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A 2-Stage Strategy for Non-Stationary Signal Prediction and Recovery Using Iterative Filtering and Neural Network

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Abstract

Predicting the future information and recovering the missing data for time series are two vital tasks faced in various application fields. They are often subjected to big challenges, especially when the signal is nonlinear and non-stationary which is common in practice. In this paper, we propose a hybrid 2-stage approach, named IF2FNN, to predict (including short-term and long-term predictions) and recover the general types of time series. In the first stage, we decompose the original non-stationary series into several “quasi stationary” intrinsic mode functions (IMFs) by the iterative filtering (IF) method. In the second stage, all of the IMFs are fed as the inputs to the factorization machine based neural network model to perform the prediction and recovery. We test the strategy on five datasets including an artificial constructed signal (ACS), and four real-world signals: the length of day (LOD), the northern hemisphere land-ocean temperature index (NHLTI), the troposphere monthly mean temperature (TMMT), and the national association of securities dealers automated quotations index (NASDAQ). The results are compared with those obtained from the other prevailing methods. Our experiments indicate that under the same conditions, the proposed method outperforms the others for prediction and recovery according to various metrics such as mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).

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References

  1. Safari N, Chung C Y, Price G C D. Novel multi-step short-term wind power prediction framework based on chaotic time series analysis and singular spectrum analysis. IEEE Transactions on Power Systems, 2018, 33(1): 590-601.

    Article  Google Scholar 

  2. Oh K J, Kim K J. Analyzing stock market tick data using piecewise nonlinear model. Expert Systems with Applications, 2002, 22(3): 249-255.

    Article  Google Scholar 

  3. Wang Y F. Mining stock price using fuzzy rough set system. Expert Systems with Applications, 2003, 24(1): 13-23.

    Article  Google Scholar 

  4. Faruk D Ö. A hybrid neural network and ARIMA model for water quality time series prediction. Engineering Applications of Artificial Intelligence, 2010, 23(4): 586-594.

    Article  MathSciNet  Google Scholar 

  5. Kasabov N K, Song Q. DENFIS: Dynamic evolving neural-fuzzy inference system and its application for time-series prediction. IEEE Transactions on Fuzzy Systems, 2002, 10(2): 144-154.

    Article  Google Scholar 

  6. Franses P H, Ghijsels H. Additive outliers, GRACH and forecasting volatility. International Journal of Forecasting, 1999, 15(1): 1-9.

    Article  Google Scholar 

  7. Sarantis N. Nonlinearities, cyclical behaviour and predictability in stock markets: International evidence. International Journal of Forecasting, 2001, 17(3): 459-482.

    Article  Google Scholar 

  8. Kalekar P S. Time series forecasting using Holt-Winters exponential smoothing. https://c.mql5.com/forextsd/forum/69/exponentialsmoothing.pdf, Jan. 2019.

  9. Hansen J V, Nelson R D. Data mining of time series using stacked generalizers. Neurocomputing, 2002, 43(1/2/3/4): 173-184.

    Article  MATH  Google Scholar 

  10. Zhang G P. Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 2003, 50: 159-175.

    Article  MATH  Google Scholar 

  11. Enke D, Thawornwong S. The use of data mining and neural networks for forecasting stock market returns. Expert Systems with Applications, 2005, 29(4): 927-940.

    Article  Google Scholar 

  12. Ture M, Kurt I. Comparison of four different time series methods to forecast hepatitis a virus infection. Expert Systems with Applications, 2006, 31(1): 41-46.

    Article  Google Scholar 

  13. Kim K J. Financial time series forecasting using support vector machines. Neurocomputing, 2003, 55(1/2): 307-319.

    Article  Google Scholar 

  14. Qian X Y. Financial series prediction: Comparison between precision of time series models and machine learning methods. arXiv:1706.00948, 2017. https://arxiv.org/abs/1706.00948, June 2018.

  15. Chen T, Guestrin C. Xgboost: A scalable tree boosting system. In Proc. the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, August 2016, pp.785-794.

  16. Ye J, Chow J H, Chen J, Zheng Z. Stochastic gradient boosted distributed decision trees. In Proc. the 18th ACM-Conference on Information and Knowledge Management, November 2009, pp.2061-2064.

  17. Kim K J, Han I. Genetic algorithms approach to feature discretization in artificial neural networks for the prediction of stock price index. Expert Systems with Applications, 2000, 19(2): 125-132.

    Article  MathSciNet  Google Scholar 

  18. Wang Y F. Predicting stock price using fuzzy grey prediction system. Expert Systems with Applications, 2002, 22(1): 33-38.

