I have a time series variable $y_t$ which I forecast $h$ steps ahead. I do that a number of times using a rolling window so that I collect a total of $T$ forecasts which form a time series $f_{t+h|t}$. Both $y_t$ and $f_{t+h|t}$ are integrated of order one, I(1). I would like to test whether $y_{t+h}$ and $f_{t+h|t}$ are cointegrated.

(I expect them to be cointegrated. It would be strange if $h$-step-ahead forecasts $f_{t+h|t}$ would diverge from the corresponding realized values $y_{t+h}$ with time; note that $h$ is fixed, only time $t$ flows).

To test for cointegration I could use the regular Johansen's procedure, for example. However, I know in advance that realized values at time $t+h$ cannot affect forecasts made at time $t$, especially if the forecasting model uses only the past values $y_{t-1},y_{t-2},...$ as its inputs (the model could AR($p$) or similar). That is, if $y_{t+h}$ and $f_{t+h|t}$ are cointegrated, and I form a vector error correction model for $y_{t+h}$ and $f_{t+h|t}$, then the error correction term will only appear in the equation for $y_{t+h}$ but not in the equation for $f_{t+h|t}$. If I obtain a corresponding VAR model, that would have some implications on it as well. Does that matter when testing for cointegration?

It seems to me that Johansen's procedure (which I do not have a full grasp of) utilizes some unrestricted VAR models of the variables of interest. I suspect that the knowledge of certain restrictions like the one discussed above might matter. I am afraid that neglecting it might be inefficient and perhaps lead to a different result of the Johansen's procedure.

The standard functions for Johansen's cointegration test such as ca.jo in urca package in R do not seem to allow incorporating restrictions such as the one discussed above.

Questions:

1. Is that a problem?
2. How could it be tackled? (Preferably it should also work for systems of more than 2 variables.)

Note: I know that once I have estimated a VECM, I can test for coefficient restrictions (e.g. whether the loading for the error correction term should be zero in the equation for $y_{t+h}$); but this is not what I am interested in. I care about testing for cointegration.