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Assume I am interested in predicting a time series variable $y_t$ using a vector of possible predictors $X_t$ of dimension $N_x$. I am interested in finding the optimal $N_z < N_x$ predictive factors stacked into a vector $Z_t$. More formally the problem is

$$Z_t=AX_t+\epsilon_t$$

$$y_{t+1}=BZ_t+e_{t+1}$$

Here the dimension of $A$ is $N_z\times N_x$. For example $N_x$ could be 200 and $N_z$ 2 so the method would select two factors from $X_t$ that are optimal for predicting $y_t$. Has this type of problem been considered in the literature? How would I go about solving such a problem?

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    $\begingroup$ partial-least-squares may be relevant. $\endgroup$ Commented Feb 23, 2023 at 18:51
  • $\begingroup$ @Richard Hardy Yes added. I think PLS seems to be what I am looking for but still need to think a bit more. $\endgroup$
    – fes
    Commented Feb 24, 2023 at 11:47

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