What is the best software for time series analysis and forecasting? Is MATLAB better than R for time series analysis and forecasting or vice versa? 
What other software is considered best for time series analysis?
 A: You can do roughly the same with the 2.


*

*Matlab is maybe cleaner and easier to use as you have only one clean library of function for each task,   

*R is maybe more flexible as you have a LOT of packages that provide several methods for each analysis.

A: Though there are lots of libraries in R for time series predictions, I frequently use "forecast" package. If my source data needs some cleaning or processing, I find python pandas very helpful, before porting data to R
A: I would suggest try Python which provides high productivity and it is free. They are some good libraries for Python. You can also have a look on a presentation Time Series with Python. FYI, Python+its packages (all free) could replace all Matlab+mathematica+... can do with additional advantages such as it is a very well know-highly appreciated fast growing programming language.
A: Stata and RATS are two other pieces of software that are popular for time-series analysis. OxMetrics also seems to be a popular choice. 
Although I'm an R user, I must say that I am quite a fan of Stata for time-series analysis. The Stata [TS] manual is rather good. I prefer R, though, because it's more flexible. Of course, there is the Mata language in Stata, but I can't say I'm a fan of it.
I haven't used MATLAB, so I won't give an answer to the first question.
A: If you are interested in simple time series forecasting, i.e. without entering in the mathematical details of the process, you can have a look at SwiftForecast. It is quite new, but I find the idea of a "Google style" predictor quite interesting...
A: Regarding the second part of your question, I would like to introduce LDT. It is free. It provides automatic forecasting with stationary vector autoregressive (VAR) models and other types of time series analysis.
PS: I am the developer of this software.
