Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

A neural network-based ARMA model for fuzzy time series data

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, a nonlinear Autoregressive Moving Average (ARMA) time series model is developed for the case where observations are affected by fuzziness. The primary motivation is to address the limitations of ARMA models, specifically their inability to effectively model complex nonlinear relationships, handle long memory processes, and manage non-Gaussian data. To achieve this, a fuzzy ARMA model is estimated using a method based on artificial neural networks. The objective is to construct a robust fuzzy time series model by employing various popular activation functions, such as logistic, hyperbolic tangent, and rectified linear unit. The effectiveness of the proposed model is rigorously evaluated using three well-established performance criteria. Furthermore, to demonstrate the practical benefits and applicability of this new time series model, a comparative analysis using both simulated data and real-world examples is conducted.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

The data that support the findings of this study are available from the respective references as mentioned in the main text.

Notes

  1. See http://polarportal.dk/en/sea-ice-and-icebergs/sea-ice-thickness-and-volume.

  2. see https://www.seatemperature.org/africa/tanzania/zanzibar.htm.

References

  • Aladag CH (2013) Using multiplicative neuron model to establish fuzzy logic relationships. Exp Syst Appl 40:850–853

    Google Scholar 

  • Aladag CH, Yolcu U, Egrioglu E (2010) A high order fuzzy time series forecasting model based on adaptive expectation and artificial neural network. Math Comput Simul 81:875–882

    MathSciNet  Google Scholar 

  • Bas E, Egrioglu E, Kolemen E (2022) A novel intuitionistic fuzzy time series method based on bootstrapped combined pi-sigma artificial neural network. Eng Appl Art Int 114:105030

    Google Scholar 

  • Bhupendra K, Sunil NY (2023) A novel hybrid model combining \(\beta \)-SARMA and LSTM for time series forecasting. Appl Soft Comput 134:110019

    Google Scholar 

  • Bijari M, Hejazi SR, Khashei M (2012) Combining seasonal ARMA models with computational intelligence techniques for time series forecasting. Soft Comput 16:1091–1105

    Google Scholar 

  • Bose M, Mali K (2018) A novel data partitioning and rule selection technique for modeling high-order fuzzy time series. Appl Soft Comput 63:87–96

    Google Scholar 

  • Box GEP, Jenkins GM, Reinsel GC, Ljung GM (2016) Time series analysis: forecasting and control, 4th edn. Wiley, New York

    Google Scholar 

  • Brockwell PJ, Davis RA (2009) Time series: theory and methods. Springer, New York

    Google Scholar 

  • Bulut E (2014) Modeling seasonality using the fuzzy integrated logical forecasting (FILF) approach. Exp Syst Appl 41:1806–1812

    Google Scholar 

  • Burges AN, Refenes A-PN (1999) Modelling nonlinear moving average processes using neural networks with error feedback: an application to implied volatility forecasting. Signal Proc 74:89–99

    Google Scholar 

  • Carvalho T, Vellasco M, Amaral JF (2023) Automatic generation of fuzzy inference systems for multivariate time series forecasting. Fuzzy Sets Syst 470:108657

    MathSciNet  Google Scholar 

  • Chen MY (2014) A high-order fuzzy time series forecasting model for internet stock trading. Future Gener Comput Syst 37:461–467

    Google Scholar 

  • Chen MY, Chen BT (2014) Online fuzzy time series analysis based on entropy discretization and a fast Fourier transform. Appl Soft Comput 14:156–166

    Google Scholar 

  • Chen SM, Chen SW (2015) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45:405–417

    Google Scholar 

  • Chen SM, Tanuwijaya K (2011) Multivariate fuzzy forecasting based on fuzzy time series and automatic clustering techniques. Exp Syst Appl 38:10594–10605

    Google Scholar 

  • Cheng SH, Chen SM, Jian WS (2016) Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures. Inf Sci 327:272–287

