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Interval type-2 fuzzy set based time series forecasting using a data-driven partitioning approach

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Abstract

Fuzzy set based time series (FTS) prediction techniques offer potential advantages in efficient and intuitive data partitioning and the effective handling of uncertainty in the data. However, such prediction models are commonly challenging to design, requiring careful and application-specific tuning of hyperparameters to provide competitive forecasting performance. We propose SODA-T2FTS, a univariate non-parametric interval type-2 fuzzy set based time series prediction model that combines the capacity of interval type-2 fuzzy sets to effectively model variations in uncertainty, with the data-driven partitioning capabilities of the Self-Organised Direction Aware Data partitioning algorithm (SODA). We detail and evaluate the proposed model in terms of the average number of rules (c.f. interpretability), error metrics, execution time, model complexity and noise sensitivity. We use three financial time series: TAIEX, NASDAQ, and S&P500, to compare the proposed approach to other prediction methods in the literature. Results show that SODA-T2FTS obtained the lowest errors in all experiments, including the ones where noise was added to the original time series, suggesting that the forecasting model can predict complex time series with high accuracy using a data-driven approach independent of user interference. In addition to outperforming in accuracy, the proposed method presents a similar number of fuzzy rules in comparison to other FTS methods, thus, delivering better performance for comparable linguistic interpretability.

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Data availibility statement

Availability of data and material: TAIEX, NASDAQ and S&P500 data sets are available in: https://github.com/arthurcaio92/SODA-T2FTS.

Code availability

Source codes and examples: https://github.com/arthurcaio92/SODA-T2FTS.

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Funding

We thank CAPES (Financing Code 001), CNPq (Grant nos. 433389/2018-4 and 312991/2020-7), FAPEMIG (Grant APQ-02922-18) and the Federal University of Juiz de Fora - UFJF for the financial support.

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Authors and Affiliations

  1. Graduate Program in Electrical Engineering, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil

    Arthur Caio Vargas Pinto

  2. Department of Industrial and Mechanical Engineering, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil

    Thiago Esterci Fernandes & Eduardo Pestana de Aguiar

  3. Federal Institute of Education, Science and Technology of the Northern Minas Gerais, Januária, MG, Brazil

    Petrônio C. L. Silva

  4. Department of Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte, MG, Brazil

    Frederico G. Guimarães

  5. Lab for Uncertainty in Data and Decision Making (LUCID), School of Computer Science, University of Nottingham, Nottingham, UK

    Christian Wagner

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  1. Arthur Caio Vargas Pinto
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  2. Thiago Esterci Fernandes
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  3. Petrônio C. L. Silva
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  4. Frederico G. Guimarães
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  5. Christian Wagner
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  6. Eduardo Pestana de Aguiar
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Contributions

ACVP and EPdA contributed to conceptualization. ACVP, TEF and PCLS contributed to software design. EPdA contributed to funding acquisition and overall supervision. All authors contributed to manuscript writing and read and approved the final manuscript.

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Correspondence to Arthur Caio Vargas Pinto.

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Pinto, A.C.V., Fernandes, T.E., Silva, P.C.L. et al. Interval type-2 fuzzy set based time series forecasting using a data-driven partitioning approach. Evolving Systems 13, 703–721 (2022). https://doi.org/10.1007/s12530-022-09452-2

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