Using Diebold-Mariano test I've got predicted results from two different types of neural networks. Now I would like to run significance testing on both of the results to prove that they do not have equal predictive accuracy. I've learnt that the only tool in the game for this is Diebold-Mariano test. What tool I can use to run this testing (Matlab? R?)
So you want to do a Diebold-Mariano test eh? How about the Diebold-Mariano test dm.test function in the forecast package of R?

dm.test {forecast}

Diebold-Mariano test for predictive accuracy
Package: 
forecast
Version: 
6.2
Description

The Diebold-Mariano test compares the forecast accuracy of two forecast methods.
Usage

dm.test(e1, e2, alternative=c("two.sided","less","greater"),
    h=1, power=2)


(Took me ten seconds to find)