Time series and forecasting · insight-1204

Estimate reconciliation weights and aggregate features only from data before each origin

Situation
A hierarchical forecast reconciles with MinT; its error covariance is estimated once from residuals over the whole history and then used in every backtest origin.
Action
Re-estimate the covariance (or shrinkage target) at each origin from residuals up to that origin. With many bottom series relative to the history length, use the shrinkage estimator rather than the sample covariance.
Reason
MinT's weights are a function of estimated error covariances. Estimated on all data they encode future errors, and the sample covariance is unreliable when series are many and history short.
Boundary
Any reconciliation with data-estimated weights, and aggregate-level features such as network mean demand.

Symptom or risk

The covariance contains the test-period errors, so reconciliation looks better than it can be in production.

Bottom-up and OLS reconciliation do not estimate weights from errors.

Per-origin estimation costs compute; shrinkage adds bias toward a diagonal matrix.

Computing a route-group mean target feature over the full year and calling it a static attribute.

MinT reconciliation chooses the combination matrix to minimise the trace of the reconciled error variance, and with many series relative to the series length a shrinkage covariance estimate is used.
Forecasting: Principles and Practice (3rd edition)Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization