Description and prediction of time series: A general framework of Granular Computing

In this paper, we address problems of description and prediction of time series by developing architectures of granular time series. Granular time series are models of time series formed at the level of information granules expressed in the representation space and time. With regard to temporal granularity, time series is split into temporal windows leading in this way to the formation of temporal information granules. Information granules are also quantified and constructed over the space of amplitude and change of amplitude of the series collected over time windows. In the description of time series we involve clustering techniques and build information granules in the representation space (viz. the space of amplitude and change of amplitude) of the temporal data. Fuzzy relations forming the essence of the prediction model are optimized using particle swarm optimization. Experimental results are reported for a number of publicly available time series.