Please list some well tested api's for arima model
Statsmodels:

Statsmodels is your best bet for a python library that includes ARIMA.  I have used it fairly extensively and am quite happy with it. But, its certainly not as well tested as R based ARIMA models. 

R:

If you want something "well-tested" then your best bet is likely to use Rpy2 to call an R based ARIMA library from python. Rpy2 can be a bit tricky based on version reconciliation between python, R and Rpy2.

Here's a turorial on calling R from python using Rpy2

Hope this helps!