Can someone guide me in acquiring an application similar to EViews? I need a free application where I can incorporate the ARIMA model.
The standard open source statistical language is R. The R-Project homepage is here. Here is a page about ARIMA in R. If you want to try using R without having to install anything, then I would recommend DataJoy, which provides a free web-based R environment.
Note that R is an entire statistical computing language, so you may find that there is quite a big overhead for learning the language before you can start doing your ARIMA analysis.
As suggested above, R is an excellent language/program and suitable for almost anything in economics.
However, if you're looking for a free graphical interface program like Eviews, I'd give gretl (http://gretl.sourceforge.net/) a try.