Time series forecasting for nonlinear and non-stationary processes: a review and comparative study

References

• Adams, R.P. and Stegle, O. (2008) Gaussian process product models for nonparametric nonstationarity, in Proceedings of the 25th International Conference on Machine Learning, ACM, New York, NY, pp. 1–8.
   Google Scholar
• Amaral, G.F.V., Letellier, C. and Aguirre, L.A. (2006) Piecewise affine models of chaotic attractors: the Rössler and Lorenz systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 16(1), 013115–013315-4.
   Web of Science ®Google Scholar
• An, X., Jiang, D., Zhao, M. and Liu, C. (2012) Short-term prediction of wind power using EMD and chaotic theory. Communications in Nonlinear Science and Numerical Simulation, 17(2), 1036–1042.
   Web of Science ®Google Scholar
• Arulampalam, M.S., Maskell, S., Gordon, N. and Clapp, T. (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174–188.
   Web of Science ®Google Scholar
• Aznarte, J.L., Benítez Sánchez, M.J.M., Lugilde, D.N., de Linares Fernández, C., de la Guardia, C.D. and Sánchez, F.A. (2007) Forecasting airborne pollen concentration time series with neural and neuro-fuzzy models. Expert Systems with Applications, 32(4), 1218–1225.
   Web of Science ®Google Scholar
• Balabin, R.M. and Lomakina, E.I. (2011) Support vector machine regression (SVR/LS-SVM)–an alternative to neural networks (ANN) for analytical chemistry? Comparison of nonlinear methods on near infrared (NIR) spectroscopy data. Analyst, 136(8), 1703–1712.
   PubMed Web of Science ®Google Scholar
• Barreto, G., Hammer, B. and Hitzler, P. (2007) Time Series prediction with the self-organizing map: a review perspectives of neural-symbolic integration, in Perspectives of Neural-Symbolic Integration, eds. B. Hammer and P. Hitzler, Springer, Berlin, pp. 135–158.
   Google Scholar
• Battaglia, F. and Protopapas, M.K. (2011) Time-varying multi-regime models fitting by genetic algorithms. Journal of Time Series Analysis, 32(3), 237–252.
   Web of Science ®Google Scholar
• Blei, D.M. and Jordan, M.I. (2005) Variational inference for Dirichlet process mixtures. Bayesian Analysis, 1, 121–144.
   Web of Science ®Google Scholar
• Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
   Web of Science ®Google Scholar
• Brahim-Belhouari, S. and Bermak, A. (2004) Gaussian process for nonstationary time series prediction. Computational Statistics & Data Analysis, 47(4), 705–712.
   Web of Science ®Google Scholar
• Broer, H.W., Huitema, G.B. and Sevryuk, M.B. (1996) Quasi-periodic motions in families of dynamical systems: order amidst chaos. Lecture Notes in Mathematics, 1645
   Web of Science ®Google Scholar
• Bukkapatnam, S.T.S. and Cheng, C. (2010) Forecasting the evolution of nonlinear and nonstationary systems using recurrence-based local Gaussian process models. Physical Review E, 82(5), 056206–056206-12.
   Web of Science ®Google Scholar
• Bukkapatnam, S.T.S., Yang, H. and Madhavi, F. (2009) Towards prediction of nonlinear and nonstationary evolution of customer preferences using local Markov models, in Product Research, Raghavan, N.R.S. and Cafeo, J.A. (eds), Springer, Dordrecht, The Netherlands, pp. 271–287.
   Google Scholar
• Cao, L. (2003) Support vector machines experts for time series forecasting. Neurocomputing, 51, 321–339.
   Web of Science ®Google Scholar
• Cao, L. and Gu, Q. (2002) Dynamic support vector machines for non-stationary time series forecasting. Intelligent Data Analysis, 6(1), 67–83.
