Discrepancies in Sum of Predictions and Reconciliation Methods

[Lenaklsk]

Hi,

I have been working with the hierarchical reconciliation notebook provided here: TourismSmall Notebook. While following the reconciliation process, I noticed that the sums of predictions across different reconciliation methods for the AutoARIMA model do not match the sums of the original predictions. However, the Naive model does not exhibit this issue.

Observed Issue

When summing up the predictions and comparing the reconciled data (using Bottom-Up and Top-Down methods), the totals do not align with the original predictions.

Outputs

Here are the outputs I obtained:

print("AutoArima pred", Y_rec_df["AutoARIMA"].sum())
print("AutoArima Topdown", Y_rec_df["AutoARIMA/TopDown_method-forecast_proportions"].sum())
print("AutoArima BottomUp", Y_rec_df["AutoARIMA/BottomUp"].sum())

print("Naive pred", Y_rec_df["Naive"].sum())
print("Naive TopDown", Y_rec_df["Naive/TopDown_method-forecast_proportions"].sum())
print("Naive BottomUp", Y_rec_df["Naive/BottomUp"].sum())

Results

AutoArima:

• AutoArima pred: 2365558.2
• AutoArima Topdown: 2357627.0
• AutoArima BottomUp: 2320906.2

Naive:

• Naive pred: 2246944.0
• Naive TopDown: 2246944.0
• Naive BottomUp: 2246944.0

Expected Behavior

The sums of the reconciled predictions (Bottom-Up, Top-Down) should ideally match the sum of the original AutoARIMA predictions.

Questions

1. Is there a known issue with the reconciliation methods causing discrepancies in the sums?
2. Are there any specific steps I might be missing that could ensure the sums align correctly?
3. Could this be related to implementation details or numerical precision issues?

Any insights or suggestions to resolve this issue would be greatly appreciated.