# 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"?

## 1 Answer

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:

• Thanks. I was aware of that and already read Zhang article and others. Yes, the residuals are fed to NN. The problem is that NN require at least 2 inputs. So, residuals are not enough. One neuron input architecture are sometimes cited in articles but have never read complete article on how to code that. – Ernest Grand Jun 27 '13 at 23:18
• I see the confusion, I added some links/comments on that. Basically, yes, residuals are enough, much in the same way that in a straightforward neural network approach or an ARIMA model you would only use observations of the same process. The distinction between inputs and outputs is time-dependent: You want to use past observations or residuals to predict future observations or residuals. – Gala Jun 28 '13 at 9:36
• Thanks. Residuals must be used to feed Neural networks. I think I must now search for the best window to define the inputs. Will test with auto-correlation. Thanks again for your help. I just need to work more about the suject. – Ernest Grand Jun 28 '13 at 20:51