Skip to main content
SpringerLink
Log in

A time-series modeling method based on the boosting gradient-descent theory

  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

The forecasting of time-series data plays an important role in various domains. It is of significance in theory and application to improve prediction accuracy of the time-series data. With the progress in the study of time-series, time-series forecasting model becomes more complicated, and consequently great concern has been drawn to the techniques in designing the forecasting model. A modeling method which is easy to use by engineers and may generate good results is in urgent need. In this paper, a gradient-boost AR ensemble learning algorithm (AREL) is put forward. The effectiveness of AREL is assessed by theoretical analyses, and it is demonstrated that this method can build a strong predictive model by assembling a set of AR models. In order to avoid fitting exactly any single training example, an insensitive loss function is introduced in the AREL algorithm, and accordingly the influence of random noise is reduced. To further enhance the capability of AREL algorithm for non-stationary time-series, improve the robustness of algorithm, discourage overfitting, and reduce sensitivity of algorithm to parameter settings, a weighted kNN prediction method based on AREL algorithm is presented. The results of numerical testing on real data demonstrate that the proposed modeling method and prediction method are effective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen S Y, Song S F, Li L X, et al. Survey on smart grid technology. Power Syst Technol, 2009, 33(8): 1–7

    Google Scholar 

  2. Guan X H, Zhai Q Z, Feng Y H, et al. Optimization based scheduling for a class of production systems with integral constraints. Sci China Ser E-Tech Sci, 2009, 52(12): 3533–3544

    Article  MATH  Google Scholar 

  3. Gao Y L, Gao F, Zhai Q Z, et al. Balance analysis of large-scale power consuming corporation. Proc CSEE, 2009, 28(19): 71–77

    Google Scholar 

  4. Gao Y L, Gao F, Pan J Y, et al. Self-scheduling for electrical energy balance and output power control of energy-intensive enterprises. Proc CSEE, 2010, 30(19): 76–83

    Google Scholar 

  5. Alexiadis M C, Dokopoulos P S, Sahsamanoglou H S. Short term forecasting of wind speed and related electrical power. Sol Energy, 1998, 63(1): 61–68

    Article  Google Scholar 

  6. Yang X Y, Xiao Y, Chen S Y. Wind Speed and generated power forecasting in wind farm. Proc CSEE, 2005, 25(11): 1–5

    Google Scholar 

  7. Zhang L, Xiong G L, Liu H S, et al. TVAR and SVM based fault diagnosis method for rotation machine. Proc CSEE, 2007, 27(9): 99–103

    MATH  Google Scholar 

  8. Xu F, Wang Z F, Wang B S. Research on AR model applied to forecast trend of vibration signals. J Tsinghua Univ (Science and Technology), 1999, 29(4): 57–59

    Google Scholar 

  9. Wang Y Q, Liu W Q. Probabilistic properties of functional coefficient auto-regression models with regularly varying tailed. J Shanxi Univ (Natural Science Edition), 2008, 31(3): 318–322

    Google Scholar 

  10. Brown B G, Katz R W, Murphy A H. Time-series models to simulate and forecast wind speed and wind power. J Appl Meteor, 1984, 23(8): 1184–1195

    Article  Google Scholar 

  11. Sun C S, Wang Y N, Li X R. A vector autoregression model of hourly wind speed and its applications in hourly wind speed forecasting. Proc CSEE, 2008, 28(14): 112–117

    Google Scholar 

  12. Franses P H, Paap R. Model selection in periodic autoregressions. Oxford Bull Econom Statist, 1994, 56(4): 421–439

    Article  Google Scholar 

  13. Zhao H W, Ren Z, Huang W Y. A short term load forecasting method based on PAR model. Proc CSEE, 1997, 17(5): 348–351

    Google Scholar 

  14. Lütkepohl H. New Introduction to Multiple Time-Series Analysis. Berlin: Springer, 2005

    MATH  Google Scholar 

  15. Allen P G, Morzuch B J. Twenty-five years of progress, problems, and conflicting evidence in econometric forecasting. What about the next 25 years? Int J Forecast, 2006, 22(3): 475–492

    Article  Google Scholar 

  16. Greene W H. Econometric Analysis. New Jersey: Prentice Hall, 2003

    Google Scholar 

  17. Ewing B T, Kruse J B, Schroeder J L, et al. Time-series analysis of wind speed using VAR and the generalized impulse response technique. J Wind Eng Ind Aerodyn, 2007, 95(3): 209–219

    Article  Google Scholar 

  18. Jin Y, An H Z. Nonlinear autoregressive models with heavy-tailed innovation. Sci China Ser A-Math, 2005, 48(3): 333–340

    Article  MATH  MathSciNet  Google Scholar 

  19. Wu Q F, Zhao Y M, Li Y, et al. Testing heteroscedasticity by wavelets in a nonparametric autoregressive model. Acta Math Appl Sin, 2009, 32(4): 595–607

    MATH  MathSciNet  Google Scholar 

  20. Fei W C, Bai L. Time-varying parameter auto-regressive models for autocovariance nonstationary time-series. Sci China Ser A-Math, 2009, 52(3): 577–584