   Google Scholar
• Casdagli, M. (1989) Nonlinear prediction of chaotic time series. Physica D: Nonlinear Phenomena, 35(3), 335–356.
   Web of Science ®Google Scholar
• Casdagli, M.C. (1997) Recurrence plots revisited. Physica D: Nonlinear Phenomena, 108(1--2), 12–44.
   Web of Science ®Google Scholar
• Chatzis, S.P. and Demiris, Y. (2012) Nonparametric mixtures of Gaussian processes with power-law behavior. IEEE Transactions on Neural Networks and Learning Systems, 23(12), 1862–1871.
   PubMed Web of Science ®Google Scholar
• Chen, R. and Liu, J.S. (2000) Mixture Kalman filters. Journal of the Royal Statistical Society Series B-Statistical Methodology, 62, 493–508.
   Web of Science ®Google Scholar
• Chen, S., Billings, S.A. and Grant, P.M. (1992) Recursive hybrid algorithm for non-linear system identification using radial basis function networks. International Journal of Control, 55(5), 1051–1070.
   Web of Science ®Google Scholar
• Chen, S., Cowan, C.F.N. and Grant, P.M. (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Transactions on Neural Networks, 2(2), 302–309.
   PubMed Web of Science ®Google Scholar
• Cheng, C., Bukkapatnam, S.T.S., Raff, L.M., Hagan, M. and Komanduri, R. (2012) Monte Carlo simulation of carbon nanotube nucleation and growth using nonlinear dynamic predictions. Chemical Physics Letters, 530, 81–85.
   Web of Science ®Google Scholar
• Crauel, H., Debussche, A. and Flandoli, F. (1997) Random attractors. Journal of Dynamics and Differential Equations, 9(2), 307–341.
   Google Scholar
• Damrongkulkamjorn, P. and Churueang, P. (2005) Monthly energy forecasting using decomposition method with application of seasonal ARIMA, in Procedings of the Seventh International Power Engineering Conference, IEEE, Singapore, pp. 1–229.
   Google Scholar
• De Gooijer, J.G. and Hyndman, R.J. (2006) 25 years of time series forecasting. International Journal of Forecasting, 22, 443–473.
   Web of Science ®Google Scholar
• De Groot, C. and Wuertz, D. (1991) Analysis of univariate time series with connectionist nets: a case study of two classical examples. Neurocomputing, 3(4), 177–192.
   Google Scholar
• Duy, N.-T. and Peters, J. (2008) Local Gaussian process regression for real-time model-based robot control, in Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Nice, France, pp. 380–385.
   Google Scholar
• Eckmann, J.P., Kamphorst, S.O. and Ruelle, D. (1987) Recurrence plots of dynamical systems. Europhysics Letters, 4(9), 973–977.
   Google Scholar
• Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.
   Web of Science ®Google Scholar
• Fan, J. and Yao, Q. (2003) Nonlinear Time Series: Nonparametric and Parametric Methods, Springer-Verlag, New York, NY.
   Google Scholar
• Finkenstädt, B. and Kuhbier, P. (1995) Forecasting nonlinear economic time series: a simple test to accompany the nearest neighbor approach. Empirical Economics, 20(2), 243–263.
   Google Scholar
• Fraser, A.M. and Swinney, H.L. (1986) Independent coordinates for strange attractors from mutual information. Physical Review A, 33(2), 1134–1140.
   PubMed Web of Science ®Google Scholar
• Frei, M.G. and Osorio, I. (2007) Intrinsic time-scale decomposition: time–frequency–energy analysis and real-time filtering of non-stationary signals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 463(2078), 321–342.
   Web of Science ®Google Scholar
• French, M.N., Krajewski, W.F. and Cuykendall, R.R. (1992) Rainfall forecasting in space and time using a neural network. Journal of Hydrology, 137(1), 31–31.
   Web of Science ®Google Scholar
• Fu, C. (2010) Forecasting exchange rate with EMD-based support vector regression, in Proceedings of the International Conference on Management and Service Science, IEEE, Wuhan, China, pp. 1–4.
