# Is it possible to build something like a recurrent neural network for time-series data?

For example, if the data is an acceleration, each input is the acceleration at a time T ?

More precisely, I'm curious if I can have the same behavior of a recurrent neural network but only with a normal artificial neural network which has "inputs over time".

In fact, I tried something like that and it doesn't work on my problem (but a RNN works). So I wonder if there is a mathematical explanation of why is it limited, why it may never have the same results?

• Check out reservoir computing, such as liquid state machine and echo state network. Sounds similar to what you say. – Kolya Ivankov Nov 9 '17 at 9:38
• Could you edit to tell us what do you mean by "imputing the same data over time"? Your description is very vague and makes it hard to answer. – Tim Nov 9 '17 at 9:41
• Hi @Tim, I added a schema and, I hope, a sufficiently detailed description – dan32 Nov 9 '17 at 9:52
• @dan32 so you mean applying NNs to something like time-series data? – Tim Nov 9 '17 at 9:54
• Yes! If I understand correctly, in the case of a RNN we just input our data at the current time, and we modify the inside memory with this input when it learns. So I guess that a RNN has a memory over time, depending on the before inputs. But if I just need a short term memory (which is the case for a RNN, no?), can I just input my data at the current time, but also the 50 past values of my input? – dan32 Nov 9 '17 at 10:00

What you're suggesting is similar to regression approach to time series. For instance, you can recast the AR(1) process as a simple regression: $$y_t=\beta_0+\phi_1y_{t-1}+\varepsilon_t$$ will become OLS problem: $$y_i=X_i\beta+\varepsilon_i$$ where the independent variable $y_i\equiv y_t$and design matrix has two columns for intercept and bona fide one regressor $x_{1i}=1,x_{2i}=y_{i-1}$
Similarly, you could build the NN with one input which is the lagged dependent variable, which outputs the one step forecast. You'd have to call it repeatedly to produce the multi-step forecast. In this case your NN would basically degenerate into the glorified nonlinear regression $y_t=f(y_{t-1})+\varepsilon_t$