Since Twitter API 1.0 was shutdown in early 2013, every API request has to be authentified via OAuth for Twitter API 1.1. You can do this on client-side in browser with JavaScript but for privacy reason, you should not share your access keys (more informations in first comment of the script in iframe below). This script can be used to backup your Twitter data.
Download script from my server: twitter_api_1.1.js
On Pastebin
On GitHub