   Google Scholar
• Genton, M. and Thompson, K. Skew-elliptical time series with application to flooding risk, in Time Series Analysis and Applications to Geophysical Systems, Brillinger, D., Robinson, E. and Schoenberg, F. (eds), Springer, New York, pp. 169–185.
   Google Scholar
• Gershman, S.J. and Blei, D.M. (2012) A tutorial on Bayesian nonparametric models. Journal of Mathematical Psychology, 56(1), 1–12.
   Web of Science ®Google Scholar
• Gestel, T.V., Suykens, J.A.K., Baestaens, D.-E., Lambrechts, A., Lanckriet, G., Vandaele, B., Moor, B.D. and Vandewalle, J. (2001) Financial time series prediction using least squares support vector machines within the evidence framework. IEEE Transactions on Neural Networks, 12, 809–821.
   PubMed Web of Science ®Google Scholar
• Ghahramani, Z. and Roweis, S. (1999) Learning nonlinear dynamical systems using an EM algorithm. Advances in Neural Information Processing Systems, 11, 431–437.
   Google Scholar
• Girard, A., Rasmussen, C.E., Quinonero-Candela, J. and Murray-Smith, R. (2003) Gaussian process priors with uncertain inputs? Application to multiple-step ahead time series forecasting, in Proceedings of the Conference on Neural Information Processing Systems, MIT Press, Cambridge, Massachusetts, pp. 9–14.
   Google Scholar
• Goldberger, A.L. (1999) Implications for neuroautonomic heart rate control in health and disease, in The Autonomic Nervous System, Bolis, C. and Licinio, J. (eds), World Health Organization, Geneva.
   Google Scholar
• Gonzalez, A.M., Roque, A.M.S. and Garcia-Gonzalez, J. (2005) Modeling and forecasting electricity prices with input/output hidden Markov models. IEEE Transactions on Power Systems, 20(1), 13–24.
   Web of Science ®Google Scholar
• Gordon, N.J., Salmond, D.J. and Smith, A.F.M. (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F, Radar and Signal Processing, 140(2), 107–113.
   Web of Science ®Google Scholar
• Grudnitski, G. and Osburn, L. (1993) Forecasting S&P and gold futures prices: an application of neural networks. Journal of Futures Markets, 13(6), 631–643.
   Web of Science ®Google Scholar
• Hachino, T. and Kadirkamanathan, V. (2007) Time series forecasting using multiple Gaussian process prior model, in Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining, IEEE, Honolulu, HI, pp. 604–609.
   Google Scholar
• Hamid, N.Z.A. and Noorani, M.S.M. (2013) Modeling of prediction system: an application of nearest neighbor approach to chaotic data. Applied Mathematics and Computational Intelligence, 2, 137–148.
   Google Scholar
• Hamilton, J.D. (1989) A new approach to the economic analysis of time series. Econometrica, 57(2), 357–384.
   Web of Science ®Google Scholar
• Heagy, J.F., Platt, N. and Hammel, S.M. (1994) Characterization of on-off intermittency. Physical Review E, 49(2), 1140–1150.
   PubMed Web of Science ®Google Scholar
• Hippert, H.S., Pedreira, C.E. and Souza, R.C. (2001) Neural networks for short-term load forecasting: a review and evaluation. IEEE Transactions on Power Systems, 16(1), 44–55.
   Web of Science ®Google Scholar
• Hong, L. (2011) Decomposition and forecast for financial time series with high-frequency based on empirical mode decomposition. Energy Procedia, 5, 1333–1340.
   Google Scholar
• Huang, N.E. (2005) Introduction to the Hilbert-Huang transform and its related mathematical problems. Interdisciplinary Mathematics, 5, 1–26.
   Google Scholar
• Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C. and Liu, H.H. (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1971), 903–995.
