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I have the following time series data:

$\{ t_i, X_i, Y_i \}$

where $i$ is the index, $t_i$ is the timestamp, $X_i$ the measured value of the external variable and $Y_{i}$ the value of the variable of interest. There are several variable components in $Y_i = (y_j)_i, j \in \{1,..,N\}$). At any point in time $i$, only one one of the components of $Y$ was measured. That means, that for example for $i=10$, the data looks like this:

$ t_{10} = $ 2019-04-23 12:34:56

$X_{10} = (2.2, 5, 67, 42, 123)$

$Y_{10} = (nan, .., 4567.89, .., nan) $

I want to train a forecasting model, that predicts the value of $ Y $, even when there is no single time step in the data that contains all the values for every component. So basically $\hat{Y} = (\hat{y}_1, .. , \hat{y}_N)$ with $\hat{y}_j <> NaN, \forall j$. Is there a standard way to deal with such incomplete data measurements?

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