A comprehensive comparison of time series described by linguistic summaries and its application to the comparison of performance of a mutual fund and its benchmark

We present a new approach to the evaluation of the similarity of time series. We consider, as in our previous works, the case of linguistic summarization of the past performance of an investment (mutual) fund and its underlying benchmark which is very important for an effective and efficient investment decision support. We propose a new comparison method based not on the comparison of the consecutive values or segments or trends of the fund and its benchmark but on linguistic summaries best describing their past behavior. Since our method derives a number of best linguistic summaries to be presented to the decision maker for consideration, we propose a new approach that boils down to the comparison of a set of linguistic summaries best describing the behavior of the fund and its benchmark, not just a pair of them. We take into account, as the measures of performance of the linguistic summaries of time series, the degree of truth and the degree of focus. The results obtained suggest that the new method proposed is very human consistent and intuitively appealing and may be relevant in the heavily human centered investment decision support task considered.