   Web of Science ®Google Scholar
• Kantz, H. and Schreiber, T. (1997) Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, UK.
   Google Scholar
• Katok, A. and Hasselblatt, B. (1995) Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, UK.
   Google Scholar
• Kennel, M.B., Brown, R. and Abarbanel, H.D. (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45(6), 3403–3411.
   PubMed Web of Science ®Google Scholar
• Khashei, M., Reza Hejazi, S. and Bijari, M. A new hybrid artificial neural networks and fuzzy regression model for time series forecasting. Fuzzy Sets and Systems, 159(7), 769–786.
   Web of Science ®Google Scholar
• Khemchandani, R., Jayadeva and Chandra, S. (2009) Regularized least squares fuzzy support vector regression for financial time series forecasting. Expert Systems with Applications, 36(1), 132–138.
   Web of Science ®Google Scholar
• Kirchgässner, G., Wolters, J. and Hassler, U. (2013) Introduction to Modern Time Series Analysis, Springer, Berlin, Germany.
   Google Scholar
• Ko, J. and Fox, D. (2009) GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models. Autonomous Robots, 27(1), 75–90.
   Web of Science ®Google Scholar
• Kodogiannis, V. and Lolis, A. (2002) Forecasting financial time series using neural network and fuzzy system-based techniques. Neural Computing & Applications, 11(2), 90–102.
   Web of Science ®Google Scholar
• Kohzadi, N., Boyd, M.S., Kermanshahi, B. and Kaastra, I. (1996) A comparison of artificial neural network and time series models for forecasting commodity prices. Neurocomputing, 10(2), 169–181.
   Web of Science ®Google Scholar
• Kong, Z., Beyca, O., Bukkapatnam, S.T.S. and Komanduri, R. (2011) Nonlinear sequential Bayesian analysis-based decision making for end-point detection of chemical mechanical planarization (CMP) processes. IEEE Transactions on Semiconductor Manufacturing, 24(4), 523–532.
   Web of Science ®Google Scholar
• Kong, Z., Oztekin, A., Beyca, O.F., Phatak, U., Bukkapatnam, S.T.S. and Komanduri, R. (2010) Process performance prediction for chemical mechanical planarization (CMP) by integration of nonlinear Bayesian analysis and statistical modeling. IEEE Transactions on Semiconductor Manufacturing, 23(2), 316–327.
   Web of Science ®Google Scholar
• Kotecha, J.H. and Djuric, P.M. (2003) Gaussian particle filtering. IEEE Transactions on Signal Processing, 51(10), 2592–2601.
   Web of Science ®Google Scholar
• Koutsoyiannis, D. and Montanari, A. (2007) Statistical analysis of hydroclimatic time series: uncertainty and insights. Water Resources Research, 43(5), W05429:1–9.
   Web of Science ®Google Scholar
• Krishnamurthy, V. and Yin, G.G. (2002) Recursive algorithms for estimation of hidden Markov models and autoregressive models with Markov regime. IEEE Transactions on Information Theory, 48(2), 458–476.
   Web of Science ®Google Scholar
• Kuan, C.M. and Liu, T. (1995) Forecasting exchange rates using feedforward and recurrent neural networks. Journal of Applied Econometrics, 10(4), 347–364.
   Web of Science ®Google Scholar
• Kumar, C., Patel, N. and Jarudi, I. (2003) 21st century physics: grand challenges. Journal of the Federation of American Scientists, 56(2), 9–11.
   Google Scholar
• Lai, K., Yu, L., Wang, S. and Wei, H. (2006) A novel nonlinear neural network ensemble model for financial time series forecasting. Lecture Notes in Computer Science, 3991, 790–793.
   Google Scholar
• Lang, T., Plagemann, C. and Burgard, W. (2007) Adaptive non-stationary kernel regression for terrain modeling, in Proceedings of the Robotics: Science and Systems Conference, MIT Press, Cambridge, MA, pp. 81–88.
