I am looking for a good python api for timeseries models such as ARIMA. Please list some well tested apis and few more advance models possible for financial time-series analysis.
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.
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.
Hope this helps!