In India, due to the blessing by the outbreak of the National Food Security Mission, the production of cereals such as wheat, rice etc, has increased in an alarming rate. In this Study, forecasting is done with the help Auto Regressive Integrated Moving Average (ARIMA) and Long Short-Term Memory Neural Network (LSTM-NN) models on the basis of the historical data of rice cultivation from the year 1950-51 to 2017-18. The well fitted ARIMA models for the parameters such as Area under Cultivation (0,1,1), Production (0,1,1) and Yielding (2,2,1) are obtained from the significant spikes of their respective Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) plots. But, the models fitted with a supervised deep learning neural network known as LSTM-NN are found much better time series forecasting model than the ARIMA models. The performances of these models validated with the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) values. From the study, the LSTM-NN's are more flexible and able to develop accurate models for predicting the behavior of agricultural parameters than the ARIMA models.