   Google Scholar
• Lapedes, A. and Farber, R. (1987) Nonlinear signal processing using neural networks: prediction and system modeling. Report, Los Alamos Nationary Laboratory, Los Alamos, NM.
   Google Scholar
• Last, M. and Shumway, R. (2008) Detecting abrupt changes in a piecewise locally stationary time series. Journal of Multivariate Analysis, 99(2), 191–214.
   PubMed Web of Science ®Google Scholar
• Lau, K.W. and Wu, Q.H. (2008) Local prediction of non-linear time series using support vector regression. Pattern Recognition, 41(5), 1539–1547.
   Web of Science ®Google Scholar
• Le, T., Cheng, C., Sangasoongsong, A., Wongdhamma, W. and Bukkapatnam, S.T.S. (2013) Wireless wearable multisensory suite and real-time prediction of sleep apnea episodes. IEEE Journal of Translational Engineering in Health and Medicine, 1(1, 2700109.
   PubMedGoogle Scholar
• Lee, T. and Ouarda, T.B.M.J. (2011) Prediction of climate nonstationary oscillation processes with empirical mode decomposition. Journal of Geophysical Research: Atmospheres, 116(D6), D06107, 1–15.
   Web of Science ®Google Scholar
• Li, J.P., Tang, L., Sun, X.L., Yu, L.A., He, W. and Yang, Y.Y. (2012) Country risk forecasting for major oil exporting countries: a decomposition hybrid approach. Computers and Industrial Engineering, 63(3), 641–651.
   Web of Science ®Google Scholar
• Lineesh, M.C. and John, C.J. (2010) Analysis of non-stationary time series using wavelet decomposition. Nature and Science, 8(1), 53–59.
   Google Scholar
• Lowe, D. and Webb, A.R. (1991) Time series prediction by adaptive networks: a dynamical systems perspective. IEE Proceedings of Radar and Signal Processing, 138(1), 17–24.
   Web of Science ®Google Scholar
• Lundbergh, S., Teräsvirta, T. and van Dijk, D. (2003) Time-varying smooth transition autoregressive models. Journal of Business & Economic Statistics, 21(1), 104–121.
   Web of Science ®Google Scholar
• Martis, R.J., Acharya, U.R., Tan, J.H., Petznick, A., Tong, L., Chua, C.K. and Ng, E.Y.K. (2013) Application of intrinsic time-scale decomposition (ITD) to EEG signals for automated seizure prediction. International Journal of Neural Systems, 23(05), 1350023.
   PubMed Web of Science ®Google Scholar
• Marwan, N., Carmen Romano, M., Thiel, M. and Kurths, J. (2007) Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329.
   Web of Science ®Google Scholar
• Meeds, E. and Osindero, S. (2006) An alternative infinite mixture of Gaussian process experts, in Advances in Neural Information Processing Systems, Weiss, Y., Scholkopf, B. and Platt, J. (eds), MIT Press, Cambridge, MA, pp. 883–890.
   Google Scholar
• Menezes, J.M.P. and Barreto, G.A. (2008) Long-term time series prediction with the NARX network: an empirical evaluation. Neurocomputing, 71(16-18), 3335–3343.
   Web of Science ®Google Scholar
• Marchesi, M. and Lux, T. (2000) Volatility clustering in financial markets: a microsimulation of interacting agents. International Journal of Theoretical and Applied Finance, 3(04), 675–702.
   Google Scholar
• McAleer, M. and Medeiros, M.C. (2008) A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries. Journal of Econometrics, 147(1), 104–119.
   Web of Science ®Google Scholar
• McNames, J. (1998) A nearest trajectory strategy for time series prediction, in Proceedings of the International Workshop on Advanced BlackBox Techniques for Nonlinear Modeling, Katholieke Universiteit, Leuven Belgium, pp. 112–128.
