Classification of cyclical time series using complex demodulation. (English) Zbl 1332.62332
Summary: A new and innovative procedure based on time varying amplitudes for the classification of cyclical time series is proposed. In many practical situations, the amplitude of a cyclical component of a time series is not constant. Estimated time varying amplitudes obtained through complex demodulation of the time series are used as the discriminating variables in classical discriminant analysis. The aim of this paper is to demonstrate through simulation studies and applications to well-known data sets, that time varying amplitudes have very good discriminating power and hence their use in classical discriminant analysis is a simple alternative to more complex methods of time series discrimination.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62-07 | Data analysis (statistics) (MSC2010) |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 94A40 | Channel models (including quantum) in information and communication theory |
| 62Pxx | Applications of statistics |
Software:
SLEXReferences:
| [1] | Alcock, R. J.; Manolopoupos, Y., Time-series similarity queries employing a feature-based approach, Ioannina, Greece |
| [2] | Andrzejak, R.G., Lehnertz, K., Rieke, C., Mormann, F., David, P., Elger, C.E.: Indications of nonlinear deterministic and finite dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. Phys. Rev. E 64, 061907 (2001) · doi:10.1103/PhysRevE.64.061907 |
| [3] | Bloomfield, P.: Fourier Analysis of Time Series: An Introduction. Wiley, New York (2000) · Zbl 0994.62093 · doi:10.1002/0471722235 |
| [4] | Chatfield, C.: The Analysis of Time Series: An Introduction, 6th edn. Chapman and Hall/CRC, New York (2004) · Zbl 1050.62089 |
| [5] | Chinganda, E.F., Subrahaniam, K.: Robustness of the linear discriminant function to nonnormality: Johnson’s system. J. Stat. Plan. Inference 3, 69-77 (1979) · Zbl 0399.62046 · doi:10.1016/0378-3758(79)90042-9 |
| [6] | Chinipardaz, R., Cox, T.F.: Nonparametric discrimination of time series. Metrika 59(1), 13-20 (2004) · Zbl 1052.62033 · doi:10.1007/s001840300267 |
| [7] | Dudoit, S., Fridlyand, J., Speed, T.P.: Comparison of discrimination methods for the classification of tumors using gene expression data. J. Am. Stat. Assoc. 97(457), 77-87 (2002) · Zbl 1073.62576 · doi:10.1198/016214502753479248 |
| [8] | Fatti, L. P.; Hawkins, D. M.; Raath, E. L.; Hawkins, D. M. (ed.), Discriminant analysis, 1-71 (1982), Cambridge · Zbl 0471.62059 · doi:10.1017/CBO9780511897375.002 |
| [9] | Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1, 3rd edn. Wiley, New York (1968) · Zbl 0155.23101 |
| [10] | Huang, H., Hernando, O., Stoffer, D.S.: Discrimination and classification of nonstationary time series using the SLEX model. J. Am. Stat. Assoc. 99(467), 763-774 (2004) · Zbl 1117.62357 · doi:10.1198/016214504000001105 |
| [11] | Kakizawa, Y., Shumway, R.H., Taniguchi, M.: Discrimination and clustering for multivariate time series. J. Am. Stat. Assoc. 93(441), 324-340 (1998) · Zbl 0906.62060 · doi:10.1080/01621459.1998.10474114 |
| [12] | Kannathal, N., Choo, M.L., Acharya, U.R., Sadasivan, U.R.: Entropies in detection of epilepsy in EEG. Comput. Methods Programs Biomed. 80(3), 187-194 (2005) · doi:10.1016/j.cmpb.2005.06.012 |
| [13] | Lachenbruch, P.A., Mickey, M.R.: Estimation of error rates in discriminant analysis. Technometrics 10, 1-12 (1968) · doi:10.1080/00401706.1968.10490530 |
| [14] | Lawoko, C.R.O., McLachlan, G.J.: Some asymptotic results on the effect of autocorrelation on the error rates on the sample linear discriminant function. Pattern Recognit. 16, 119-121 (1983) · Zbl 0515.62059 · doi:10.1016/0031-3203(83)90014-6 |
| [15] | Maharaj, E.A.: Comparison of non-stationary time series in the frequency domain. Comput. Stat. Data Anal. 40, 131-141 (2002) · Zbl 0990.62078 · doi:10.1016/S0167-9473(01)00100-1 |
| [16] | Maharaj, E.A., Alonso, A.M.: Discrimination of locally stationary time series using wavelets. Comput. Stat. Data Anal. 52, 879-889 (2007) · Zbl 1452.62661 · doi:10.1016/j.csda.2007.05.010 |
| [17] | McLachlan, G.J.: Discriminant Analysis and Statistical Pattern Recognition. Wiley, Hoboken (2004) · Zbl 1108.62317 |
| [18] | Nigam, V.P., Graupe, D.: A neural-network-based detection of epilepsy. Neurol. Res. 26(1), 55-60 (2004) · doi:10.1179/016164104773026534 |
| [19] | Pham, D.T., Chan, A.B.: Control Chart pattern recognition using a new type of self-organizing neural network. Proc. Inst. Mech., 115-127 (1998) · Zbl 0906.62060 |
| [20] | Rawlings, R.R., Faden, V.B.: A study on discriminant analysis techniques applied to lognormal data. J. Stat. Comput. Simul. 26, 79-100 (1986) · Zbl 0609.62103 · doi:10.1080/00949658608810950 |
| [21] | Sakiyama, K., Taniguchi, M.: Discriminant analysis for locally stationary processes. J. Multivar. Anal. 90(2), 282-300 (2004) · Zbl 1050.62066 · doi:10.1016/j.jmva.2003.08.002 |
| [22] | Shumway, R.H.: Time-frequency clustering and discriminant analysis. Stat. Probab. Lett. 63(3), 307-314 (2003) · Zbl 1116.62364 · doi:10.1016/S0167-7152(03)00095-6 |
| [23] | Shumway, R.H., Stoffe, D.S.: Time Series Analysis and Its Applications. Springer, Berlin (2000) · Zbl 0942.62098 · doi:10.1007/978-1-4757-3261-0 |
| [24] | Young, P.C., Pedregal, D.J., Tych, W.: Dynamic harmonic regression. J. Forecast. 18, 369-394 (1999) · doi:10.1002/(SICI)1099-131X(199911)18:6<369::AID-FOR748>3.0.CO;2-K |
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