There are a number of documentation articles and code samples on pushing data from devices you control to Azure and for analyzing in combination with other streaming or static data.
What’s not as well documented is how to pull data from a public website you don’t control, then push that data into an Azure Event Hub. A recent article and code sample I produced with Dinar Gainitdinov shows how build a simple application with a few lines of C#, does this. We used a beefed up version of this code to combine real-time motor vehicle data with maintenance records in Microsoft Dynamics and another version to analyze how traffic in the Seattle region was affected by the weather. Make sure, of course, that you are not harvesting copyrighted data from websites, and are complying with all the terms of use!
Check out the technical documentation and the GenericWebToEH solution code to try it out on some of your favorite data feeds.