Advertisement

Advances in Data Analysis and Classification

, Volume 11, Issue 4, pp 759–783 | Cite as

A novel method for forecasting time series based on fuzzy logic and visibility graph

  • Rong Zhang
  • Baabak Ashuri
  • Yong Deng
Regular Article

Abstract

Time series attracts much attention for its remarkable forecasting potential. This paper discusses how fuzzy logic improves accuracy when forecasting time series using visibility graph and presents a novel method to make more accurate predictions. In the proposed method, historical data is firstly converted into a visibility graph. Then, the strategy of link prediction is utilized to preliminarily forecast the future data. Eventually, the future data is revised based on fuzzy logic. To demonstrate the performance, the proposed method is applied to forecast Construction Cost Index, Taiwan Stock Index and student enrollments. The results show that fuzzy logic is able to improve the accuracy by designing appropriate fuzzy rules. In addition, through comparison, it is proved that our method has high flexibility and predictability. It is expected that our work will not only make contributions to the theoretical study of time series forecasting, but also be beneficial to practical areas such as economy and engineering by providing more accurate predictions.

Keywords

Forecasting Time series Fuzzy logic Visibility graph Link prediction 

Mathematics Subject Classification

40B99 

Notes

Acknowledgements

The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61573290, 61503237).

References

  1. Ashuri B, Lu J (2010) Time series analysis of ENR construction cost index. J Constr Eng Manag 136(11):1227–1237CrossRefGoogle Scholar
  2. Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley, Hoboken, New JerseyMATHGoogle Scholar
  3. Brown RG (1957) Exponential smoothing for predicting demand. In: Operations research. In: Inst operations research management sciences, vol 5145–145. LinthicumGoogle Scholar
  4. Chen SM (1996) Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst 81(3):311–319CrossRefGoogle Scholar
  5. Cheng C-H, Chen T-L, Teoh HJ, Chiang C-H (2008) Fuzzy time-series based on adaptive expectation model for TAIEX forecasting. Exp Syst Appl 34(2):1126–1132CrossRefGoogle Scholar
  6. Chliamovitch G, Dupuis A, Golub A, Chopard B (2015) Improving predictability of time series using maximum entropy methods. Eur Lett 110(1):10003CrossRefGoogle Scholar
  7. Deng Y (2015) Generalized evidence theory. Appl Intell 43(3):530–543CrossRefGoogle Scholar
  8. Deng Y, Chen Y, Zhang Y, Mahadevan S (2012) Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment. Appl Soft Comput 12(3):1231–1237CrossRefGoogle Scholar
  9. Derde LPG, Cooper BS, Goossens H, Malhotra-Kumar S, Willems RJL, Gniadkowski M, Hryniewicz W et al (2014) Interventions to reduce colonisation and transmission of antimicrobial-resistant bacteria in intensive care units: an interrupted time series study and cluster randomised trial. Lancet Infect Dis 14(1):31–39CrossRefGoogle Scholar
  10. Donner R, Donges J (2012) Visibility graph analysis of geophysical time series: potentials and possible pitfalls. Acta Geophys 60(3):589–623CrossRefGoogle Scholar
  11. Donner RV, Small M, Donges JF, Marwan N, Zou Y, Xiang R, Kurths J (2011) Recurrence-based time series analysis by means of complex network methods. Int J Bifurc Chaos 21(04):1019–1046MathSciNetCrossRefMATHGoogle Scholar
  12. ENR (2011) Engineering News-Record. http://enr.construction.com/
  13. Gao Z-K, Yang Y-X, Fang P-C, Zou Y, Xia C-Y, Du M (2015) Multiscale complex network for analyzing experimental multivariate time series. Eur Lett 109(3):30005CrossRefGoogle Scholar
