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Suppose the two univariate time series $X_{1,T}=(x_1, x_2, ..., x_T)$ and $Y_{1,T}=(y_1, y_2, ..., y_T)$. The next step would be to train an RNN or LSTM with input $X_{1,T}$ and output $Y_{1,T}$, in order to model the function $f(x_t) = y_t$. The model produced will be denoted $M$.

The questions regards the application of $M$ on new data $x_{t},t>T$.

  • If $x_{T+1},x_{T+2},x_{T+3}$ are unknown, but $x_{T+4}$ is known, can $M$ be used to predict $y_{T+4}$? Or is it necessary first for the model to predict $y_{T+1},y_{T+2},y_{T+3}$ beforehand?
  • I know that for standard machine learning algorithms e.g. decision trees or svm, applying the model for prediction does not change the model in any way. Is this also generally true for RNN/LSTM? For instance, if $M$ is applied twice in row on $x_{T+1}$, will I get two different results for $y_{t+1}$, as the model assumes that I am providing $x_{T+1}$ and $x_{T+2}$?
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