For what specific models is multicolinearity a problem in the context of making predictions For what predictive models (regression and classification) does multicollinearity cause a problem? 
The reason I ask is the following quote that I read today:

Multicollinearity makes it hard to assess the relative importance of independent variables, but it does not affect the usefulness of the regression equation for prediction. Even when multicollinearity is great, the least-squares regression equation can be highly predictive. So, if you are only interested in prediction, multicollinearity is not a problem.

As well as this blurb from Wikipedia, which seems to back up the above:
"Remedies for Multicollinearity":


  
*Leave the model as is, despite multicollinearity. The presence of multicollinearity doesn't affect the efficiency of extrapolating the fitted model to new data provided that the predictor variables follow the same pattern of multicollinearity in the new data as in the data on which the regression model is based.

So one obvious answer to my question would be "worry about it when the new data does not have the same multicollinearity as the data you trained your model on". I'm not sure when such a scenario would occur, or what other instances might raise issues. 
 A: Like you quoted, multicollinearlity presents a much bigger problem for inference than prediction. Prediction is mostly fine under multicollinearity as long as the variables stay collinear (although if you get close to perfect collinearity, you can get some precision issues with regards to things like matrix inversion). But there is the issue that we don't really know which variable is having the impact which becomes a problem, like you said, when new data is no longer collinear. There aren't too many instances where that can happen though. 
A dumb example would be something like say you're training on resumes to predict quality hires and say that in the training data, almost all the people with only high school degrees work in the service industry and almost all the people who work in the service industry only have high school degrees. Obviously some issues would start happening if you had to predict people in the service industry who had a college degree or a high school graduates who don't work in the service industry.
But in general, if your training data is representative and you don't believe the multicollinearity is somehow time based and could change in the future, you're usually fine with multicollinearity (with the above caveat about precision errors). 
A: If you addressed the multicollinearity issue by mean centering the data, then no issue with short-range prediction.
With longer horizons, however, the question is do the historical means, to which you are adding the expected change per the regression model, remain valid? 
A lesser issue if your interest is in percent change forecast and your variables are already log transformed. 
