Comparison of fuzzy forecaster to a statistically motivated forecaster

Recently a fuzzy forecaster (also called a fuzzy controller) was proposed as one method for forecasting an autoregressive time series. The approach in the fuzzy forecaster is similar to the approach in statistically motivated curve smoothers. However, the curve smoothers perform a beneficial type of data averaging that the current fuzzy forecasters do not employ. Also, the curve smoothers have a mature methodology for choosing the degree of smoothing. Therefore, in this paper we develop an enhanced fuzzy forecaster that uses some of the curve-smoother methodology and we compare the performance of the improved fuzzy forecaster to one particular curve smoother (loess) on five real and five simulated data sets. The performance criterion is the one-step-ahead forecast error variance, and the loess method outperforms the fuzzy forecaster on all five simulated data sets, and four of the five real data sets.