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

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.