The ARIMA model extends an ARMA model. It can model non-stationary time series using differencing and is leveraged in many areas of research.
ARIMA is a powerful and flexible methodology where patterns of the data are identified, individual observation errors are identified and forecasts are generated.
Because of its power and flexibility, ARIMA is a complex technique and requires experience to use effectively. Results are often dependent on the user's level of expertise.
"Auto" refers to Automatic convenience and performance features. Automatic features within the Auto_ARIMA function include:
IMSL Library Neural Network Implementation
The IMSL Library implementation is a multi-layer feed-forward neural network. It is well-suited for forecasting and classification in challenging data circumstances. With its advanced technology, it provides sophisticated control and flexibility to fine tune. You also get full control over network attributes such as number of layers, number of training epochs, and interconnections. This also allows performance and forecasting accuracy to be tailored and fine-tuned to the application

Neural Network Forecasting Process
Neural Network vs. Traditional Regression / Time Series