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

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.