    MathSciNet  Google Scholar 

  • Chukhrova N, Johannssen A (2019) Fuzzy regression analysis: systematic review and bibliography. Appl Soft Comput 84:105708

    Google Scholar 

  • Chukhrova N, Johannssen A (2021) Fuzzy hypothesis testing: systematic review and bibliography. Appl Soft Comput 106:107331

    Google Scholar 

  • Chukhrova N, Johannssen A (2021) Stochastic claims reserving methods with state space representations—a review. Risks 9(11):198

    Google Scholar 

  • Chukhrova N, Johannssen A (2023) Employing fuzzy hypothesis testing to improve modified \(p\) charts for monitoring the process fraction nonconforming. Inf Sci 633:141–157

    Google Scholar 

  • Connor JT, Martin RD (1994) Recurrent neural networks and robust time series prediction. IEEE Trans Neural Netw 5:240–254

    Google Scholar 

  • Coppi R, D’Urso P, Giordani P, Santoro A (2006) Least squares estimation of a linear regression model with \(LR\)-fuzzy response. Comput Stat Data Anal 51:267–286

    MathSciNet  Google Scholar 

  • Duru O, Bulut E (2014) A nonlinear clustering method for fuzzy time series: histogram damping partition under the optimized cluster paradox. Appl Soft Comput 24:742–748

    Google Scholar 

  • Efendi R, Ismail Z, Deris MM (2015) A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand. Appl Soft Comput 28:422–430

    Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U (2013) Fuzzy time series forecasting with a novel hybrid approach combining fuzzy c-means and neural networks. Exp Syst Appl 40:854–857

    Google Scholar 

  • Gaxiola F, Melin P, Valdez F, Castillo O (2014) Interval type-2 fuzzy weight adjustment for back propagation neural networks with application in time series prediction. Inf Sci 260:1–14

    Google Scholar 

  • Grzegorzewski P (2000) Testing statistical hypotheses with vague data. Fuzzy Sets Syst 11:501–510

    MathSciNet  Google Scholar 

  • Hesamian G, Akbari MG (2018) A semi-parametric model for time series based on fuzzy data. IEEE Trans Fuzzy Syst 26:2953–2966

    Google Scholar 

  • Hesamian G, Akbari MG (2018) Fuzzy absolute error distance measure based on a generalized difference operation. Int J Syst Sci 49:2454–2462

    Google Scholar 

  • Hesamian G, Akbari MG (2022) A fuzzy quantile method for AR time series model based on triangular fuzzy random variables. Comput Appl Math 41:1–12

    MathSciNet  Google Scholar 

  • Hesamian G, Torkian F, Yarmohammadi M (2022) A fuzzy nonparametric time series model based on fuzzy data. Iran J Fuzzy Syst 19:61–72

    MathSciNet  Google Scholar 

  • Hesamian G, Johannssen A, Chukhrova N (2023) A three-stage nonparametric kernel-based time series model based on fuzzy data. Mathematics 11(13):2800

    Google Scholar 

  • Hesamian G, Johannssen A, Chukhrova N (2024) Fuzzy nonlinear regression modeling with radial basis function networks. IEEE Trans Fuzzy Syst 32(4):1733–1742

    Google Scholar 

  • Hesamian G, Johannssen A, Chukhrova N (2024) An explainable fused lasso regression model for handling high-dimensional fuzzy data. J Comput Appl Math 441:115721

    MathSciNet  Google Scholar 

  • Hesamian G, Torkian F, Johannssen A, Chukhrova N (2024) A learning system-based soft multiple linear regression model. Int Syst Appl 22:200378

    Google Scholar 

  • Huang YL, Horng SJ, He M, Fan P, Kao TW, Khan MK, Lai JL, Kuo IH (2011) A hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization. Exp Syst Appl 38:8014–8023

    Google Scholar 

  • Katijani Y, Hipel WK, Mcleod AI (2005) Forecasting nonlinear time series with feedforward neural networks: a case study of Canadian lynx data. J Forecast 24:105–117

    MathSciNet  Google Scholar 

  • Kocak C (2017) ARMA(\(p, q\))-type high order fuzzy time series forecast method based on fuzzy logic relations. Appl Soft Comput 58:92–103

    Google Scholar 

  • Li ST, Kuo SC, Cheng YC, Chen CC (2010) Deterministic vector long-term forecasting for fuzzy time series. Fuzzy Sets Syst 161:1852–1870

    MathSciNet  Google Scholar 

  • Lin CF, Granger CWJ, Terasvirta T (1993) Power of the neural network linearity test. J Time Ser Anal 14:54–67

    Google Scholar 

  • Mills TC (2019) Applied time series analysis: a practical guide to modelling and forecasting. Academic Press, London

    Google Scholar 

  • Palma W (2016) Time series analysis. Wiley, New York

    Google Scholar 

  • Peng HW, Wu SF, Wei CC, Lee SJ (2015) Time series forecasting with a neuro-fuzzy modeling scheme. Appl Soft Comput 32:481–493

    Google Scholar 

  • Qi M, Zhang GP (2019) An investigation of model selection criteria for neural network time series forecasting. Eur J Oper Res 132:1–20

    Google Scholar 

  • Sadaei HJ, Enayatifar R, Abdullah AH, Gani A (2014) Short-term load forecasting using a hybrid model with a refined exponentially weighted fuzzy time series and an improved harmony search. Int J Electr Power Energy Syst 62:118–129

    Google Scholar 

  • Sadaei HJ, Enayatifar R, Lee MH, Mahmud M (2016a) A hybrid model based on differential fuzzy logic relationships and imperialist competitive algorithm for stock market forecasting. Appl Soft Comput 40:132–149

    Google Scholar 

  • Sadaei HJ, Enayatifar R, Guimaraes FG, Mahmud M, Alzamil ZA (2016b) Combining ARFIMA models and fuzzy time series for the forecast of long memory time series. Neurocomputing 175:782–796

    Google Scholar 

  • Shumway RH, Stoffer DS (2017) Time series analysis and its applications. Springer, London

    Google Scholar 

  • Singh P (2017) A brief review of modeling approaches based on fuzzy time series. Int J Mach Learn Cybern 8:397–420

    Google Scholar 

  • Singh P (2018) Rainfall and financial forecasting using fuzzy time series and neural networks based model. Int J Mach Learn Cybern 9:491–506

    Google Scholar 

  • Singh P (2021) FQTSFM: a fuzzy-quantum time series forecasting model. Inf Sci 566:57–79

    MathSciNet  Google Scholar 

  • Singh P, Borah B (2013) High-order fuzzy-neuro expert system for daily temperature forecasting. Knowl Based Syst 46:12–21

    Google Scholar 

  • Singh P, Borah B (2014) Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization. Int J Approx Reason 55:812–833

    MathSciNet  Google Scholar 

  • Soares E, Costa P Jr, Costa B, Leite D (2018) Ensemble of evolving data clouds and fuzzy models for weather time series prediction. Appl Soft Comput 64:445–453

    Google Scholar 

  • Song Q, Chissom BS (1993) Fuzzy time series and its models. Fuzzy Sets Syst 54:269–277

    MathSciNet  Google Scholar 

  • Stefenon SF, Ribeiro MH, Nied A, Yow K-C, Mariani VC, Coelho L, Seman LO (2022) Time series forecasting using ensemble learning methods for emergency prevention in hydroelectric power plants with dam. Electr Power Syst Res 202:107584

    Google Scholar 

  • Sugeno M (1985) An introductory survey of fuzzy control. Inf Sci 36:59–83

    MathSciNet  Google Scholar 

  • Talarposhtia FM, Hossein JS, Rasul E, Guimaraesc FG, Mahmud M, Eslami T (2016) Stock market forecasting by using a hybrid model of exponential fuzzy time series. Int J Approx Reason 70:79–98

