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Fuzzy Rule-Based Modeling for Interval-Valued Data: An Application to High and Low Stock Prices Forecasting

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Predictive Maintenance in Dynamic Systems

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Abstract

Financial interval time series (ITS) describe the evolution of the highest and lowest prices of an asset throughout time. The difference of these prices, the range, is a measure of volatility. Therefore, their accurate forecasts play an important role in many applications such as risk management, derivatives pricing, and portfolio selection, as well as supplement the information by the time series of the closing price values. This chapter proposes an interval fuzzy rule-based model (iFRB) for ITS forecasting. iFRB is a fuzzy rule-based model with affine consequents which provide a nonlinear approach that naturally processes interval-valued data. It is suggested as empirical application the prediction of the main index of the Brazilian stock market, the IBOVESPA. Interval forecasts are compared against traditional univariate and multivariate time series benchmark models and with an interval multilayer perceptron neural network in terms of traditional accuracy metrics, statistical tests, and quality measures for interval-valued data. The results indicate that iFRB method appears as a promising alternative for interval-valued financial time series forecasting.

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Notes

  1. 1.

    The literature has introduced several interval time series forecasting methods. Examples include [18, 28, 44, 47].

  2. 2.

    The literature that considers the high–low range prices as a proxy for volatility dates back to the 1980s with the work of [34].

  3. 3.

    Arroyo et al. [3] provide a survey on ITS forecasting methodologies in finance and economics.

  4. 4.

    For instance, the work of Leite et al. [26] proposes an interval-based evolving modeling (IBeM) approach that recursively adapts both parameters and structure of rule-based models. In IBeM the clusters are represented by intervals, i.e., granular local models, such that the consequents of the rules are also represented by intervals. Therefore, the model is able to produce interval outputs but is not designed to process interval-valued data.

  5. 5.

    One must notice that the subtraction of intervals can produce intervals with negative extremes. However, in all operations related to the current approach, the subtraction operation between intervals is not needed, which is also one of the advantages by using a distance metric such as the Hausdorff distance.

  6. 6.

    Brandt and Diebold [2] show that global optimization does not guarantee locally adequate behavior of the sub-models that form the TS model.

  7. 7.

    The proof of (22) can be found in [7].

  8. 8.

    Data were collected in Economatica.

  9. 9.

    According to the Johansen test, the lower and upper bounds time series are cointegrated.

  10. 10.

    iFRB control parameters depend on the data and could be selected based on simulations. An alternative to automatic parameters selection is, for instance, the use of smart grid search techniques.

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Acknowledgements

The authors thank the Brazilian Ministry of Education (CAPES) and the São Paulo Research Foundation (FAPESP) for their support.

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Authors and Affiliations

  1. São Paulo School of Politics, Economics and Business, Federal University of São Paulo, Osasco, SP, Brazil

    Leandro Maciel

  2. Institute of Economics, University of Campinas, Campinas, SP, Brazil

    Rosangela Ballini

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  1. Leandro Maciel
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  2. Rosangela Ballini
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Correspondence to Leandro Maciel .

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Editors and Affiliations

  1. Fuzzy Logic Laboratorium Linz-Hagenberg, Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz, Linz, Austria

    Edwin Lughofer

  2. Institute Mines-Telecom Lille Douai, Douai, France

    Moamar Sayed-Mouchaweh

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Maciel, L., Ballini, R. (2019). Fuzzy Rule-Based Modeling for Interval-Valued Data: An Application to High and Low Stock Prices Forecasting. In: Lughofer, E., Sayed-Mouchaweh, M. (eds) Predictive Maintenance in Dynamic Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-05645-2_14

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  • DOI: https://doi.org/10.1007/978-3-030-05645-2_14

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