Are Your Inputs Correlated? by Clifford J. Sherry, Ph.D.
If you use neural nets to model the behavior of equity markets in an effort to develop a trading strategy, it's likely that your model has multiple inputs. You may very well find that two or more of your inputs are cross-correlated.
Basic modeling theory suggests that you should avoid inputs that contain significant cross-correlations. If two of the inputs to your model were perfectly correlated, then removing one of them should have no impact on your model's efficiency. On the other hand, if the correlation is not perfect and removing one of these inputs decreases the model's efficiency, then it is possible that your model responds favorably when the two inputs agree or when they do not. If this is the case, you may want to consider combining the two inputs into one that summarizes the interrelationships of the two inputs and maximizes one of these relationships. If you have inputs that are cross-correlated and if removing one of these inputs decreases the efficiency and predictiveness of your model, you may want to consider one of these methods.