Store the data locally? Easily. Set up the necessary back-end infrastructure to sift, twist, and churn the data efficiently? Now you're talking hiring some people to set up an infrastructure for that... Or you could upload it to Google and use their infrastructure.
The bold byline of BigQuery (https://developers.google.com/bigquery/) is "Analyze terabytes of data in seconds."
Store the data locally? Easily. Set up the necessary back-end infrastructure to sift, twist, and churn the data efficiently? Now you're talking hiring some people to set up an infrastructure for that... Or you could upload it to Google and use their infrastructure.