  14. Hayes JW, Shearer KA, Goodwin EO, Hay J, Allen C, Olsen DA, Jowett IG (2015) Test of a benthic macroinvertebrate habitat -flow time series model incorporating disturbance and recovery processes. River Res Appl 31(7):785–797CrossRefGoogle Scholar
  15. Holt CC (2004) Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20(1):5–10CrossRefGoogle Scholar
  16. Hu Y, Du F, Zhang HL (2016) Investigation of unsteady aerodynamics effects in cycloidal rotor using RANS solver. Aeronautical J 120(1228):956–970CrossRefGoogle Scholar
  17. Hwang JR, Chen SM, Lee CH (1998) Handling forecasting problems using fuzzy time series. Fuzzy Sets Syst 100(1–3):217–228CrossRefGoogle Scholar
  18. Hyndman R, Khandakar Y (2018) Automatic time series forecasting: the forecast package for RGoogle Scholar
  19. Jiang W, Wei B, Zhan J, Xie C, Zhou D (2016) A visibility graph power averaging aggregation operator: a methodology based on network analysis. Comput Ind Eng 101:260–268CrossRefGoogle Scholar
  20. Jiang W, Wei B, Tang Y, Zhou D (2017) Ordered visibility graph average aggregation operator: an application in produced water management. Chaos Interdiscip J Nonlinear Sci 27(2):023117CrossRefGoogle Scholar
  21. Kaya B, Poyraz M (2015) Age-series based link prediction in evolving disease networks. Comput Biol Med 63:1–10CrossRefGoogle Scholar
  22. Kayacan E, Ulutas B, Kaynak O (2010) Grey system theory-based models in time series prediction. Exp Syst Appl 37(2):1784–1789CrossRefGoogle Scholar
  23. Lacasa L, Luque B, Ballesteros F, Luque J, Nuño JC (2008) From time series to complex networks: the visibility graph. Proc Natl Acad Sci 105(13):4972–4975MathSciNetCrossRefMATHGoogle Scholar
  24. Lacasa L, Luque B, Luque J, Nuno JC (2009) The visibility graph: a new method for estimating the Hurst exponent of fractional Brownian motion. Europhys Lett 86(3):30001CrossRefGoogle Scholar
  25. Liu W, Lü L (2010) Link prediction based on local random walk. Europhys Lett 89(5):58007CrossRefGoogle Scholar
  26. Liu J, Lian F, Mallick M (2016) Distributed compressed sensing based joint detection and tracking for multistatic radar system. Inf Sci 369:100–118MathSciNetCrossRefGoogle Scholar
  27. Lü L, Zhou T (2011) Link prediction in complex networks: a survey. Phys A Stat Mech Appl 390(6):1150–1170CrossRefGoogle Scholar
  28. Lu W, Chen X, Pedrycz W, Liu X, Yang J (2015) Using interval information granules to improve forecasting in fuzzy time series. Int J Approx Reason 57:1–18CrossRefMATHGoogle Scholar
  29. Luque B, Lacasa L, Ballesteros F, Luque J (2009) Horizontal visibility graphs: exact results for random time series. Phys Rev E 80(4):046103CrossRefGoogle Scholar
  30. McDowall D (2014) Time series properties of crime rate changes: comments related to David Greenbergs paper. Justice Q 31(1):189–192CrossRefGoogle Scholar
  31. Melin P, Castillo O (2014) A review on type-2 fuzzy logic applications in clustering, classification and pattern recognition. Appl Soft Comput 21:568–577CrossRefGoogle Scholar
  32. Michas G, Sammonds P, Vallianatos, (2014) Dynamic multifractality in earthquake time series: insights from the Corinth Rift. Greece. Pure Appl Geophys 172(7):1909–1921Google Scholar
  33. Mo H, Yong D (2016) A new aggregating operator in linguistic decision making based on D numbers. Int J Uncertain Fuzziness Knowl Based Syst 24(6):831–846MathSciNetCrossRefGoogle Scholar
  34. Richard E, Gaiffas S, Vayatis N (2012) Link prediction in graphs with autoregressive features. In: Pereira F, Burges CJC, Bottou L, Weinberger KQ (eds) Advances in neural information processing systems, vol 25. Curran Associates, Inc., New York, pp 2834–3842Google Scholar
