For simplicity, I assume that the following timeseries $X_{A}$ and $Y_{A}$ are univariate.

I am familiar with training RNN networks, such as LSTM, on a given timeseries $X_{A} = (X_{A0}, X_{A1}, X_{A2}, ...X_{AN})$ and targets $Y_{A} = (Y_{A0}, Y_{A1}, Y_{A2}, ...Y_{AN})$, such that $Y_{AN} \approx \hat{f}(X_{AN} | X_{A(N-1)}, ... X_{A1})$. Especially, in this direction forecasting problems can be modeled as $Y_{Ai}=X_{A(i+h)}$.

However, I care about a different problem. If my training set has multiple (univariate) time series $X_{A}$, $X_{B}$, ..., $X_{K}$ along with their target univariate series $Y_{A}$, $Y_{B}$, ..., $Y_{K}$, is it possible to structure this as a single deep learning architecture?

There are two necessities for prediction application:

(1) As new data arrive for a timeseries that actually was in the training set (like $X_A$ in the example), for instance the new values $X_{A(N+1)},X_{A(N+2)}$, to predict $Y_{A(N+1)},Y_{A(N+2)}$

(2) To also be able to predict $Y_L$ values for a new timeseries $X_{L}$ that was not in the original training set $\{(X_A,Y_A), .., (X_K,Y_K)\}$

In summary, to be able continue predicting for known timeseries, but also generalize for new timeseries. I am interested in any references towards problem formulation or solution that is similar to what I have described.


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