TEYMUR Index · Method 1.0

How TEYMUR is built

TEYMUR is a GDP-weighted measure of world money. It prices every currency in TYMR, a synthetic unit of account, so that the movement of a currency can be read against the whole world rather than against one counterpart. This page states the definition, the data, the rules and the controls — precisely enough that any published value can be recomputed from its inputs.

1. Definition

Take the member currencies i with normalized GDP weights w_i (summing to 1) and their values in a common unit V_i (in practice USD: V_i = 1 / units per USD).

• Mass: ln M = Σ w_i · ln V_i — a weighted geometric mean.
• Price of a currency in TYMR: P_i = k · V_i / M. Series are named {CCY}TYMR = how many TYMR one unit of CCY buys.
• Parity: on 3 January 2005, 1 USD = 1 TYMR, which fixes k₀ = M(2005-01-03) = 0.352857263515.

Why geometric: the result does not depend on which currency is used as the measuring unit, it is symmetric under inverting a quotation, and every cross rate is preserved exactly (P_i/P_j = V_i/V_j). The weighted product Π P_i^w_i equals k on every day — an invariant we test.

2. The chain constant k

When the membership or the weights change (annual rebalancing, an accession or an exit), the mass is computed twice on the first calculation day of the new configuration — once with the previous configuration and once with the new one, both on that day's rates. The ratio cf = M_new/M_old (rounded to 12 decimals) rescales k: k_new = round₁₂(k_old · cf). Because one scalar multiplies every series, no {CCY}TYMR series jumps at a configuration change. A currency that leaves enters M_old with the rate published on the event day (or its last published rate). Every chain event is recorded with its date, type, factor and resulting k; the current value is 0.331003528828 (from 2 January 2026).

3. Calendar

4. Membership — a written rule, applied point-in-time

• Threshold: share of world nominal GDP — entry at ≥ 0.40%, exit after two consecutive vintages below 0.30% (hysteresis). Comparisons use exact arithmetic.
• Data precondition: a reliable official daily reference rate and a single exchange-rate regime (currencies with an official/parallel spread are excluded; pegs are fine).
• Blocks: pegged currencies enter with their own rate and their own GDP (SAR 3.75, AED 3.6725, HKD band, DKK in ERM II); the euro area enters as one block with the IMF euro-area aggregate.
• Annual rebalancing: on the first TARGET day of each year, using the previous autumn's IMF World Economic Outlook vintage; chained as in §2.
• Emergency exit: when a membership condition fails (data interruption, multiple rates), the currency exits on that date as its own chain event. Re-entry opens a new membership period once the conditions hold again.
• Exit dates are never assigned retroactively to days that have already been calculated.

Membership ledger (32 periods, 29 current members). Founders on 2005-01-03: USD EUR JPY GBP CNY INR BRL CAD KRW MXN AUD IDR TRY SAR CHF PLN TWD SEK NOK DKK HKD ZAR and RUB (exited 2022-03-01, data interruption). Rule-derived accessions: ARS 2007-01-02 → 2011-10-31 and 2017-01-02 → 2019-09-01 (capital controls, both times); THB 2008; AED 2010; MYR 2013; ILS 2017; PHP 2018; SGD 2019; VND 2022. No other currency has crossed the entry threshold.

5. Weights

Nominal GDP from the IMF World Economic Outlook, taken point-in-time: the weight for year Y uses the Y−2 GDP estimate from the autumn Y−1 vintage (the last completed year, never a projection). Weights are normalized within the vintage; in the calculation they are re-normalized over the active member set. Twenty-two vintages (2005–2026) are stored with their source channel; two early vintages that no public archive serves any more are documented as a reconstruction (Sep 2004, from the archived per-capita table) and a proxy (2006, from the Sep 2006 vintage) — neither coincides with a membership event.

6. Input data — central-bank reference rates

One daily rate per currency, stored as units per USD, labelled by source, insert-only. Only days actually published by the source are stored; gaps are carried forward in the calculation and counted as staleness (§8). Sources: ECB euro reference rates (most currencies), Federal Reserve H.10 (INR 2005–2008, BRL/MXN 2005–2007, CNY early 2005), Central Bank of the Republic of China (Taiwan) for TWD, Bank of Russia for RUB (early 2005), Bank Indonesia for IDR (early 2005), BCRA Communication A3500 for ARS, State Bank of Vietnam central rate for VND, fixed pegs for SAR and AED, and USD = 1 by definition.

First print is final. Each official value is computed from the rates present at the moment of calculation (stored as its snapshot time) and is never recomputed. A rate that arrives or is revised later affects later days only. Verification replays the same as-of snapshot.

7. Two layers: Official and Live

8. Quality controls

Hard checks (the day is not written and an alert is raised): previous-day series set equals the member set; the invariant Π P^w = k holds to 1e-12; one active configuration; member count matches the ledger; chained k matches round₁₂(k_old·cf) exactly; Σ w = 1 to 1e-13; stale-weight limit — members whose rate is stale may not exceed 5% of total weight, nor 3% for any single member.

Soft checks (written, with an alert): derived cross rates (USD/TRY, EUR, CNY, JPY) versus market quotes around the ECB concertation time (14:10–14:20 Frankfurt) differ by more than 0.5%; a daily move above 10%; staleness beyond 5 calculation days (TWD 7, VND 15); a future-dated input. Known historical input gaps are listed as data notes on the index page.

Determinism: IEEE-754 float64, fixed alphabetical order, compensated summation, 12-decimal rounding of k and of published prices. Recomputation reproduces every stored value exactly on the same platform and to ≤ 1e-12 across platforms.

9. Verify any day yourself

1. Take the active members and raw weights for day t; normalize the weights.
2. For each member take the newest rate with fix_date ≤ t that existed at the day's snapshot time; V_i = 1 / units per USD.
3. ln M = Σ w_i ln V_i.
4. k = the chain row with the latest event date ≤ t.
5. P_i = k · V_i / M, rounded to 12 decimals.
6. Compare with the published value. Our own replay of the full record (148,510 values over 5,539 days at the method-1.0 load) reproduced every value with zero differences.

Chain constants of record (method 1.0): k₀ = 0.352857263515 · ARS exit 2011-10-31 cf 1.002217011490 · ARS exit 2019-09-02 cf 1.023042100923 · RUB exit 2022-03-01 cf 1.064142753270 · rebalance 2026-01-02 cf 1.017243263134, k = 0.331003528828.

10. Governance

Every official value and chain row carries a method version. Data revisions are not method revisions: a published day is never re-issued under the same method version. A methodological change starts a new version computed side by side; the published record of the old version stays intact. The input, weight, chain and output tables form a self-contained audit kit with no trading data in it. Machine-readable files (latest values, full series, daily immutable snapshots and the manifest chain) are prepared for publication; a public data endpoint will be announced on this page.

Method 1.0 · live record from 2026-08-22 · TEYMUR Index · Disclaimer — informational only, not investment advice. TEYMUR and TYMR are designations of Keltis.