Detecção de mudança de nível em séries temporais não lineares usando Descritores de Hjorth
Detecting a level change in a nonlinear time series using Hjorth’s Descriptors
Amorim, Gabriela da Fonseca de; Balestrassi, Pedro Paulo; Paiva, Anderson Paulo de; Oliveira-Abans, Mariângela de
http://dx.doi.org/10.1590/0103-6513.123313
Production, vol.25, n4, p.812-825, 2015
Resumo
O propósito deste artigo é apresentar um método de detecção de mudança de nível na dinâmica de séries temporais não lineares que consiste no uso de um gráfico de Controle Multivariado T2 de Hotelling monitorando a variação de três descritores normalizados: os Descritores de Hjorth de atividade, mobilidade e complexidade. Esta abordagem foi aplicada em diferentes séries temporais não lineares criadas artificialmente e é ilustrada neste artigo por um exemplo detalhado. Também foi feito um estudo de caso com seis séries reais do consumo de energia elétrica no meio industrial, confirmando a eficácia do método.
Palavras-chave
Séries temporais não lineares. Descritores de Hjorth. Gráficos de Controle Multivariado T2 de Hotelling. Mudança de nível.
Abstract
The purpose of this paper is to present a method for detecting the dynamic changes in a nonlinear time series that uses the Hotelling T2 multivariate control chart to monitor the variation in three normalized descriptors: Hjorth’s descriptors of activity, mobility and complexity. This approach was applied to different simulated nonlinear time series and is illustrated in this paper with a detailed example. A case study with six time series of short-term electricity load consumption was also used to confirm the method’s effectiveness.
Keywords
Nonlinear time series. Hjorth’s Descriptors. Hotelling T2 control chart. Level change.
References
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Gooijer, J. G. (1998). On threshold moving-average models. Journal of Time Series Analysis, 19(1), 1-18. http://dx.doi.org/10.1111/1467-9892.00074
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Karathanassi, V., Iossifidis, C., & Rokos, D. (1996). Application of machine vision techniques in the quality control of pharmaceutical solutions. Computers in Industry, 32(2), 169-179. http://dx.doi.org/10.1016/S0166-3615(96)00063-2
Klöppelberg, C., & Mikosch, T. (1996). Gaussian limit fields for the integrated periodogram. The Annals of Applied Probability, 6(3), 969-991. http://dx.doi.org/10.1214/aoap/1034968236
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Morgenstern, V. M., Upadhyaya, B. R., & Benedetti, M. (1988). Signal anomaly detection using modified cusum method. In Proceedings of the 27th IEEE Conference on Decision and Control, Knoxville, Texas. http://dx.doi.org/10.1109/CDC.1988.194756
Mount, T. (2001). Market power and price volatility in restructured markets for electricity. Decision Support Systems, 30, 311-325. http://dx.doi.org/10.1016/S0167-9236(00)00108-1
Ombao, H., Heo, J., & Stoffer, D. (2004). Statistical analysis of seismic signals: an almost real-time approach, time series analysis and applications to geophysical systems (IMA Series 139). New York: Wiley.
Pai, PF., & Hong, W. C. (2005). Support vector machines with simulated annealing algorithms in electricity load forecasting. Energy Conversion and Management, 46, 2669-2688. http://dx.doi.org/10.1016/j.enconman.2005.02.004
Percival, D. B., & Walden, A. T. (2000). Wavelet methods for time series analysis. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511841040
Priestley, M. B. (1980). State-dependent models: a general approach to nonlinear time series analysis. Journal of Time Series Analysis, 1, 47-71. http://dx.doi.org/10.1111/j.1467-9892.1980.tb00300.x
Ramirez-Beltran, N. D., & Montes, J. A. (1997). Neural networks for on-line parameter change detections in time series models. Computers & Industrial Engineering, 33, 337-340. http://dx.doi.org/10.1016/S0360-8352(97)00106-X
Souza, R. C. (1981). Metodologias para a análise e previsão de séries temporais univariadas e multivariadas. Revista de Econometria, 77, 105.
