Ask HN: Affordable service for Twitter historic data (research ML project)?

I'm working on a pretty cool research pet project.

The idea is to build a tool that look for correlations between social media data (basically tweets) and consumer spending habits in a particular area. Once a promising correlation has been found, the second step is to apply a machine learning model for prediction, and measure its performance.

I already have the anonymous financial data, but I don't know where to find an API or historic database of tweets for that period (6 months between 2012/2013). I've asked to Datasift and they kindly pointed me to their subscription plans (starting at $5K), which are far out of my budget as a personal research pet project.

Any clue on where to get the twitter data I need?