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FNN a fuzzy version of the nearest neighbor time series forecasting technique

The kNN time series forecasting method is based on a very simple idea: similar states, observed in the past, most likely have produced similar output values. One has to look for nearest neighbors, according to some distance measure. The first idea that comes to mind when we see the nearest neighbor time series forecasting technique is to weigh the contribution of the different neighbors, according to distance to the present observation. The fuzzy version of the nearest neighbor time series forecasting technique (FNN), implicitly weighs the contribution of the different neighbors to the prediction, using the fuzzy membership of the linguistic terms as a kind of distance to the current observation. The training phase compiles all different scenarios of what has been observed in the time series past as a set of fuzzy rules. When we encounter a new situation and need to predict the future outcome, just like in normal fuzzy inference systems, the current observation is fuzzified, the set of rules is traversed to see which ones of them are activated (i.e., their antecedents are satisfied) and the outcome of the forecast is defuzzified by the common center of gravity rule. FNN was tested with a set of nonlinear chaotic time series, and the results compared with ARIMA. Its performance is satisfactory at this point and encouraging to continue evaluating the method, poising and improving it.