    MathSciNet  Google Scholar 

  • Tealab A, Hefny H, Badr A (2017) Forecasting of nonlinear time series using ANN. Future Comput Inf J 2:39–47

    Google Scholar 

  • Torbat S, Khashei M, Bijari M (2018) A hybrid probabilistic fuzzy ARMA model for consumption forecasting in commodity markets. Econ Anal Policy 58:22–31

    Google Scholar 

  • Uslu VR, Bas E, Yolcu U, Egrioglu E (2014) A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations. Swarm Evol Comput 15:19–26

    Google Scholar 

  • Wang W, Liu X (2015) Fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification. Inf Sci 294:78–94

    MathSciNet  Google Scholar 

  • Wei LY (2016) A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting. Appl Soft Comput 42:368–376

    Google Scholar 

  • Woodward WA, Gray HL, Elliott AC (2012) Applied time series analysis. CRC Press, Boca Raton

    Google Scholar 

  • Woodward WA, Sadler BP, Robertson S (2022) Time series for data science: analysis and forecasting. Chapman & Hall, Cambridge

    Google Scholar 

  • Ye F, Zhang L, Zhang D, Fujita H, Gong Z (2016) A novel forecasting method based on multi-order fuzzy time series and technical analysis. Inf Sci 367–368:41–57

    Google Scholar 

  • Yeganeh A, Pourpanah F, Shadman A (2021) An ANN-based ensemble model for change point estimation in control charts. Appl Soft Comput 110:107604

    Google Scholar 

  • Yolcu OC, Alpaslan F (2018) Prediction of TAIEX based on hybrid fuzzy time series model with single optimization process. Appl Soft Comput 66:18–33

    Google Scholar 

  • Yolcu OC, Lam HK (2017) A combined robust fuzzy time series method for prediction of time series. Neurocomputing 247:87–101

    Google Scholar 

  • Yolcu OC, Yolcu U, Egrioglu E, Aladag CH (2016) High order fuzzy time series forecasting method based on an intersection operation. Appl Math Model 40:8750–8765

    MathSciNet  Google Scholar 

  • Yu HK (2005) Weighted fuzzy time-series models for TAIEX forecasting. Phys A 349:609–624

    Google Scholar 

  • Zarei R, Akbari MG, Chachi J (2020) Modeling autoregressive fuzzy time series data based on semi-parametric methods. Soft Comput 24:7295–7304

    Google Scholar 

  • Zhang G, Patuwo BE, Hu YM (1998) Forecasting with artificial neural networks: the state of the art. Int J Forecast 14:35–62

    Google Scholar 

Download references

Acknowledgements

The authors thank three anonymous reviewers for their valuable feedback and suggestions, which were important and helpful to improve the paper.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Department of Statistics, Payame Noor University, Tehran, 19395-3697, Iran

    Gholamreza Hesamian

  2. Faculty of Business Studies, Harz University of Applied Sciences, 38855, Wernigerode, Germany

    Arne Johannssen

  3. Faculty of Engineering, The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, 5230, Odense, Denmark

    Nataliya Chukhrova

Authors
  1. Gholamreza Hesamian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arne Johannssen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nataliya Chukhrova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arne Johannssen.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ethical standards

(i) This manuscript is the authors’ original work, which has not been published nor submitted simultaneously elsewhere; (ii) all authors have checked the manuscript and agreed to the submission, and (iii) there is no Conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hesamian, G., Johannssen, A. & Chukhrova, N. A neural network-based ARMA model for fuzzy time series data. Comp. Appl. Math. 43, 445 (2024). https://doi.org/10.1007/s40314-024-02950-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-024-02950-w

Keywords

Mathematics Subject Classification

Search

Navigation