This paper proposes a new Self Evolving Recurrent Neuro-Fuzzy Inference System (SERNFIS) for efficient prediction of highly fluctuating and irregular financial time series data like stock market indices over varying time frames. The network is modeled including the first order Takagi Sugeno Kang (TSK) type fuzzy if then rules with two types of feedback loops. The recurrent structure in the proposed model comes from locally feeding the firing strength of the fuzzy rule back to itself and by including a few time delay components at the output layer. The novelty of the model is based on the fact that the internal temporal feedback loops and time delayed output feedback loops are used for further enhancing the prediction capability of traditional neuro-fuzzy system in handling more dynamic financial time series data. Another recurrent functional link artificial neural network (RCEFLANN) model is also presented for a comparative study. In the second part of the paper a modified differential harmony search (MDHS) technique is proposed for estimating the parameters of the model including the antecedent, consequent and feedback loop parameters. Experimental results obtained by implementing the model on two different stock market indices demonstrate the effectiveness of the proposed model compared to existing models for stock price prediction.