# How to handle partial observations of the variable of interest when training a time series model?

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?