Preliminary Draft Notes on a Similarity-Based Analysis of Time-Series with Applications to Prediction, Decision and Diagnostics

Abstract

Abstract Wiener's highly classified wartime work on prediction used the least squares approach and did not involve probabilities. The approach described in this paper, call it SBPD, for short, is probability-based, but is non-traditional. Moreover, SBPD employs some concepts and techniques drawn from fuzzy logic. Underlying SBPD is what may be called a qualitative Prediction Principle: to a considerable degree the Future replicates the Past and the degree increases when the Future is close to Present and Past. Additionally: in similar circumstances (contexts) similar inputs produce similar outputs. The point of departure in SBPD is a time-series of descriptive variables which take values in a finite set V or finite set W depending on whether the variables are prediction variables or decision variables. X plays the role of History. In SBPD, History is examined and searched for contexts which are similar to the present context. Prediction and conclusion are expressed as probability distributions. SBPD has a potential for applications in many directions which go beyond those which appear in the title of the paper. An algorithm which plays an important role in SBPD involves competition of the degree of similarity of two time-series.