I have a model that works well on predicting the target variable $Y$ on time $t$ based on the input variables $X$. However, since I need to predict the $Y$ at $t+1$, for which I don't have the data (the $X$) for $t+1$. I decided to fill the void with Monte Carlo simulation. However, when feeding the simulated $X$ at $t+1$ into the model trained above, the performance deteriorates. I'm not sure which part can possibly go wrong and where to start my investigations. Please advise. Thank you!
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1$\begingroup$ "the performance deterioates" compared to what? You would expect the performance of the forecast of $Y_{n+1}$ to be worse than the forecast of $Y_{n}$ as you have less contemporary information about the thing that influences it. $\endgroup$– HenryCommented Mar 31, 2023 at 17:19
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2$\begingroup$ It depends on what your X is. If this is an intervention variable (e.g., promotions or the sales price), you should use the planned value. If it is something else, you may be able to forecast X itself, like tomorrow's weather. Yes, this will introduce added uncertainty that will directly propagate to your focal forecasts of Y. $\endgroup$– Stephan KolassaCommented Mar 31, 2023 at 17:20
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