There is an editorial by Chris Chatfield in the International Journal of Forecasting 9 (1993) 1-3 entitled "Neural networks: Forecasting breakthrough or passing fad?" It is focused on comparing ARIMA models and neural networks. He warns that sometimes apparently successful applications of neural networks in business and economic forecasting are reported without comparing the results with any more established alternatives. Chatfield concludes:
In summary it is possible that neural nets will outperform standard forecasting
procedures when a fair comparison is made, at least for certain types of situation, but
there is little systematic evidence of this as yet.
There is also a paper co-authored by Chatfield published in Applied Statistics. It compares NN with Box-Jenkins and Holt-Winters and reports on many potential problems in using NN for forecasting. The authors advise "it is unwise to apply NN blindly in a 'black-box' as has sometimes been suggested", which I think answers your questions.
If you are currently working on neural networks for time series forecasting, I would suggest that you build your own collection of quality references. The two references above is a good start. Brian Ripley discussed NN for time series neither in this piece of R news nor in his "Pattern Recognition and Neural Network" book, but you probably can find his work on neural networks for time series prediction elsewhere.
You may also check this review paper: Forecasting with artificial neural networks:
The state of the art in the IJF, even though it is dated 1998. It has references to work on applying NN to multivariate time series problem. In particular, it says that
Gorr (1994) believes that ANNs can be more appropriate for the following situations:
(1) large data sets;
(2) problems with nonlinear structure;
(3) the multivariate time series forecasting problems.
There is also "...A Review from a Statistical Perspective" (and Leo Breimann remarked in his commentary to it that "room is left for other statistical perspective") published in Statistical Science, Vol. 9, No. 1 (Feb., 1994)