Linguistic Summaries of Time Series as Tools for the Analysis of Trends

An approach to a linguistic summarization of numeric time series data is presenteded. Basically, the proposed summaries of time series refer to the linguistic summaries of what happens - in the sense of dynamics - to trends identified here with straight line segments of a piece-wise linear approximation of time series. Main attributes which are used for the summarization are: the duration, dynamics (slope) and variability of trends. The derivation of a linguistic summary of a time series is then related to a linguistic quantifier driven aggregation of trends. For this purpose the classic Zadeh's calculus of linguistically quantified propositions in its basic form is employed. An application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an eight year period is presented as well as some interesting linguistic summaries obtained.