Is there any library like LOESS or ARIMA in Java/C# or Python? I try to implement a time series data analysis project, but I have to do in Java, C# or Python, is there any good libary such like LOESS, ARIMA in R you can recommend? 
 A: R is an open source project, so you can look at the file src/library/stats/src/loessc.c which implements the C-level computation behind loess().  You should be able to use that for an extension module to the other languages you listed. Or, and this may be easier, you some of the existing ways to access R from Java, Python or C#.
A: With respect to loess the BioPython project has a lowess() function.
As for ARIMA model fitting, PyIMSL Studio contains a number of very useful time series analysis functions, including ones for automatically fitting the best ARIMA model and identifying outliers from it. These same functions are available in the other IMSL libraries if you choose to instead code in C, C#, Java, or Fortran.
A: Gretl is a very good and standard open source time series library.
A: As far as I know there aren't many options. Libraries for time series analysis free or otherwise are hard to come by. 
If you are doing this for work you can have a look at NAG. It's commercial and not Java native. But you can use JNI with their C library. 
They have a time series chapter which does quite a bit.
On the free side there is gretl looks good, but I have no direct experience with it. If anyone does, I'd like to hear their opinions.
Have a look at this question on stackoverflow as well.
