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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.