More specifically, I would like to know the main advantages and disadvantages in using one or the other method please and in which situation I should use them. Thanks!
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By the way are you aware of any good [references to learn how to efficiently use neural networks for time series prediction](http://stats.stackexchange.com/q/250443/12359)? – Franck Dernoncourt Dec 12 '16 at 15:22
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Assuming you mean a linear AR model by "time series regression":
Typically a neural network (or machine learning methods in general) can get a better predictive performance (remember to verify this out of sample), but they can be harder or require more training to use and the regression is simpler to interpret on, whereas the neural net is a bit more black box. Moreover, there are well developed methods for conducting statistical tests, e.g. Whether the first lag is significant.
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