A hybrid interval-valued time series prediction model incorporating intuitionistic fuzzy cognitive map and fuzzy neural network

The definition of interval-valued time series is now a valid tool that can be used to model uncertainty with known numerical bounds. However, how to provide accurate predictions of interval-valued time series remains an open problem. The goal of this paper is to develop a hybrid interval-valued time series prediction model that incorporates an intuitionistic fuzzy cognitive map and a fuzzy neural network. The causal relationship and adjacency matrix among nodes of the intuitionistic fuzzy cognitive map are defined and quantified using mutual subsethhood, in which the hesitation weight is added to the connection weight among concept nodes. The approach directly constructs concept nodes and a weight matrix for automatic recognition of intuitionistic fuzzy cognitive maps from original sequence data and combines the particle swarm optimization algorithm and back propagation algorithm to run with less manual intervention. The confidence intervals of forecasted interval values are also discussed. The developed prediction model is applied to forecast interval-valued financial time series (i.e., the Nasdaq-100 stock index), which is composed of daily minimum price and maximum price. The feasibility and validity of the proposed developed prediction model are shown through comparisons with some existing prediction models on interval-valued time series.