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I have a time series target, let's say $Y_1$. This quantity depends on two other time-series quantities deterministically, $Y_2 \text{ and } Y_3$. That is, we have some function which takes $Y_2$ and $Y_3$ and computes $Y_1$. This function was verified by carrying out simultaneous lab sampling for $Y_1, Y_2,$ and $Y_3$.

Now, I have created a Dynamic Partial Least Squares Regression model for determining the values of $Y_2$ and $Y_3$ in between lab samples, using lab sample data for training the model. The R-squared of fit for $Y_1$ was 0.78 and for $Y_2$ was 0.59.

Next, I try to calculate $Y_1$ using the predicted values of $Y_2$ and $Y_3$ by the function mentioned above (Modelling $Y_1$ directly gives bad results). However, the R-squared for $Y_1$ for even this type of calculated model was only 0.05, even though the calculation is deterministic and accurate. I am failing to understand why this is happening. Is this simply a matter of propagation of errors for the two models for $Y_2$ and $Y_3$? Based on the advice here, I am looking to either completely abandon this approach of modeling $Y_1$ indirectly, or look into it further.

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