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The model proposed in this paper, is a hybridization of fuzzy neural network (FNN) and a functional link neural system for time series data prediction. The TSK-type feedforward fuzzy neural network does not take the full advantage of the use of the fuzzy rule base in accurate input-output mapping and hence a hybrid model is developed using the Chebyshev polynomial functions to construct the consequent part of the fuzzy rules. The model to be known as locally recurrent neuro fuzzy information system (LRNFIS) is used to provide an expanded nonlinear transformation to the input space thereby increasing its dimension which will be adequate to capture the nonlinearities and chaotic variations in the time series. The locally recurrent nodes will provide feedback connections between outputs and inputs allowing signal flow in both forward and backward directions, giving the network a dynamic memory useful to mimic dynamic systems. For training the proposed LRNFIS, an improved firefly-harmony search (IFFHS) learning algorithm is used to estimate the parameters of the consequent part and feedback loop parameters. Three real world time series databases like the electricity price of PJM electricity market, the widely studied currency exchange rates between US Dollar (USD) and other four currencies i.e. Australian Dollar (AUD), Swiss Franc (CHF), Mexican Peso (MXN), Brazilian Real (BRL), along with S&P 500 and Nikkei 225 stock market data are used for performance validation of the newly proposed LRNFIS.

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