  35. Sabahi K, Ghaemi S, Pezeshki S (2014) Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches. Appl Soft Comput 21:1–11CrossRefGoogle Scholar
  36. Schuster A (1906) On the periodicities of sunspots. Philos Trans R Soc Lond Ser A Contain Pap Math Phys Character 206:69–100CrossRefGoogle Scholar
  37. Song Q, Chissom BS (1993) Forecasting enrollments with fuzzy time series part I. Fuzzy Sets Syst 54(1):1–9CrossRefGoogle Scholar
  38. Song Q, Chissom BS (1994) Forecasting enrollments with fuzzy time series part II. Fuzzy Sets Syst 62(1):1–8CrossRefGoogle Scholar
  39. Telesca L, Lovallo M (2012) Analysis of seismic sequences by using the method of visibility graph. Eur Lett 97(5):50002CrossRefGoogle Scholar
  40. Tiwari AK, Suresh KG, Arouri M, Teulon F (2014) Causality between consumer price and producer price: evidence from Mexico. Econ Modell 36:432–440CrossRefGoogle Scholar
  41. Tseng FM, Tzeng GW (2002) A fuzzy seasonal ARIMA model for forecasting. Fuzzy Sets Syst 126(3):367–376MathSciNetCrossRefMATHGoogle Scholar
  42. Wang D, Podobnik B, Horvatić D, Stanley HE (2011) Quantifying and modeling long-range cross correlations in multiple time series with applications to world stock indices. Phys Rev E 83(4):046121CrossRefGoogle Scholar
  43. Wang S, Du Y, Deng Y (2017) A new measure of identifying influential nodes: efficiency centrality. Commun Nonlinear Sci Numer Simul 47:151–163MathSciNetCrossRefGoogle Scholar
  44. Wong JM, Chan AP, Chiang YH (2005) Time series forecasts of the construction labour market in Hong Kong: the Box–Jenkins approach. Constr Manag Econ 23(9):979–991CrossRefGoogle Scholar
  45. Yang P, Wang G, Zhang F, Zhou X (2015) Causality of global warming seen from observations: a scale analysis of driving force of the surface air temperature time series in the Northern Hemisphere. Clim Dyn 46(9–10):3197–3204Google Scholar
  46. Yule GU (1927) On a method of investigating periodicities in disturbed series, with special reference to Wolfer’s sunspot numbers. Philos Trans R Soc Lond Ser A Contain Pap Math Phys Charact 226:267–298CrossRefMATHGoogle Scholar
  47. Zadeh LA (1965) Fuzzy Sets Inf. Control 8(3):338–353MathSciNetCrossRefMATHGoogle Scholar
  48. Zhang H, Wei D, Hu Y, Lan X, Deng Y (2016) Modeling the self-similarity in complex networks based on Coulombs law. Commun Nonlinear Sci Numer Simul 35:97–104MathSciNetCrossRefGoogle Scholar
  49. Zhang R, Ran X, Wang C, Deng Y (2016) Fuzzy evaluation of network vulnerability. Qual Reliab Eng Int 32(5):1715–1730CrossRefGoogle Scholar
  50. Zhang X, Adamatzky A, Yang X-S, Yang H, Mahadevan S, Deng Y (2016) A physarum-inspired approach to supply chain network design. Sci China Inf Sci 59(5):052203MathSciNetCrossRefGoogle Scholar
  51. Zhou T-T, Jin ND, Gao ZK, Luo YB (2012) Limited penetrable visibility graph for establishing complex network from time series. Acta Phys Sin 61(3):030506Google Scholar
  52. Zhou X, Deng X, Deng Y, Mahadevan S (2017) Dependence assessment in human reliability analysis based on D numbers and AHP. Nucl Eng Des 313:243–252CrossRefGoogle Scholar
  53. Zhou X, Shi Y, Deng X, Deng Y (2017) D-DEMATEL: a new method to identify critical success factors in emergency management. Saf Sci 91:93–104CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of Fundamental and Frontier ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.School of Computer and Information ScienceSouthwest UniversityChongqingChina
  3. 3.Brook Byers Institute for Sustainable Systems (BBISS), Economics of Sustainable Built Environment (ESBE) Lab, School of Building Construction and School of Civil & Environmental EngineeringGeorgia Institute of TechnologyAtlantaGeorgia

Personalised recommendations