Statsoft, Inc. (2005). Statistica: version 7.1. Recuperado em 6 de fevereiro de 2013, de ww.statsoft.com
Tong, H. (1978). On a threshold model. In C. H. Chen (Ed.), Pattern recognition and signal processing (pp. 575-586). Amsterdam: Sijhoff & Noordhoff. http://dx.doi.org/10.1007/978-94-009-9941-1_24
Tsay, R. S. (2005). Analysis of financial time series. New Jersey: Wiley. http://dx.doi.org/10.1002/0471746193
Ye, N. (2000). Confidence assessment of quality prediction from process measurement in sequential manufacturing processes. IEEE Transactions on Electronics Packaging Manufacturing, 23(3), 177-184. http://dx.doi.org/10.1109/6104.873245
Zhang, G. P., Patuwo, B. E., & Hu, M. Y. (2001). A simulation study of artificial neural networks for nonlinear time-series forecasting. Computers & Operations Research, 28, 381-396. http://dx.doi.org/10.1016/S0305-0548(99)00123-9
Basseville, M., & Nikiforov, I. (2000). Detection of abrupt changes: theory and application. New Jersey: Prentice- Hall.
Bersimis, S., Psarakis, S., & Panaretos, J. (2007). Multivariate statistical process control charts: an overview. Quality and Reliability Engineering International, 23(5), 517-543. http://dx.doi.org/10.1002/qre.829
Box, G. E. P., & Jenkins, G. M. (1976). Time series analysis: forecasting and control. San Francisco: Holden-Day.
Burrell, A., & Papantoni, T. (2000). Sequential algorithms for detecting changes in acting stochastic processes and on-line learning of their operational parameters. In Proceedings of the 15th International Conference on Pattern Recognition, Barcelona, Spain. http://dx.doi.org/10.1109/ICPR.2000.906160
Cabrerizo, M., Ayala, M., Goryawala, M., Jayakar, P., & Adjouadi, M. (2012). A new parametric feature descriptor for the classification of epileptic and control EEG records in pediatric population. International Journal of Neural Systems, 22(2). PMid:23627587. http://dx.doi.org/10.1142/S0129065712500013
Castanie, F., & Denjean, F. (1992). Mean value jump detection using wavelet decomposition. In Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Victoria, Canada. http://dx.doi.org/10.1109/TFTSA.1992.274207
Chen, R., & Tsay, R. S. (1993). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88(421), 298-308.
Gooijer, J. G. (1998). On threshold moving-average models. Journal of Time Series Analysis, 19(1), 1-18. http://dx.doi.org/10.1111/1467-9892.00074
Granger, C. W. J., & Anderson, A. P. (1978). An introduction to bilinear time series models. Göttingen: Vandenhoeck & Ruprecht.
Granger, C. W. J., & Terasvirta, T. (1993). Modeling nonlinear economic relationship. New York: Oxford University Press.
Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57(2), 357-384. http://dx.doi.org/10.2307/1912559
Hjorth, B. (1970). EEG analysis based on time domain properties. Electroencephalography and Clinical Neurophysiology, 29(3), 306-310. http://dx.doi.org/10.1016/0013-4694(70)90143-4
Inclan, C. (1993). Detection of multiple changes of variance using posterior odds. Journal of Business & Economic Statistics, 11(3), 289-300.
Inclan, C., & Tiao, G. (1994). Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of the American Statistical Association, 89(427), 913-923.
