Trend‐cycle Estimation Using Fuzzy Transform and Its Application for Identifying Bull and Bear Phases in Markets

Abstract

Summary This paper is focused on one of the fundamental problems in financial time‐series analysis; namely, the identification of the historical bull and bear phases. We start with the proof that the trend‐cycle can be well estimated using the technique of a higher degree fuzzy transform. Then, we suggest a mathematical definition of the bull and bear phases and provide a novel technique for their identification. As a consequence, the turning points (i.e. the points where the market changes its phase) are detected. We illustrate our methodology on several examples.