How can I get tweets older than a week (using tweepy or other python libraries)

As you have noticed Twitter API has some limitations, I have implemented a code that do this using the same strategy as Twitter running over a browser. Take a look, you can get the oldest tweets: https://github.com/Jefferson-Henrique/GetOldTweets-python

You cannot use the twitter search API to collect tweets from two years ago. Per the docs:

Also note that the search results at twitter.com may return historical results while the Search API usually only serves tweets from the past week. - Twitter documentation.

If you need a way to get old tweets, you can get them from individual users because collecting tweets from them is limited by number rather than time (so in many cases you can go back months or years). A third-party service that collects tweets like Topsy may be useful in your case as well (shut down as of July 2016, but other services exist).

Found one code that would help retrieve older tweets.https://github.com/Jefferson-Henrique/GetOldTweets-python

To get old tweets, run the following command in the directory where the code repository got extracted.

python Exporter.py --querysearch 'keyword' --since 2016-01-10 --until 2016-01-15 --maxtweets 1000

And it returned a file 'output_got.csv' with 1000 tweets during the above days with your keyword

You need to install a module 'pyquery' for this to work

PS: You can modify 'Exporter.py' python code file to get more tweet attributes as per your requirement.