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I want to predict a time-dependent outcome (y) using current/past features (exogenous variables x) and past outcomes (y). The features also change with time.

In other words, for each sample (different time t), I would have these features: x1(t-2), x1(t-1), x1(t), x2(t-2), x2(t-1), x2(t), y(t-2), y(t-1). And this label: y(t).

I tried using Time-series LSTM. Does it even make sense in my case? Every tutorial I see about time-series LSTM uses an input size of (samples, timesteps, features). However, in my case, if I consider the past outcomes as features AND the current exogenous variables, it's not possible because the number of features would not be the same for each timestep [because obviously I don't use y(t) to predict y(t)].

My dataset (X) for supervised learning would look like:

And my labels would be:

y(t)
0.250896
0.301075
0.261649
0.075269
0.143369

I feel like I would need to either:

  • Not use the previous outcomes as features in the training [only features: x1(t-2), x1(t-1), x1(t), x2(t-2), x2(t-1), x2(t)], then the input size would be (5, 3, 2).
  • Not use the present exogenous variables in the training [only features: x1(t-2), x1(t-1), x2(t-2), x2(t-1), y(t-2), y(t-1)], then the input size would be (5, 2, 3).

What should I do? Does it matter? Does LSTM make sense in my case?

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