    Article  MATH  MathSciNet  Google Scholar 

  21. Du X L, Wang F Q. Modal parameter identification under non-stationary ambient excitation based on continuous time AR Model. Sci China Ser E-Tech Sci, 2009, 52(11): 3180–3187

    Article  MATH  Google Scholar 

  22. Du X L, Wang F Q. Modal identification of system driven by lévy random excitation based on continuous time AR model. Sci China Ser E-Tech Sci, 2009, 52(12): 3649–3653

    Article  MATH  Google Scholar 

  23. Granger C W J, Joyeux R. An introduction to long-memory time-series models and fractional differencing. J Time-Ser Anal, 1980, 1(1): 15–29

    Article  MATH  MathSciNet  Google Scholar 

  24. Hannan E J, Deistler M. The Statistical Theory of Linear Systems. New York: Springer, 1988

    MATH  Google Scholar 

  25. Chen R, Tsay R S. Nonlinear additive ARX models. J Am Statist Assoc, 1993, 88(423): 955–967

    Article  MathSciNet  Google Scholar 

  26. Liu C H. Theories and Methods in Power Load Forecasting. Haerbin: Harbin Institute of Technology Press, 1987

    Google Scholar 

  27. Zhao H W, Ren Z, Huang W Y. Short term load forecasting considering weekly period based on PAR. Proc CSEE, 1997, 17(3): 211–216

    Google Scholar 

  28. Schapire R E, Singer Y. Improved Boosting algorithms using confidence-rated predictions. Mach Learn, 1999, 37(3): 297–336

    Article  MATH  Google Scholar 

  29. Drucker H, Cortes C, Jackl L D, et al. Boosting and other ensemble methods. Neural Comput, 1994, 6(6): 1289–1301

    Article  MATH  Google Scholar 

  30. Schapire R E, Freund Y, Bartlett P L, et al. Boosting the margin: A new explanation for the effectiveness of voting methods. Ann Stat, 1998, 26(5): 1651–1686

    Article  MATH  MathSciNet  Google Scholar 

  31. Wang R X. Stochastic Process. Xi’an: Xi’an Jiaotong University Press, 1995

    Google Scholar 

  32. Hu F. Hierarchical identification for paramters of autoregressive models. ACTA Autom Sin, 1994, 20(4): 464–469

    MATH  Google Scholar 

  33. Lin Z H, Feng R Z. A least square estimation of autoregressive processes. Acta Scientiarium Naturalium Universitatis Jilinensis, 2001, (2): 1–4

    MathSciNet  Google Scholar 

  34. Meng Z W. Maximum liklihood estimation for vector autoression models. J Shandong Inst Technol, 2001, 15(2): 25–28

    Google Scholar 

  35. Gu L. The Application of Time-Series Analysis Technique in Economy. Beijing: Urban Statistical Yearbook of China, 1994

    Google Scholar 

  36. Koutsoyiannis A. Theory of Econometrics, an Introductory Exposition of Econometric Method. London and Basingstoke: The Macmillan Press LTD, 1977

    Google Scholar 

  37. Valiant L G. A theory of the learnable. Commun ACM, 1984, 27(11): 1134–1142

    Article  MATH  Google Scholar 

  38. Kearns M, Valiant L G. Cryptographic limitations on learning Boolean formulae and finite automata. J ACM, 1994, 41(1): 67–95

    Article  MATH  MathSciNet  Google Scholar 

  39. Schapire R E. The strength of weak learnability. Mach Learn, 1990, 5(2): 197–227

    Google Scholar 

  40. Freund Y. Boosting a weak algorithm by majority. Inf Comput, 1995, 121(2): 256–285

    Article  MATH  MathSciNet  Google Scholar 

  41. Freund Y, Schapire R E. A decision theoretic generation of online learning and an application to boosting. J Comput Syst Sci, 1997, 55(1): 119–139

    Article  MATH  MathSciNet  Google Scholar 

  42. Friedman J H. Greedy function approximation: A gradient boosting machine. Ann Stat, 2001, 29(5): 1189–1232

    Article  MATH  Google Scholar 

  43. Gao Y L, Gao F. Edited AdaBoost by weighted kNN. Neurocomputing, 2010, 73(16–18): 3079–3088

    Article  Google Scholar 

  44. Vapnic V N. The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995

    Google Scholar 

  45. Lange M. On the uncertainty of wind power predictions—Analysis of the forecast accuracy and statistical distribution of errors. J Sol Energy Eng, 2005, 127(2): 177–184

    Article  Google Scholar 

  46. Möhrlen C. Uncertainty in Wind Energy Forecasting. Cork: National University of Ireland, 2004

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Xiamen University, Xiamen, 361005, China

    YunLong Gao & GuoLi Ji

  2. SKLMS Laboratory, Xi’an Jiaotong University, Xi’an, 710049, China

    YunLong Gao & Feng Gao

  3. College of Information Engineering, Jimei University, Xiamen, 361021, China

    JinYan Pan

Authors
  1. YunLong Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JinYan Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. GuoLi Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Feng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to YunLong Gao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Y., Pan, J., Ji, G. et al. A time-series modeling method based on the boosting gradient-descent theory. Sci. China Technol. Sci. 54, 1325–1337 (2011). https://doi.org/10.1007/s11431-011-4340-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-011-4340-1

Keywords

Search

Navigation