Non-stationary time-series prediction using fuzzy clustering

Applying clustering analysis to sliding windows of non-stationary time-series is useful for grouping related temporal patterns that are dispersed along the time-series. Since the input patterns are time-series, a similar series of events that lead to a similar result would be clustered together. The switches from one stationary state to another (changes of regime), which are usually vague and not focused on any particular time point, are naturally treated by means of fuzzy clustering. In the first stage of the method, the time-series is rearranged into sliding widows of temporal patterns. In the next stage, similar temporal patterns are grouped together into clusters, which may represent the different states of the dynamic system, by an unsupervised fuzzy clustering procedure. A time-series prediction model is fitted to each cluster separately using its similar past temporal patterns as a training set. In the last stage, the future samples of the time-series are predicted by a fuzzy mixture of the above prediction models weighted by the degree of membership of the latest temporal pattern in each of the corresponding clusters. The hybrid algorithm suggested for the clustering is a hierarchical version of the unsupervised optimal fuzzy clustering algorithm. One of the advantages of this new algorithm is its adaptive hierarchical selection of the number of clusters (the number of underlying processes, or states, in the time-series), which can overcome the general non-stationary nature of real-life time-series (biomedical, physical, economical, etc.). The method is demonstrated for well-known time-series benchmarks.