   Google Scholar
• Mehrotra, R. and Sharma, A. (2006) Conditional resampling of hydrologic time series using multiple predictor variables: a K-nearest neighbour approach. Advances in Water Resources, 29(7), 987–999.
   Web of Science ®Google Scholar
• Moradkhani, H., Sorooshian, S., Gupta, H.V. and Houser, P.R. (2005) Dual state–parameter estimation of hydrological models using ensemble Kalman filter. Advances in Water Resources, 28(2), 135–147.
   Web of Science ®Google Scholar
• Mukherjee, S., Osuna, E. and Girosi, F. (1997) Nonlinear prediction of chaotic time series using support vector machines, in Proceedings of the 1997 IEEE Workshop on Neural Networks for Signal Processing, IEEE, Amelia Island, FL, pp. 511–520.
   Google Scholar
• Nayak, P.C., Sudheer, K.P., Rangan, D.M. and Ramasastri, K.S. (2004) A neuro-fuzzy computing technique for modeling hydrological time series. Journal of Hydrology, 291(1–2), 52–66.
   Web of Science ®Google Scholar
• Palm, R. (2007) Multiple-step-ahead prediction in control systems with Gaussian process models and TS-fuzzy models. Engineering Applications of Artificial Intelligence, 20(8), 1023–1035.
   Web of Science ®Google Scholar
• Park, J. and Sandberg, I.W. (1991) Universal approximation using radial-basis-function networks. Neural Computation, 3(2), 246–257.
   PubMed Web of Science ®Google Scholar
• Plagemann, C., Kersting, K. and Burgard, W. (2008) Nonstationary Gaussian process regression using point estimates of local smoothness. Lecture Notes in Computer Science, 5212, 204–219.
   Google Scholar
• Rabiner, L. (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77(2), 257–286.
   Web of Science ®Google Scholar
• Rao, K.P., Bukkapatnam, S.T.S., Beyca, O.F., Kong, Z. and Komanduri, R. (2013) Real-time identification of incipient surface morphology variations in ultra-precision machining process. ASME Journal of Manufacturing Science and Engineering, 136(2), 021008 1–11.
   Web of Science ®Google Scholar
• Rasmussen, C.E. and Williams, C.K.I. (2006) Gaussian Process for Machine Learning, MIT Press, Cambridge, MA.
   Google Scholar
• Regonda, S., Rajagopalan, B., Lall, U., Clark, M. and Moon, Y.-I. (2005) Local polynomial method for ensemble forecast of time series. Nonlinear Processes in Geophysics, 12, 397–406.
   Web of Science ®Google Scholar
• Rosen, O., Wood, S. and Stoffer, D.S. (2012) AdaptSPEC: Adaptive spectral estimation for nonstationary time series. Journal of the American Statistical Association, 107(500), 1575–1589.
   Web of Science ®Google Scholar
• Sa-ngasoongsong, A. (2012) Long-term demand prediction using long-run equilibrium relationship of intrinsic time-scale decomposition components, in Proceedings of the 2012 Industrial and Systems Engineering Research Conference, Orlando, FL.
   Google Scholar
• Sa-ngasoongsong, A. and Bukkapatnam, S.T.S. (2011) Willingness-to-pay prediction based on empirical mode decomposition, in Proceedings of the Industrial Engineering Research Conference, Reno, NV, USA.
   Google Scholar
• Sa-ngasoongsong, A., Bukkapatnam, S.T.S., Kim, J., Iyer, P.S. and Suresh, R.P. (2012) Multi-step sales forecasting in automotive industry based on structural relationship identification. International Journal of Production Economics, 140(2), 875–887.
   Web of Science ®Google Scholar
• Schreiber, T. (1999) Interdisciplinary application of nonlinear time series methods. Physics Reports, 308(1), 1–64.
