Bitcoinwisdom shows in their charts lines for weekly and montly averages. Are these numbers somewhere available in an API? If so, one could setup an automated strategy for trading BTC based on this data.
I have not heard about an API that would return averages per se. But there are APIs that will provide you with a historical price data which you can use to calculate averages on your own.
One example would be CoinDesk, but I am pretty sure there are more. They have a JSON endpoint that will return closing prices for a given period (1 month by default). Examples:
Default (one months period): https://api.coindesk.com/v1/bpi/historical/close.json