Fuzzy volatility models with application to the Russian stock market

Volatility modeling and forecasting is a topical problem both in scientific circles and in the practice. This paper develops an approach combining the GARCH model and fuzzy logic. The Takagi–Sugeno fuzzy inference scheme is adopted to fuzzify an original autoregression model (the conditional heteroskedasticity model). As a result, several different local GARCH models can be used in different input data domains with soft switching between them. This approach allows considering such phenomena as volatility clustering and asymmetric volatility (the properties of real financial markets). The proposed algorithm is applied to the historical values of the RTS Index and is compared with the classical GARCH model. As demonstrated below, in several cases, fuzzy models have advantages over traditional ones, namely, higher forecasting accuracy. Thus, the proposed method should be considered among others when modeling the volatility of the Russian financial market instruments: it demonstrates qualities superior to the conventional counterparts.