Reconciliation Strategies: Top Down, Bottom Up, and Optimal Methods

Once you have base forecasts at one or more levels of a hierarchy, reconciliation enforces aggregation constraints so that parent totals equal the sum of children. There are four standard strategies, ordered by computational cost and flexibility. Top down forecasts only the top level, then allocates to children using historical proportions. If the national forecast is 1 million units and Store A historically captured 2 percent of sales, it receives 20,000 units. This is extremely fast: one model run plus a multiplication by a proportion vector. The downside is that allocations are rigid. If Store A runs a promotion or changes assortment, historical proportions no longer hold and the allocation will be wrong. Top down works well when children are stable and the aggregate signal is strong. Bottom up forecasts only the leaves and sums upward. This preserves all granular signals and naturally handles local shifts. For 10 million leaves, you generate 10 million base forecasts and aggregate them into parents using a sparse summation matrix. Reconciliation is trivial because you never forecast parents independently; coherence is automatic. The weakness is noise: if leaves are intermittent or sparse, summing them propagates high variance upward. Retail datasets with many zero sales days at the SKU store level often show bottom up producing unstable aggregates. Middle out forecasts at an intermediate level, aggregates upward to parents, and allocates downward to children. This is a hybrid that balances cost and accuracy when you have three or more levels. For example, forecast at the store level, sum to state and national, and allocate to SKU store leaves using proportions. This keeps the forecast count manageable (5,000 stores instead of 10 million leaves) and avoids the noisiest level. Optimal reconciliation, often called Minimum Trace (MinT) in the literature, forecasts all levels independently, then solves a weighted linear system to find the coherent forecast that minimizes variance. The weights come from the covariance matrix of base forecast errors. When the covariance is accurate, this method often gives the best overall error across all levels. The cost is high: at scale you must estimate a covariance matrix over potentially millions of nodes and solve a large linear system. Companies approximate this by shrinking covariance to diagonal or block diagonal by subtree, which turns one global solve into many small solves that fit in memory and finish in seconds per branch. Netflix and Meta capacity planning teams use optimal reconciliation weekly for long range planning, where a few hour batch is acceptable, and fall back to bottom up or diagonal weighted MinT for daily operational forecasts that must complete in under one hour. Uber reconciles by city, solving thousands of independent 100 to 1,000 node problems in parallel rather than one million node global problem, keeping per city reconciliation under 10 seconds and total batch under one hour.

Netflix capacity planning: Run optimal MinT reconciliation weekly for long range forecasts (acceptable few hour batch), use diagonal MinT daily for operational forecasts (under one hour SLA)

Uber demand: Reconcile by city, each city is 100 to 1,000 node problem solved independently in parallel, keeps per city reconciliation under 10 seconds and avoids global million node linear system

Walmart M5 competition: Winning solution used bottom up gradient boosted forecasts at 30,490 leaves, then optimal reconciliation with sample covariance over 42,840 total series to ensure store and category totals aligned