Improving the quality of Wind Speed Interval prediction is important to maximize the usage of integrated wind energy as well as to reduce the adverse effects of the uncertainties, introduced by the random fluctuations of wind, to the power systems. This paper utilizes independently recurrent neural network to propose two new interval prediction frameworks. This network possesses the ability to retain memory at different lengths, which is helpful in capturing temporal features, especially for multi-horizon forecasts where the local dynamics get quite involved. In the first approach, we integrated a quantile regression loss function into this network to generate the intervals. This framework however, require to train different regressors to generate the conditional quantiles. Removing this limitation, a new simple and intuitive approach, is proposed which estimates the prediction intervals using a Gaussian function centered on the prediction and estimated error by a point prediction model and an error prediction model respectively. In our computational experiments, which involve two different wind fields contributing to eight different cases, an improvement of 43% and 12%, in average coverage width criterion index, over traditional models and LSTM based model respectively is remarkable. Thus, the proposed framework is able to produce high quality PIs while simultaneously reducing the computational cost.