Indian Ocean Dipole (IOD) and Equatorial Indian Ocean oscillation (EQUINOO) are important climatic system oscillation events in the Indian Ocean region that affects the Indian summer monsoon rainfall (ISMR). The prime focus of this study is to deliberate the influence of these events on ISMR and an attempt has been made to predict these events for future time scales using a Long short term memory (LSTM) deep learning model. LSTM is a special kind of recurrent neural network (RNN) which specializes in learning long-term dependencies and extracting important features. The features learnt by the model is then ranked using correlational analysis (linear and nonlinear). This approach helps in selecting decisive and imperative set of relevant predictors, which can be employed to predict IOD and EQUINOO. Nonlinear correlational identified predictors are found to forecast with greater precision as to their linear counterparts. The model-calibrated correlation coefficient for IOD and for EQUNIOO was 0.90 and 0.88 respectively at a lead of 5 months. Our proposed model was observed to work at par with the other existing models in terms of various statistical evaluation measures.