California, p. 273-280.
13. Kullback, S. (1978), Information Theory and Statistics, Dover Publications, Inc, New York.
14. Kullback, S. & Leibler, R. A. (1951), 'On information and sufficiency', The Annals Mathematical Statistics 22, 79-86.
15. Maharaj, E. A. & Alonso, A. M. (2007), 'Discrimination of locally stationary time series using wavelets', Computational Statistics and Data Analysis 52, 879-895.
16. Nason, G. P., von Sachs, R. & Kroisandt, G. (2000), 'Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum', Journal of Royal Statisticl Society, Series B 62, 271-292.
17. Ombao, H., Raz, J., von Saches, R. & Guo, W. (2002), 'The SLEX model of a non-stationary random process', Annals of the Institute of Statistical Mathematics 54, 171-200.
18. Ombao, H., Raz, J., von Saches, R. & Malow, B. (2001), 'Automatic statistical analysis of bivariate non stationary time series', Journal of American Statistical Association 96, 543-560.
19. Parzen, E. (1990), Time Series, Statistics and Information, IMA Preprint Series 663, Institute for Mathematics and Its Applications, University of Minnesota.
20. Sakiyama, K. & Taniguchi, M. (2004), 'Discriminant analysis for locally stationary processes', Journal of Multivariate Analysis 90, 282-300.
21. Shumway, R. H. (2003), 'Time-frequency clustering and discriminant analysis', Statistics and Probability Letters 63, 307-314.
22. Shumway, R. H. & Stoffer, D. S. (2011), Time Series Analysis and Applications, 3 edn, v, University of Minnesota.
23. Shumway, R. H. & Unger, A. N. (1974), 'Linear discriminant function for stationary time series', Journl of American Statistical Association 69, 948-956.
24. Zhang, G. & Taniguchi, M. (1992), 'Discriminant analysis for stationary vector series', ournal of Time Series Analysis 15, 117-126.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv39n1a06,
AUTHOR = {Mansouri, Behzad and Chinipardaz, Rahim},
TITLE = {{Asymptotic Information Measures Discrimination of Non-Stationary Time Series Based on Wavelet Domain}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2016},
volume = {39},
number = {1},
pages = {81-95}
}
References
Blandford, R. (1993), Discrimination of earthquakes and explosions. AFTAC-TR- 93-044 HQ, Air Force Technical Applications Center, Patrick Air Force Base, Florida.
Chernoff, H. (1952), ‘A measure of asymptotic efficiency for tests of a hypothesis based on the sum of the observations’, The Annals of Mathematical Statistics 23(4), 573–578.
Dahlhaus, R. (1997), ‘Fitting time series models to non stationary processes’, The Annals of Statistics 25, 1–37.
Dargahi-Noubary, G. R. & Laycock, P. J. (1981), ‘Spectral ratio discriminants and information theory’, Journal of Time Series Analysis 2, 71–86.
Daubechies, I. (1992), Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia.
Fryzlewicz, P. (2003), Wavelet Techniques for Time Series and Poisson Data, Phd thesis, University of Bristol.
Fryzlewicz, P. & Ombao, H. (2009), ‘Consistent classification of non stationary time series using stochastic wavelet representations’, Journl of American Statistical Association 104, 299–312.
Gersch, W., Yeager, C. L., Diamond, S. L., Spire, J. P., Gerry, Z. M. & Gevins, A. H. (1975), Automated analysis of the electrical activity of the human brain (eeg), Proceedings of the IEEE 63, University of California Medical Center.
Gersch, W. & Yonemoto, J. (1977), ‘Automatic classification of multivariate eeg, using an amount of information measure and the eigenvalues of parametric time series model features’, Compute. Biomed. Reserch 10, 297–316.
Huang, H. S., Ombao, H. & Stoffer, D. (2004), ‘Discrimination and classification of non-stationary time series using the slex model’, Journl of American Statistical Association 99, 763–774.
Kakizawa, Y., Shumway, R. & Taniguchi, M. (1998), ‘Discrimination and clustering for multivariate time series’, Journl of American Statistical Association 93, 328–340.
Kalpakis, K., Gada, D. & Puttagunta, V. (2001), Distance measures for effective clustering of arima time-series, in ‘Proceedings of the IEEE International Conference on Data Mining’, San Jose, California, pp. 273–280.
Kullback, S. (1978), Information Theory and Statistics, Dover Publications, Inc, New York.
Kullback, S. & Leibler, R. A. (1951), ‘On information and sufficiency’, The Annals Mathematical Statistics 22, 79–86.
Maharaj, E. A. & Alonso, A. M. (2007), ‘Discrimination of locally stationary time series using wavelets’, Computational Statistics and Data Analysis 52, 879–895.
Nason, G. P., von Sachs, R. & Kroisandt, G. (2000), ‘Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum’, Journal of Royal Statistical Society, Series B 62, 271–292.
Ombao, H., Raz, J., von Saches, R. & Guo, W. (2002), ‘The SLEX model of a nonstationary random process’, Annals of the Institute of Statistical Mathematics 54, 171–200.
Ombao, H., Raz, J., von Saches, R. & Malow, B. (2001), ‘Automatic statistical analysis of bivariate non stationary time series’, Journal of American Statistical Association 96, 543–560.
Parzen, E. (1990), Time Series, Statistics and Information, IMA Preprint Series 663, Institute for Mathematics and Its Applications, University of Minnesota
Sakiyama, K. & Taniguchi, M. (2004), ‘Discriminant analysis for locally stationary processes’, Journal of Multivariate Analysis 90, 282–300.
Shumway, R. H. (2003), ‘Time-frequency clustering and discriminant analysis’, Statistics and Probability Letters 63, 307–314.
Shumway, R. H. & Stoffer, D. S. (2011), Time Series Analysis and Applications, 3 edn, v, University of Minnesota.
Shumway, R. H. & Unger, A. N. (1974), ‘Linear discriminant function for stationary time series’, Journl of American Statistical Association 69, 948–956.
Zhang, G. & Taniguchi, M. (1992), ‘Discriminant analysis for stationary vector series’, ournal of Time Series Analysis 15, 117–126.
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
CrossRef Cited-by
Dimensions
PlumX
- Captures
- Mendeley - Readers: 4
Article abstract page views
Downloads
License
Copyright (c) 2016 Revista Colombiana de Estadística
This work is licensed under a Creative Commons Attribution 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