   Google Scholar
• Shi, J.Q., Murray-Smith, R. and Titterington, D.M. (2005) Hierarchical Gaussian process mixtures for regression. Statistics and Computing, 15(1), 31–41.
   Web of Science ®Google Scholar
• Smola, A. and Schölkopf, B. (2004) A tutorial on support vector regression. Statistics and Computing, 14(3), 199–222.
   Web of Science ®Google Scholar
• Soltani, S. (2002) On the use of the wavelet decomposition for time series prediction. Neurocomputing, 48(1-4), 267–277.
   Web of Science ®Google Scholar
• Stark, H. and Woods, J. (2011) Probability, Statistics, and Random Processes for Engineers, Prentice Hall, Englewood Cliffs, NJ.
   Google Scholar
• Stroeer, A., Cannizzo, J.K., Camp, J.B. and Gagarin, N. (2009) Methods for detection and characterization of signals in noisy data with the Hilbert-Huang transform. Physical Review D, 79(12), 124022 1–10.
   Web of Science ®Google Scholar
• Takens, F. (1981) Detecting strange attractors in turbulence. Lecture Notes in Mathematics, 898, 366–381.
   Google Scholar
• Tay, F.E.H. and Cao, L.J. (2002) Modified support vector machines in financial time series forecasting. Neurocomputing, 48(1), 847–861.
   Web of Science ®Google Scholar
• Teräsvirta, T. (1994) Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89(425), 208–218.
   Web of Science ®Google Scholar
• Tian, Q., Price, N.D. and Hood, L. (2012) Systems cancer medicine: towards realization of predictive, preventive, personalized and participatory (P4) medicine. Journal of Internal Medicine, 271(2), 111–121.
   PubMed Web of Science ®Google Scholar
• Tiao, G.C. and Tsay, R.S. (1994) Some advances in non-linear and adaptive modelling in time-series. Journal of Forecasting, 13(2), 109–131.
   Web of Science ®Google Scholar
• Tong, H. (1990) Non-Linear Time Series: A Dynamical System Approach, Clarendon Press, Oxford, UK.
   Google Scholar
• Van der Merwe, R. and Wan, E. (2003) Gaussian mixture sigma-point particle filters for sequential probabilistic inference in dynamic state-space models, in Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal, IEEE, Vancouver, BC, Canada, pp. . VI-701-4.
   Google Scholar
• Wan, E.A. and van der Merwe, R. (2000) The unscented Kalman filter for nonlinear estimation, in The IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, IEEE, Lake Louise, Alberta, Canada, pp. 153–158.
   Google Scholar
• Wang, J.M.J. Fleet, D.J. and Hertzmann, A. (2008) Gaussian process dynamical models for human motion. IEEE Transactions on Pattern Analysis and Machine Intellegence, 30, 283–298.
   PubMed Web of Science ®Google Scholar
• Wang, X., Ma, J.J., Wang, S. and Bi, D.W. (2007) Time series forecasting energy-efficient organization of wireless sensor networks. Sensors, 7(9), 1766–1792.
   PubMed Web of Science ®Google Scholar
• Wang, Z., Bukkapatnam, S.T.S., Kumara, S.R.T., Kong, Z. and Katz, Z. (2014) Change detection in precision manufacturing processes under transient conditions. CIRP Annals - Manufacturing Technology, 63, 449–452.
   Web of Science ®Google Scholar
• Wang, Z., Liu, X., Liu, Y., Liang, J. and Vinciotti, V. (2009) An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series. IEEE Transactions on Computational Biology Bioinformatics, 6(3), 410–419.
   PubMed Web of Science ®Google Scholar
• Weron, R. and Misiorek, A. (2008) Forecasting spot electricity prices: a comparison of parametric and semiparametric time series models. International Journal of Forecasting, 24(4), 744–763.
   Web of Science ®Google Scholar
• Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A. (1985) Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285–317.
