We attempt to design artificial neural networks that can help in the automatic identification of the Autoregressive Moving Average (ARMA) model. For this purpose, we adopt the Extended Sample Autocorrelation Function (ESACF) as a feature extractor, and the Multi-Layered Perceptron as a Pattern Classification Network. Since the performance test from the network is sensitive to the noise in input ESACF patterns, we suggest a preprocessing Noise Filtering Network. It turns out that the Noise Filtering Network significantly improves the performance. To reduce the computational burden of training the full Pattern Classification Network, we suggest a Reduced Network that can still perform as good as the full network. The two-stage filtering and classifying networks performed very well (90% of accuracy) not only with the artificially generated data sets but also with the real world time series. We have also reconfirmed that the performance of ESACF is superior to that of ACF and PACF.