Fuzzy Nearest Neighbor Time Series Forecasting - Computational Complexity

The Fuzzy Nearest Neighbor time series forecasting technique (FNN), compiles a time series into a set of fuzzy rules capable of inferring the next value, based on the current observation. The training phase compiles all different scenarios of what has been observed in the past as a set of fuzzy rules. FNN has been tested against other methodologies, showing a satisfactory performance. This article proves that this forecasting approximation can be done efficiently. The proof shows that the number of rules is bounded by a constant, thus building the rule base can be done in linear time - O(n), forecasting can be done in constant time - O(1). These facts enable the method to work with time series sizes that qualify as big data.