    Article  Google Scholar 

  19. Shen L, Han T L. Applying rough sets to market timing decisions. Decision Support Systems, 2004, 37(4): 583-597.

    Article  Google Scholar 

  20. Vellido A, Lisboa P J G, Meehan K. Segmentation of the on-line shopping market using neural networks. Expert Systems with Applications, 1999, 17(4): 303-314.

    Article  Google Scholar 

  21. Chen A S, Leung M T, Daouk H. Application of neural networks to an emerging financial market: Forecasting and trading the Taiwan stock index. Computers and Operations Research, 2003, 30(6): 901-923.

    Article  MATH  Google Scholar 

  22. Rather A M, Agarwal A, Sastry V N. Recurrent neural network and a hybrid model for prediction of stock returns. Expert Systems with Applications, 2015, 42(6): 3234-3241.

    Article  Google Scholar 

  23. Yang Z, Yang L, Qi D. Detection of spindles in sleep EEGs using a novel algorithm based on the Hilbert-Huang transform. In Wavelet Analysis and Applications, Qian T, Vai M I, Xu Y S (eds.), Birkhäuser, 2007, pp.543-559.

  24. Wang J Z, Wang J J, Zhang Z G, Guo S P. Forecasting stock indices with back propagation neural network. Expert Systems with Applications, 2011, 38(11): 14346-14355.

    Google Scholar 

  25. Liu H, Chen C, Tian H Q, Li Y F. A hybrid model for wind speed prediction using empirical mode decomposition and artificial neural networks. Renewable Energy, 2012, 48: 545-556.

    Article  Google Scholar 

  26. Kao L J, Chiu C C, Lu C J, Chang C H. A hybrid approach by integrating wavelet-based feature extraction with MARS and SVR for stock index forecasting. Decision Support Systems, 2013, 54(3): 1228-1244.

    Article  Google Scholar 

  27. Zhang L, Wu X, Ji W, Abourizk S M. Intelligent approach to estimation of tunnel-induced ground settlement using wavelet packet and support vector machines. Journal of Computing in Civil Engineering, 2016, 31(2): Article No. 04016053.

  28. Wei L Y. A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting. Applied Soft Computing, 2016, 42: 368-376.

    Article  Google Scholar 

  29. Zhou F, Zhou H, Yang Z, Yang L. EMD2FNN: A strategy combining empirical mode decomposition and factorization machine based neural network for stock market trend prediction. Expert Systems with Applications, 2019, 115: 136- 151.

    Article  MathSciNet  Google Scholar 

  30. Thompson W R, Weil C S. On the construction of tables for moving-average interpolation. Biometrics, 1952, 8(1): 51-54.

    Article  Google Scholar 

  31. Watson D F. A refinement of inverse distance weighted interpolation. GeoProcessing, 1985, 2(4): 315-327.

    MathSciNet  Google Scholar 

  32. Liu G R, Zhang G Y. A novel scheme of strain-constructed point interpolation method for static and dynamic mechanics problems. International Journal of Applied Mechanics, 2009, 1(1): 233-258.

    Article  Google Scholar 

  33. Schoenberg I J. Contributions to the problem of approximation of equidistant data by analytic functions (part A). Quarterly of Applied Mathematics, 1946, 4: 3-57.

    Google Scholar 

  34. Schoenberg I J. Cardinal Spline Interpolation. Society for Industrial and Applied Mathematics, 1973.

  35. Lin L, Wang Y, Zhou H. Iterative filtering as an alternative algorithm for empirical mode decomposition. Advances in Adaptive Data Analysis, 2009, 1(4): 543-560.

    Article  MathSciNet  Google Scholar 

  36. Cicone A, Liu J, Zhou H. Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis. Applied and Computational Harmonic Analysis, 2016, 41(2): 384-411.

    Article  MathSciNet  MATH  Google Scholar 

  37. Cicone A, Zhou H. Multidimensional iterative filtering method for the decomposition of high-dimensional nonstationary signals. Numerical Mathematics: Theory, Methods and Applications, 2017, 10(2): 278-298.

    MathSciNet  MATH  Google Scholar 

  38. Huang N E, Shen Z, Long S R, Wu M C, Shih H H, Zheng Q, Yen N C, Chi C T, Liu H H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 1998, 454(1971): 903-995.

    Article  MathSciNet  MATH  Google Scholar 

  39. Holt C C. Forecasting seasonals and trends by exponentially weighted moving averages. International Journal of Forecasting, 2004, 20(1): 5-10.

    Article  Google Scholar 

  40. Winters P R. Forecasting sales by exponentially weighted moving averages. Management Science, 1960, 6(3): 231-362.

    Article  MathSciNet  MATH  Google Scholar 

  41. Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. IEEE Signal Processing Letters, 2004, 11(2): 112-114.

