Differenced targets & variable lag lengths per target in DeepVAREstimator

[pragmaticml]

Hello,

I am trying to model time series that are differenced over various intervals (e.g., for sales growth)

Example -- given time series y, i am using a differencing transformation for targets for 1 day and 7 days:

y_(t+7) - y_(t)
y_(t+1) - y_(t)

If I run these through as 2 regular series, the problem will be feature-target leakage: y_(t+7)- y_(t) for t = 1 contains information we don't have in the real world for t = 2. i.e., y_(t+8)-y(t+1) would be predicted using y(t+7)-y_(t), which would be cheating!

In a regular regression setting, we would be able to fix this by preprocessing a "lagged" column. e.g., for 7-day returns, I would take a 7-day lag. e.g., in linear regression:

y_(t+7) - y_(t) = [y_(t)- y_(t-7)]*B + e

However, it is not clear to me that I could do something like pass the unlagged series to 'target' and lagged series to 'feature' in ListDataset. This is because I believe the algorithms would still use lagged information in the 'target' series to predict, leading to the target leakage issue above.

Ultimately, I am interested in jointly modeling series across these different differencing levels -- e.g., y_(t+g) - y_(t) for g = 1,7,14,30, etc. And of course for multiple targets (e.g., different product lines). Differencing/converting to growth rate helps make the data much more stationary and easier to predict.

Is there a straightforward way to accomplish this w/ GluonTS?

Thank you!