A fuzzy trend model for long-term financial time series and its identification

The identification problem of a fuzzy trend model is considered for long-term financial time series such as stock returns. The fuzzy trend model is based on fuzzy if-then rules. Usually the level of time series is assumed to be constant when the ARCH or GARCH model, which is the typical model for financial time series, is fitted to time series. However this assumption does not hold for the long-term time series. The fuzzy trend model permits the changing level by introducing the latent variables. The applicability of the proposed modeling procedure is considered by a simulation study and the practical analysis is achieved for the real time series