    Article  Google Scholar 

  42. Zhou F, Yang L, Zhou H, Yang L. Optimal averages for nonlinear signal decompositions — Another alternative for empirical mode decomposition. Signal Processing, 2016, 121: 17-29.

    Article  Google Scholar 

  43. Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: The Hilbert spectrum. Annual Review of Fluid Mechanics, 1999, 31(1): 417-457.

    Article  MathSciNet  Google Scholar 

  44. Huang W, Shen Z, Huang N E, Yuan C F. Engineering analysis of biological variables: An example of blood pressure over 1 day. Proceedings of the National Academy of Sciences of the United States of America, 1998, 95(9): 4816-4821.

    Article  Google Scholar 

  45. Yang Z, Qi D, Yang L. Signal period analysis based on Hilbert-Huang transform and its application to texture analysis. In Proc. the 3rd International Conference on Image and Graphics, April 2005, pp.430-433.

  46. Smith J S. The local mean decomposition and its application to EEG perception data. Journal of the Royal Society Interface, 2005, 2(5): 443-454.

    Article  Google Scholar 

  47. Delechelle E, Lemoine J, Niang O. Empirical mode decomposition: An analytical approach for sifting process. IEEE Signal Processing Letters, 2005, 12(11): 764-767.

    Article  MATH  Google Scholar 

  48. Diop E H S, Alexandre R, Boudraa A O. Analysis of intrinsic mode functions: A PDE approach. IEEE Signal Processing Letters, 2010, 17(4): 398-401.

    Article  Google Scholar 

  49. Hong H, Wang X, Tao Z. Local integral mean-based sifting for empirical mode decomposition. IEEE Signal Processing Letters, 2009, 16(10): 841-844.

    Article  Google Scholar 

  50. Peng S, Hwang WL. Null space pursuit: An operator-based approach to adaptive signal separation. IEEE Transactions on Signal Processing, 2010, 58(5): 2475-2483.

    Article  MathSciNet  MATH  Google Scholar 

  51. Daubechies I, Lu J, Wu H T. Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Applied and Computational Harmonic Analysis, 2011, 30(2): 243-261.

    Article  MathSciNet  MATH  Google Scholar 

  52. Ren S, He K, Girshick R, Sun J. Faster R-CNN: Towards real-time object detection with region proposal networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39(6): 1137-1149.

    Article  Google Scholar 

  53. Shelhamer E, Long J, Darrell T. Fully convolutional networks for semantic segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39(4): 640-651.

    Article  Google Scholar 

  54. Hinton G, Deng L, Yu D, Dahl G E, Mohamed A, Jaitly N, Senior A, Vanhoucke V, Nguyen P, Sainath T N. Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Processing Magazine, 2012, 29(6): 82-97.

    Article  Google Scholar 

  55. Chen C H. Handbook of Pattern Recognition and Computer Vision (5th edition). World Scientific Publishing, 2016.

  56. Goldberg Y. Neural Network Methods for Natural Language Processing. Morgan and Claypool Publishers, 2017.

  57. Rendle S. Factorization machines. In Proc. the 10th IEEE International Conference on Data Mining, December 2010, pp.995-1000.

  58. Han J, Moraga C. The influence of the sigmoid function parameters on the speed of backpropagation learning. In Proc. International Workshop on Artificial Neural Networks: From Natural to Artificial Neural Computation, June 1995, pp.195-201.

  59. Lecun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444.

    Article  Google Scholar 

  60. He K, Zhang X, Ren S, Sun J. Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification. In Proc. the 2015 IEEE International Conference on Computer Vision, December 2015, pp.1026-1034.

  61. Clevert D A, Unterthiner T, Hochreiter S. Fast and accurate deep network learning by exponential linear units (ELUs). arXiv:1511.07289, 2015. https://arxiv.org/pdf/1511.07289.pdf, November 2018.

  62. Makridakis S. Accuracy measures: Theoretical and practical concerns. International Journal of Forecasting, 1993, 9(4): 527-529.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Information Science, Guangdong University of Finance and Economics, Guangzhou, 510320, China

    Feng Zhou & Zhi-Hua Yang

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, U.S.A.

    Hao-Min Zhou

  3. Guangdong Province Key Laboratory of Computational Science, Guangzhou, 510275, China

    Li-Hua Yang

  4. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Li-Hua Yang

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  1. Feng Zhou
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Correspondence to Feng Zhou.

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Zhou, F., Zhou, HM., Yang, ZH. et al. A 2-Stage Strategy for Non-Stationary Signal Prediction and Recovery Using Iterative Filtering and Neural Network. J. Comput. Sci. Technol. 34, 318–338 (2019). https://doi.org/10.1007/s11390-019-1913-0

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