NXS-GRX methodology – GLOBAL RISKS INDEX (GRIx)

01Principles

Eight principles

A family of indices, not one monolithic score

NXS-GRX (canonical data, provenance and risk) publishes twenty domain indices, four pillar indices, a composite and six instruments. The composite never appears without every pillar and domain beside it, and no independent dimension is collapsed silently.

Classes with intervals, never league tables

Every value carries a 90% interval from Monte Carlo analysis over normalisation, weights, imputation and aggregation. Countries are placed in risk classes with a stated class probability; pages list countries by name or code, never by value.

No data is not zero

A missing input is shown as missing, an imputed input is flagged, and a value is withheld when coverage falls below the method's minimum. An empty profile, an unavailable source and an observed zero render differently.

Every value resolves to its source

Each value carries its source release, licence, retrieval time, method version and transformation chain (W3C PROV). A correction anywhere propagates to every dependent value and is logged publicly.

Measured, modelled and perceived are kept apart

Status glyphs separate observed, reported, estimated, inferred, forecast, simulated, scenario and expert input. Perception signals form their own instrument and are never blended into measured risk.

Systemic by construction

Standalone risk and coupling-adjusted risk are reported side by side, from typed dependency networks across trade, finance, energy, food, infrastructure and information.

Licence-gated and reproducible

A source enters a public value only when its licence admits that use; withheld values are counted, not hidden. Methods, code paths, seeds and digests are published per release so any value can be recomputed.

Information, not authority

NXS-GRX is research and risk-analytics information. It is not a rating, an official classification, a warning, a benchmark or advice, and it never decides for an institution.

02Pipeline

Source to profile

Every indicator declares its place on the risk chain and its polarity, so aggregation never mixes directions silently.

computation

The NXS-GRX pipeline, from source to profile

Graph24 nodes

Graph

01Sources

02Harmonise

03Indicators

04Sub-indices

05Domains

06Pillars

07Composite and instruments

08Outputs

100%

List

Event streams
SOURCES · SOURCES · near real time
Admitted alert, Earth-observation, conflict-event, price and market streams for the Pulse instrument.
208 registered sources
SOURCES · SOURCES · licence-gated
Every source is registered with its licence; nothing enters a public value its licence does not admit.
Scenario families
SOURCES · SOURCES · labelled
Socio-economic and warming pathways and transition families, used as labelled scenario structures.
Surveys and elicitation
SOURCES · SOURCES · perception
Structured expert elicitation and public surveys, kept apart from measured risk.
Dependency network
NETWORK · NETWORK · six layers
Trade and input–output, finance and debt, energy, food trade, infrastructure and information links.
Harmonised series
HAR · HAR · units, areas, time
Source series mapped to Nexus concepts and code lists; units, areas and frequency aligned; no imputation.
451 indicators
IND · IND · Indicator Standard
Native indicators with definitions, units, polarity, levels and crosswalks; flagged imputation only here.
86 sub-indices
SUB · SUB · normalised
Normalised, weighted and aggregated components inside each domain.
20 domain indices
IDX · IDX · 1,000 draws
Twenty domain indices with Monte Carlo intervals and sensitivity.
Systemic coupling score
COUPLING · COUPLING · S
Contagion on the dependency network: DebtRank, clearing and threshold cascades.
Hazard and threat exposure
PILLAR · PILLAR · HTE
What can strike, how often, how hard and who and what stands in its way?
Human and systems vulnerability
PILLAR · PILLAR · VUL
How susceptible are people, livelihoods, ecosystems and essential systems to harm when a shock arrives?
Macro-financial and structural fragility
PILLAR · PILLAR · MSF
How much fiscal, financial, external, digital and technological room does the system have before stress turns into crisis?
Lack of coping and adaptive capacity
PILLAR · PILLAR · LCC
Can institutions anticipate, absorb, respond, recover and adapt?
Pulse
INSTRUMENT · INSTRUMENT · weekly
Nowcast anomaly against each country's own history.
Outlook
INSTRUMENT · INSTRUMENT · 1 to 36 months
Calibrated event probabilities with verification scorecards.
Tail
INSTRUMENT · INSTRUMENT · exceedance
Exceedance curves, return-period losses, catastrophic register.
Pathways
INSTRUMENT · INSTRUMENT · to 2100
Fan charts under named scenario families.
Perception
INSTRUMENT · INSTRUMENT · separate
Perceived severity and the perception gap.
NXS-GRX Composite Risk
COMPOSITE · COMPOSITE · geometric
Composite = (HTE × VUL × MSF × LCC)^(1/4), each pillar on 0–10 floored at 0.1; pillar = expert-weighted geometric mean of its domain indices
195 country profiles
PROFILES · PROFILES · classes, intervals
Every domain, pillar and instrument per country, never ranked.
54 series indices
SERIES · SERIES · global to technology
Specialised indices from the same domain indices.
API, tiles and bulk files
ACCESS · ACCESS · machine
Public cut, SDMX keys, vector tiles, bulk files.
NXS-GRX Coupled Risk
COMPOSITE · COMPOSITE · × (1 + κ·S)
Coupled = Composite × (1 + κ·S), S = systemic coupling score in [0,1] from the dependency network, κ disclosed per release (baseline κ = 0.25); reported beside the standalone composite, never instead of it

