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    <p>Neural networks are <strong>not</strong> extrapolation methods (no matter - recurrent or not), this is completely out of their capabilities. They are used to fit a function on the provided data, they are completely free to build model outside the subspace populated with training points. So in non very strict sense one should think about them as an <strong>interpolation</strong> method.</p> <p>To make things clear, neural network should be capable of generalizing the function inside subspace spanned by the training samples, but not outside of it <img src="https://i.stack.imgur.com/8WNGY.png" alt="source www.vias.org/tmdatanaleng/cc_ann_extrapolation.html"></p> <p>Neural network is trained only in the sense of consistency with training samples, while extrapolation is something completely different. Simple example from "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8" shows how NN behave in this context <img src="https://i.stack.imgur.com/diBJV.png" alt="source www.vias.org/tmdatanaleng/cc_ann_extrapolation.html"></p> <p>All of these networks are consistent with training data, but can do <strong>anything</strong> outside of this subspace.</p> <p>You should rather reconsider your problem's formulation, and if it can be expressed as a regression or classification problem then you can use NN, otherwise you should think about some completely different approach.</p> <p>The only thing, which can be done to somehow "correct" what is happening outside the training set is to:</p> <ul> <li>add artificial training points in the desired subspace (but this simply grows the training set, and again - outside of this new set, network's behavious is "random")</li> <li>add strong regularization, which will force network to create very simple model, but model's complexity will not guarantee any extrapolation strength, as two model's of exactly the same complexity can have for example completely different limits in -/+ infinity.</li> </ul> <p>Combining above two steps can help building model which to some extent "extrapolates", but this, as stated before, is not a <strong>purpose</strong> of a neural network.</p>
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    1. COThank you very much for your detailed answer. I know, however, that people do use neural network for forecasting the stock market, future demand for different services, etc - it's called "time series". Isn't this forecasting considered as extrapolation?
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    2. COThe thing is **how** they do it. One problem can be modeled in many different ways. In case of **time series predictions** the most common idea is to actualy **interpolate** data, which is created by "chunking" the time series to constant size windows, so you are actually trying to model only **inside** the subspace of trianing data, and you just **interpret** this as some kind of **extrapolation**. This is why such models only can predict few steps ahead (as they don't acutally extrapolate in the well formulated way), but rather-interpolate artificial data "chunks".
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    3. COmaybe you know where can I read more about such predictions techniques with neural networks?
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