Karathanassi, V., Iossifidis, C., & Rokos, D. (1996). Application of machine vision techniques in the quality control of pharmaceutical solutions. Computers in Industry, 32(2), 169-179. http://dx.doi.org/10.1016/S0166-3615(96)00063-2
Klöppelberg, C., & Mikosch, T. (1996). Gaussian limit fields for the integrated periodogram. The Annals of Applied Probability, 6(3), 969-991. http://dx.doi.org/10.1214/aoap/1034968236
Lavielle, M., & Lebarbier, E. (2001). An application of MCMC methods for the multiple change-points problem. Signal Process, 81(1), 39-53. http://dx.doi.org/10.1016/S0165-1684(00)00189-4
Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE Transactions, 27(5), 800-810. http://dx.doi.org/10.1080/07408179508936797
Macdougall, S., Nandi, A. K., & Chapman, R. (1998). Multiresolution and hybrid bayesian algorithms for automatic detection of change points. IEE Proceedings - Vision, Image and Signal, 145(4), 280-286. http://dx.doi.org/10.1049/ip-vis:19982150
Malladi, D. P., & Speyer, J. L. (1999). A generalized shiryayev sequential probability ratio test for change detection and isolation. IEEE Transactions on Automatic Control, 44(8), 1522-1534. http://dx.doi.org/10.1109/9.780416
Mariani, S., Manfredini, E., Rosso, V., Mendez, M. O., Bianchi, A. M., Matteucci, M., Terzano, M. G., Cerutti, S., & Parrino, L. (2011). Characterization of a phases during the cyclic alternating pattern of sleep. Clinical Neurophysiology, 122(10), 2016-2024. PMid:21439902. http://dx.doi.org/10.1016/j.clinph.2011.02.031
Morgenstern, V. M., Upadhyaya, B. R., & Benedetti, M. (1988). Signal anomaly detection using modified cusum method. In Proceedings of the 27th IEEE Conference on Decision and Control, Knoxville, Texas. http://dx.doi.org/10.1109/CDC.1988.194756
Mount, T. (2001). Market power and price volatility in restructured markets for electricity. Decision Support Systems, 30, 311-325. http://dx.doi.org/10.1016/S0167-9236(00)00108-1
Ombao, H., Heo, J., & Stoffer, D. (2004). Statistical analysis of seismic signals: an almost real-time approach, time series analysis and applications to geophysical systems (IMA Series 139). New York: Wiley.
Pai, PF., & Hong, W. C. (2005). Support vector machines with simulated annealing algorithms in electricity load forecasting. Energy Conversion and Management, 46, 2669-2688. http://dx.doi.org/10.1016/j.enconman.2005.02.004
Percival, D. B., & Walden, A. T. (2000). Wavelet methods for time series analysis. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511841040
Priestley, M. B. (1980). State-dependent models: a general approach to nonlinear time series analysis. Journal of Time Series Analysis, 1, 47-71. http://dx.doi.org/10.1111/j.1467-9892.1980.tb00300.x
Ramirez-Beltran, N. D., & Montes, J. A. (1997). Neural networks for on-line parameter change detections in time series models. Computers & Industrial Engineering, 33, 337-340. http://dx.doi.org/10.1016/S0360-8352(97)00106-X
Souza, R. C. (1981). Metodologias para a análise e previsão de séries temporais univariadas e multivariadas. Revista de Econometria, 77, 105.
Statsoft, Inc. (2005). Statistica: version 7.1. Recuperado em 6 de fevereiro de 2013, de ww.statsoft.com
Tong, H. (1978). On a threshold model. In C. H. Chen (Ed.), Pattern recognition and signal processing (pp. 575-586). Amsterdam: Sijhoff & Noordhoff. http://dx.doi.org/10.1007/978-94-009-9941-1_24
Tsay, R. S. (2005). Analysis of financial time series. New Jersey: Wiley. http://dx.doi.org/10.1002/0471746193
Ye, N. (2000). Confidence assessment of quality prediction from process measurement in sequential manufacturing processes. IEEE Transactions on Electronics Packaging Manufacturing, 23(3), 177-184. http://dx.doi.org/10.1109/6104.873245
Zhang, G. P., Patuwo, B. E., & Hu, M. Y. (2001). A simulation study of artificial neural networks for nonlinear time-series forecasting. Computers & Operations Research, 28, 381-396. http://dx.doi.org/10.1016/S0305-0548(99)00123-9
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