RETRACTED: A two stage forecasting approach for interval-valued time series

In this paper, a two stage forecasting process is proposed for interval-valued time series viz. time series whose values are intervals instead of numbers. The forecasting of interval-valued time series is realized through predicting the centers and the radii of the intervals. The proposed model con sists of two functional modules: interval-valued threshold autoregression (ITAR) model followed by a granular fuzzy system. Fuzzy C-Means (FCM) method is used to determine the threshold parameters of the ITAR model while the least square error algorithm is used to estimate the values of its coefficients. To improve the forecasting accuracy, a granular fuzzy system is designed to further compensate for the series of residual errors. The proposed model can effectively capture the nonlinear feature of the original system. The piecewise compensation scheme can help to boost the prediction capability of the hybrid model. Some experiments demonstrate the performance of the model.