Suppose I get a forecast, from MLP or LSTM - next 7 time steps into the future. I can assess its quality using mean absolute error using cross validation. However, it is not clear, what I should do with residuals.
I met mentioning in a few sources that when fitting a regression model, it is important to investigate residuals, so that they are close to normality/have no autocorrelations. Neural networks ARE non-linear regression models. However, while residual analysis is straightforward to do for OLS regression, it is not clear if it is done, or should be investigated for neural network models?
Suppose I fit an MLP model on the training set using window of 30 time steps, and forecast (dependent vector) of 7 time steps forward, do I calculate residual statistics on the training set, or test set? And if so, how is it done for a horizon of 7 days? Does it even make sense since the procedure fitting the values is not OLS? In case they are far from normality, what does it mean in terms of NNs? (since they overlap, because the window moves by 1 forward, but forecast is 7 days, at any time step, 6 forecasts overlap).