Analysis of Time Series via their Linguistic Summarization: the Use of the Sugeno Integral

We propose here some new types of linguistic summaries of time series by extending our previous works. First, the linguistic summaries of time series refer to the summaries of (partial) trends identified here with straight line segments of a piece-wise linear approximation of a time series that is proposed in the paper. To characterize the trends we use the slope of the line segment, the goodness of approximation and the length of the trend. A linguistic summary of a time series is then derived by a linguistic quantifier driven aggregation of trends that is performed using the Sugeno integral. We show an application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an eight year period. The results are very promising.