Solved – What ARIMA data to feed to neural networks in hybrid model for forecasting

In the hybrid forecasting model using ARIMA and neural networks (multilayer perceptron), the time series is first processed in ARIMA for linear processing. You get forecast values and also statistical values as residuals, various errors measures.

My question is: what items do you use to feed to neural networks as you need at least two items for the input layer: input and "desired output"?

From limited readings on the topic, my understanding is that the inputs for the neural network would be the residuals of the ARIMA. The idea being that the observed time series is the sum of a linear and a non-linear component. The ARIMA model captures the linear component of the time series and the ANN can model any non-linear component left.

The following article explains it quite clearly:

Zhang, G.P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159-175.

Once you have done that, you are back to a standard neural network. For time series, one way to train the network is, for each time t, to use $x_{t-1}$ to $x_{t-n}$ (with n defining some reasonable window) as inputs and $x_t$ as output. Your neural network can then be used to predict the value one period ahead using n observations in the past. Several other questions/answers on this site provide relevant material:

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