How can one use unstructured data for forecasting?
How you use data depends mostly on the domain problem you're trying to address.

In the case you mention, it would depend on what exactly you're trying to forecast. For example, if you're trying to forecast sales or renewalls, there are some immediate use cases where you can leverage "unstructured" data to increase the number and/or the quality of the signals (features) that you are feeding into your model: 1) process audio data from contact centre interactions to determine the overall sentiment of a customer (i.e. "is he up for a sales call?"); 2) process text from customer reviews and use sentiment/keywords as a preditor for a churn model; etc!


  it seems that they always end up reducing the unstructured data to
  some structured format first, then feed it to whatever forecasting
  method they are using.


Probably because their forecasting algorithm or method requires that data is inputted in a specific format, like most forecasting or classification algorithms do; different algorithms will have different tolerances to data issues like missing values or outliers. So you process a piece of data that is unstructured with the goal of using it, usually by adding it to a data model or inputting it as data for a report or as a feature for a predictive model.

PS: I'm curious if anyone knows a case where you just throw unstructured data at a predictive algorithm (e.g. a neural network) and get something meaningful or useful out of it.