   Web of Science ®Google Scholar
• Xu, X., Qi, Y. and Hua, Z. (2010) Forecasting demand of commodities after natural disasters. Expert Systems with Applications, 37(6), 4313–4317.
   Web of Science ®Google Scholar
• Yadav, P.K., Pope, P.F. and Paudyal, K. (1994) Threshold autoregressive modeling in finance: the price differences of equivalent assets. Mathematical Finance, 4(2), 205–221.
   Google Scholar
• Yang, H., Bukkapatnam, S.T.S. and Barajas, L.G. (2011) Local recurrence based performance prediction and prognostics in the nonlinear and nonstationary systems. Pattern Recognition, 44(8), 1834–1840.
   Web of Science ®Google Scholar
• Yang, H., Bukkapatnam, S.T.S. and Komanduri, R. (2007) Nonlinear adaptive wavelet analysis of electrocardiogram signals. Physical Review E, 76(2), 026214: 1–8.
   Web of Science ®Google Scholar
• Yang, P., Wang, G., Bian, J. and Zhou, X. (2010) The prediction of non-stationary climate series based on empirical mode decomposition. Advances in Atmospheric Sciences, 27(4), 845–854.
   Web of Science ®Google Scholar
• Yankov, D., DeCoste, D. and Keogh, E. (2006) Ensembles of nearest neighbor forecasts. Lecture Notes in Computer Science, 4212, 545–556.
   Google Scholar
• Yee, P. and Haykin, S. (1999) A dynamic regularized radial basis function network for nonlinear, nonstationary time series prediction. IEEE Transactions on Signal Processing, 47(9), 2503–2521.
   Web of Science ®Google Scholar
• Young, T., Palta, M., Dempsey, J., Skatrud, J., Weber, S. and Badr, S. (1993) The occurrence of sleep-disordered breathing among middle-aged adults. New England Journal of Medicine, 328(17), 1230–1235.
   PubMed Web of Science ®Google Scholar
• Yu, C., He, Y. and Quan, T. (2008) Frequency spectrum prediction method based on EMD and SVR, in Proceedings of the Eighth International Conference on Intelligent Systems Design and Applications, IEEE, Kaohsiung, Tawain, pp. 39–44.
   Google Scholar
• Zhang, G.P. (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175.
   Web of Science ®Google Scholar
• Zhang, G.P. (2012) Neural networks for time-series forecasting, in Handbook of Natural Computing, Rozenberg, G., Bäck, T. and Kok, J. (eds), Springer, Berlin, Germany, pp. 461–477.
   Google Scholar
• Zhang, G.P. and Berardi, V.L. (2001) Time series forecasting with neural network ensembles: an application for exchange rate prediction. Journal of the Operational Research Society, 52, 652–664.
   Web of Science ®Google Scholar
• Zhang, G.P. and Qi, M. (2005) Neural network forecasting for seasonal and trend time series. European Journal of Operational Research, 160(2), 501–514.
   Web of Science ®Google Scholar
• Zhang, L., Zhou, W. and Jiao, L. (2004) Wavelet support vector machine. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 34(1), 34–39.
   PubMed Web of Science ®Google Scholar
• Zhou, B., Shi, A., Cai, F. and Zhang, Y. (2004) Wavelet neural networks for nonlinear time series analysis, in Advances in Neural Networks, Yin, F.L., Wang, J. and Guo, C. (eds), Springer, Berlin/Heidelberg, pp. 430–435.
   Google Scholar
• Zhou, Y., Zhang, T. and Li, X. (2006) Predicting nonstationary time series with multi-scale Gaussian processes model. Lecture Notes in Computer Science, 4232, 513–520.
   Google Scholar
• Zhu, Z., Sun, Y. and Li, H. (2007) Hybrid of EMD and SVMs for short-term load forecasting, in Proceedings of the IEEE International Conference on Control and Automation, IEEE, Guangzhou, China, pp. 1044–1047.
   Google Scholar