If you are looking for a 'free' software you must check all the available open-source alternatives. You can start from R (http://www.r-project.org/) that have many packages focused on forecasting.
For time series prediction with neural networks there is no dedicated free software ackage. However, Alyuda, NeuroDimensions, and Neuralware all offer commercial neural network packages that allow some time series data althoguh the emphasis is clearly on classificaiton or pattern recognition.
Through our university sipnn-off we have been developing the software "Intelligent Forecaster" (see www.bis-lab.com) dedicated to forecasting with Neural Networks, Support Vector Regression, k-nearest Neighbours and / or Decision Trees ensembles on time series data, which is due to be launched shortly - but I am sorry to say that it will also not be free of charge.
So your only choice for free forecasting software is R, WEKA etc. Note that SAS has a free educational version of their software announced, and while this has neural networks and also forecasting procedures but it does not have a ready-made routine for forecasting with neural networks.
Hi Luiza. Last time I checked Mathlab was not free! And it does not allow you to directly dig into time series data (see, e.g., the recommendations on how to evaluate if a forecasting algorithm predicts well using rolling origin evaluation etc. in Tashman (2000) Out-of-sample tests of forecasting accuracy - an analysis and review science ... all of this needs to be implemented in mathlab in order to get some reasonable results, and that is quite demanding!
Hi Luiza, thanks for the reference. But just as Sven said, MATLAB is not entirely free. I only came across a test-drive MATLAB version, with a free 30-day trial. I am trying, but apparently it is quite demading to make my own code.