On Wavelet Transform for Stock Price Modeling by Fuzzy Systems

Models for time series are very important for the stock market. Fuzzy Takagi – Sugeno models (functional fuzzy systems) are a promising and already common approach, in which different regression dependencies are used for different areas of variation of certain parameters, and soft switching is performed using the fuzzy logic rules. This is the advantage of this approach over conventional stochastic models. Each Takagi-Sugeno model is based on its set of fuzzy rules. These models can be viewed as a generalization of classical econometric models, if one such model corresponds to one fuzzy rule. This paper studies the possibility of using the wavelet transform and fuzzy Takagi – Sugeno model to analyze the dynamics of stock prices for the following Russian companies: Gazprom, Sberbank, Magnit, Yandex and Aeroflot; this approach was previously used to study some foreign stock markets. Wavelet analysis quite often acts as a tool for signal processing, including time series, as it allows for a multi-level approximation. In this paper, the Takagi – Sugeno model is based on untransformed data as well as data transformed using Haar wavelets. Fuzzy clustering is used to construct membership functions. Calculations show that the use of wavelets often improves the predictive characteristics of the model.