Not runIn progressDone

FIG 2. Select a stage to trace it; Simulate run plays the pipeline in order. Every stage keeps provenance, so a correction at a source reaches every value that depends on it.

HazardExposureVulnerabilityImpactLikelihoodRiskCapacityResponseFinancingOutcome

03Pillars

Pillars and domain indices

Pillar values are expert-weighted geometric means of their domain indices (equal weights in the baseline, recorded per release); a pillar needs two thirds of its domains, otherwise it is withheld.

04Composite

Composite and coupled composite

The composite never appears alone: profiles show each pillar and domain beside it.

Composite: Composite = (HTE × VUL × MSF × LCC)^(1/4), each pillar on 0–10 floored at 0.1; pillar = expert-weighted geometric mean of its domain indices
Coupled composite: Coupled = Composite × (1 + κ·S), S = systemic coupling score in [0,1] from the dependency network, κ disclosed per release (baseline κ = 0.25); reported beside the standalone composite, never instead of it
Uncertainty: 1,000 Monte Carlo runs over normalisation, weights, imputation, aggregation (geometric, arithmetic, Mazziotta–Pareto); 90% intervals; Sobol first-order and total-order indices per release
Coverage: Each pillar needs two thirds of its domain indices; otherwise the composite is withheld and the pillar shown alone

FIG 3 · Simulator: four pillars to the composite and coupled composite

Pillars (0 to 10)

HTE · Hazard and threat exposure4.2

VUL · Human and systems vulnerability5.1

MSF · Macro-financial and structural fragility3.6

LCC · Lack of coping and adaptive capacity4.8

Coupling and uncertainty

Systemic coupling score S0.4

Coupling multiplier κ0.25

Input uncertainty (sd)0.4

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runs in your browser

Simulator: Composite = (HTE × VUL × MSF × LCC)^¼ with each pillar floored at 0.1; Coupled = Composite × (1 + κ·S). Draws vary weights, aggregation and inputs. The positions are starting points, not NXS-GRX values.

05Classes

Classes and intervals, never league tables

A class is printed with its probability (share of Monte Carlo draws inside the class). Below 60% the adjacent class is printed too (for example High, 54% · Very high, 41%). Fixed bounds keep classes comparable across editions; intervals show when two countries cannot be told apart. Lists are ordered by name or code.

Very low0.0 to < 2.0

Low2.0 to < 3.5

Medium3.5 to < 5.0

High5.0 to < 6.5

Very high6.5 to 10.0

06Construction

Ten construction steps

The steps follow the OECD/JRC handbook on composite indicators and the statistical audit practice of the JRC Competence Centre on Composite Indicators, referenced for method only.

Theoretical frameworkRisk chain from hazard to outcome; four pillars; twenty index domains; explicit polarity and risk component for every indicator.

Data selectionindicator definitions with SDMX-compatible keys, crosswalks to source code lists, evidence class A–E and the licence register.

Missing dataFlagged imputation only at IND layer (dimension mean, indicator median, multiple imputation); modelled share capped per composite; coverage minimum two thirds.

Multivariate analysisCorrelation structure, principal components and Cronbach's alpha per sub-index; incoherent components are re-specified before release.

NormalisationMin–max with fixed goalposts, percentile rank or identity on native 0–10 scales; skew and kurtosis treatment (winsorisation, log) above |skew| 2 and kurtosis 3.5.

Weighting and aggregationEqual or expert weights recorded per composite; geometric, arithmetic, Mazziotta–Pareto, product or geometric-complement aggregation as each definition declares; floor 0.1 before geometric means.

Uncertainty and sensitivityAt least 1,000 Monte Carlo runs over the declared alternatives; 90% intervals, class probabilities and Sobol indices published with every release.

Back to the dataDriver decomposition to indicator level; every value opens to its inputs, sources and transformation chain.

Links to other indicatorsPublished crosswalks and correlation checks against established indices, used as validity evidence, never as inputs to be re-weighted.

Visualisation and disseminationClasses and intervals, never league tables; machine access through API, SDMX keys, tiles and bulk files; corrections and versions public.

