FMI’s Forecasting & Measurement — A Story You Can Audit

1. Where the story begins: a single country, real vendors

The taxonomy is fixed first (Product × Technology × Application × Channel × Region). Units and currency basis are locked. Then the canvass starts: each vendor in country c, year t, shows shipments and prices.

Shipments rule (one count only)

• OEM hand-offs are not double counted; attribution goes to the brand on the final product.
• Subsidiary inventory is excluded until it enters the channel.

Value math

V_{v,c,t} = U_{v,c,t} × P_{v,c,t}

V_{c,t}^{tracked} = Σ_v (U_{v,c,t} × P_{v,c,t})

“Other vendors” tail (tier model)

V_{c,t}^{tail} = Σ_{k in tiers} ( R̄_{k,c,t} × N_{k,c,t} )

# mean revenue per vendor in tier k times number of players

2. The country has to make physical sense

Numbers must pass a supply–use check. Country production, trade, and stocks must rhyme with your demand-side value.

Q_{c,t} + M_{c,t} − X_{c,t} ± ΔS_{c,t} ≈ C_{c,t} ≈ (V_{c,t}^{tracked} + V_{c,t}^{tail}) / P̄_{c,t}

Capacity sanity check

Cap_{c,t} ≈ Production_{c,t} / φ_{c,t} , φ ∈ [0.80, 0.90]

• Mirror statistics for trade and re-export corridors (FOB/CIF harmonized).
• Price corridor and channel margins checked for coherence.

3. Gaps happen; you fill them transparently

CAGR fill (history gap)

CAGR = ( V_{t2} / V_{t1} )^{1/(t2−t1)} − 1

V̂_{t1+1} = V_{t1} × (1 + CAGR)

Lineage note example: “CAGR interpolation (2017–2019), log-linear, confidence tier: B.”

BED growth fill (driver blend)

V̂_{t} = V_{t−1} × Π_j (1 + w_j × g_{j,t}) , Σ w_j = 1, w_j ≥ 0

# drivers include direct and indirect Business Environment Drivers with cross-validated weights

4. From countries to regions: add up, then adjust softly

V_{r,t} = Σ_{c in r} ( V_{c,t}^{tracked} + V_{c,t}^{tail} )

Large companies disclose regional splits. We respect them with a soft constraint that nudges (not overwrites) country shares, keeping each country inside its price and capacity corridors.

Minimize Σ_r [ ( V_{r,t} − V̂_{r,t}^{filings} ) / σ_r ]^2 subject to:

Σ_{c in r} V_{c,t} = V_{r,t} , V_{c,t} ≥ 0

5. World numbers: the big picture must balance

V_t = Σ_r V_{r,t}

Global closure: Σ_r Q_{r,t} ?≈ Σ_r C_{r,t}

• Diebold–Mariano tests compare forecast vintages.
• Stability tracked with sMAPE and MASE.

6. How we measure things (so audits are short)

• Shipments: counted once at final brand; re-exports reassigned to final use when determinable.
• ASP (distributor-level): includes freight/insurance/import duties in vendor/channel pricing; excludes POS taxes; outliers normalized; regional means weighted by vendor mix.
• Value: Value = Units × ASP.
• Installed base: IB_t = IB_{t−1} + Shipments_t − Retirements_t (Weibull survival).
• Capacity: Cap ≈ Production / φ .
• FX: history in current USD; forecasts at constant FX unless scenario work requires otherwise.

Pocket formulas

Value: V = U × ASP

Tail: V^{tail} = Σ_k ( R̄_k × N_k )

Consumption: C = Q + M − X ± ΔS

Capacity: Cap = Q / φ

Installed Base: IB_t = IB_{t−1} + Ship_t − Retire_t

7. Brands, channels, and leakage (the commercial layer)

When EPOS is unavailable, brand value is triangulated from filings, tenders, distributor catalogs, and public social/search proxies (SRAP/PII/RHI). We publish corridors to enforce plausibility.

Share_{b,c,t} = V_{b,c,t} / Σ_b V_{b,c,t}

S_min^{cap} ≤ Share_{b,c,t} ≤ S_max^{price}

Channels & margin ladders

Mix_{h,c,t} = V_{h,c,t} / Σ_h V_{h,c,t} , h ∈ {Direct, Distributor, Retail, Pharmacy, eCom, Tender, SI/EPC}

• Leakage flags appear where price anomalies persist by channel.
• Corridors are disclosed next to the share/mix tables.

8. Forecast engines: two ways, one answer

Method 1 — Regression (elasticities + lags)

ln V_{c,t} = α + Σ_j β_j ln D_{j,c,t−ℓ_j} + γ Z_{c,t} + μ_c + τ_t + ε_{c,t}

# Diagnostics: ADF/PP, VIF, HAC/cluster, Chow/Bai-Perron breaks

# OOS metrics: sMAPE, MASE; DM tests vs naïve

Method 2 — Driver growth-rate blend

V̂_{t+1} = V_t × Π_j (1 + w_j g_{j,t+1}) , Σ w_j = 1

# Weights via cross-validation; optional state-space smoothing for high-frequency inputs

9. Quality control: the second opinion that never sleeps

• Accuracy metrics: MAPE, sMAPE, MASE; correlation for blends; DM for forecast comparisons.
• Residual discipline: ACF/PACF, Ljung–Box, ARCH; parameter drift (CUSUM).
• Context sanity: compare with history and prior edition; reject unjustified kinks.
• Reconciliation: supply–use closure; price and capacity corridors; FX consistency.
• Governance: dual-analyst sign-off; change log with reasons (rebase, driver updates).

10. Miniature end-to-end worked example

• Country (2024): Tracked = $420m; Tail = $80m; Total = $500m. Price mid = $410 → Units ≈ 1.22m.
• Supply–use closure: Q=0.95m, M=0.35m, X=0.08m, ΔS≈0 → Consumption ≈ 1.22m (closes).
• Gap-fill (2023): BED growth with Utilization, Orders, Energy(−), Policy dummy; weights 0.40/0.30/0.20/0.10; Tier B.
• Region: Countries sum to EMEA; filings band $1.20B ± $0.06B; constrained least squares → $1.23B (inside band).
• World: Regions sum $3.48B; supply–use gap 1.7% within historical band → Tier A.
• Brand & channel: Brand B = 16–17% (capacity floor 12%, price ceiling 19%); Direct 35%, Distributor 40%, eCom 15%, Tender 10%.
• Forecast: Regression sMAPE 6.8%; Driver blend corr 0.91; blended published; DM p=0.04 vs naïve; forecasts at constant FX.

Appendix — Factor‑100 driver families (10×10)