I will use an extremely simplified example to ilustrate the question, but I think the answer shsould hold for more generalised cases.
Let's say I want to create a time series regression model (the model itself is not relevant as the question is related to the information present in the data) to predict a target variable (sales).
To do so, I have the historical data and, additionally, a regressor variable which I know explains some of the variability of the target variable. (A typical case is some Weather indicator)
The problem is, I only have data until the current period of time, and I'm interested in the prediction two time steps ahead.
What whould be the best way to incorporate this information into the model?
Dummy example The data:
The objective is to predict Sales for t+2, and we assume Weather has some degree of covariance with Sales
- Train up to t0 using weather and then forecast Weather forward with another model and use it to predict with the trained model - In this case the forecast error of the Weather variable will impact directly the final prediction, as the model will be trained with quality real data and the prediction with low quality forecasted data
- Train model using lagged (in this case Lag2) Weather - In this case Lag2 Weather might not explain the target variance as well as the non-lagged variable
- For each timestep, use Weather up to t-(i-2) to forecast X-i and train the model using these values.
- Not use Weather data at all - Loss of potentially useful information
- Other approaches
EDIT: The auto review says the question might be subjective, but I think not. The answer should be general and take into account the forecasted Weather can be of good/bad quality and Lag2 Weather can retain a lot/very little information