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A test for the homoscedasticity of the residuals in fuzzy rule-based forecasters

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Abstract

Heteroscedasticy is the property of having a changing variance throughout the time. Homoscedasticity is the converse, that is, having a constant variance. This is a key property for time series models which may have serious consequences when making inferences out of the errors of a given forecaster. Thus it has to be conveniently assessed in order to establish the quality of the model and its forecasts. This is important for every model including fuzzy rule-based systems, which have been applied to time series analysis for many years. Lagrange multiplier testing framework is used to evaluate wether the residuals of an FRBS are homoscedastic. The test robustness is thoroughly evaluated through an extensive experimentation. This is another important step towards a statistically sound modeling strategy for fuzzy rule-based systems.

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Author information

Authors and Affiliations

  1. Dept. of Artificial Intelligence, UNED, Madrid, Spain

    José Luis Aznarte

  2. Dept. Computer Languages and Systems, University of Cádiz, Cádiz, Spain

    Daniel Molina

  3. Dept. Software Engineering, University of Granada, Granada, Spain

    Ana M. Sánchez

  4. Dept. of Computational Sciences and A. I., CITIC-UGR, Universidad de Granada, Granada, Spain

    José M. Benítez

Authors
  1. José Luis Aznarte
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  2. Daniel Molina
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  3. Ana M. Sánchez
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  4. José M. Benítez
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Corresponding author

Correspondence to José Luis Aznarte.

Additional information

This work is part of the first author’s Ph.D. thesis and has been partially funded by Spanish Ministerio de Ciencia e Innovación (MICINN) under Project grants MICINN TIN2009-14575 and CIT-460000-2009-46.

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Aznarte, J.L., Molina, D., Sánchez, A.M. et al. A test for the homoscedasticity of the residuals in fuzzy rule-based forecasters. Appl Intell 34, 386–393 (2011). https://doi.org/10.1007/s10489-011-0288-x

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