07Release

One edition, run as a workflow

An edition is a run: the evidence cut freezes, sources pass the licence gate, 451 indicators are computed for 195 profiles, 1,000 draws give the intervals, and two approval gates stand before anything is published.

on: evidence cut

Edition release run

In progressTriggered by NXS-GRX run service13 jobs2 approval gates6 matrix jobs

Graph

01Cut

02Ingest

03Ingest

04Indicators

05Indices

06Indices

07Indices

08Uncertainty

09Uncertainty

10Review

11Review

12Publish

100%

Timeline

Job0 d5 d10 d15 d20 dTarget

Evidence cut frozenNXS-GRX run service1 h

Licence gateLicence register1 h

HarmoniseNXS-GRX run service6 h

IndicatorsNXS-GRX run service4 h

Sub-indicesNXS-GRX run service1 h

Domain indicesNXS-GRX run service1 h

Coupling scoreNXS-GRX run service2 h

1,000 Monte Carlo drawsMonte Carlo engine3 h

Intervals, classes, SobolMonte Carlo engine1 h

Statistical auditIndependent reviewer10 d

Steward reviewStewards10 d

Profiles and seriesFoundry2 h

Tiles and bulk filesFoundry2 h

End to end on the longest path: about 20.9 d of proposed target service levels. Gates wait for the people named; bars with a fading end have no fixed length.

Steps

Evidence cut frozen
Cut · NXS-GRX run service · 1 hour
Input vintages pinned
NXS-GRX run servicePostgreSQL ledger (row-level security)
Licence gate
Ingest · Licence register · 1 hour
Admitted, isolated or withheld
Licence register
Harmonise matrix · 150 sources
Ingest · NXS-GRX run service · 6 hours
Units, areas, time
NXS-GRX run serviceindicator standard
Indicators matrix · 451 × 195
Indicators · NXS-GRX run service · 4 hours
Derivations, flagged imputation
NXS-GRX run serviceindicator standard
Sub-indices matrix · 86
Indices · NXS-GRX run service · 1 hour
Normalise, weight, aggregate
NXS-GRX run serviceTested model kernels
Domain indices matrix · 20
Indices · NXS-GRX run service · 1 hour
Twenty domain indices
NXS-GRX run serviceTested model kernels
Coupling score
Indices · NXS-GRX run service · 2 hours
DebtRank, clearing, cascades
Dependency networkTested model kernels
1,000 Monte Carlo draws matrix · 1,000
Uncertainty · Monte Carlo engine · 3 hours
Weights, normalisation, aggregation, imputation
Monte Carlo engine
Intervals, classes, Sobol
Uncertainty · Monte Carlo engine · 1 hour
90% intervals · Class probabilities · Sensitivity
Monte Carlo engine
Statistical audit approval
Review · Independent reviewer · 10 days
Coherence, stability
Tested model kernels
Steward review approval
Review · Stewards · 10 days
Method, evidence, public-safe screen
PostgreSQL ledger (row-level security)
Profiles and series matrix · 195 + 59
Publish · Foundry · 2 hours
Published with intervals
Public cut APINS-1 UNI catalogue
Tiles and bulk files
Publish · Foundry · 2 hours
ISO3, ADM1, ADM2, H3 · Deposit with DOI
Vector tilesZenodo deposit

Artifacts

Artifact	Job	Who	Stage
Cut record	Evidence cut frozen	NXS-GRX run service	Cut
Withheld counts	Licence gate	Licence register	Ingest
HAR series	Harmonise	NXS-GRX run service	Ingest
IND values	Indicators	NXS-GRX run service	Indicators
SUB values	Sub-indices	NXS-GRX run service	Indices
IDX values	Domain indices	NXS-GRX run service	Indices
S per country	Coupling score	NXS-GRX run service	Indices
Draw set with seed	1,000 Monte Carlo draws	Monte Carlo engine	Uncertainty
Uncertainty report	Intervals, classes, Sobol	Monte Carlo engine	Uncertainty
Audit note	Statistical audit	Independent reviewer	Review
Release decision	Steward review	Stewards	Review
Edition	Profiles and series	Foundry	Publish
Tiles	Tiles and bulk files	Foundry	Publish
DOI	Tiles and bulk files	Foundry	Publish

DoneIn progressWaiting for approvalQueuedApproval gateMatrix jobYou are here

From the evidence cut to published profiles, tiles and API: every stage keeps provenance and two review gates stand before release. The canvas shows where a request stands at the marked job; it is an illustration, not the status of a real request. Durations are proposed target service levels. Select a job for its steps, the people who act, the technology it runs on and what it produces.

08Aggregation

Five aggregation shapes

Try them on the fiscal and public debt index: switch the aggregation and watch the class and interval move.

Aggregation	What it does	Domain indices using it
geometric	Weighted geometric mean after a floor of 0.1: partial compensation, so weakness in one component cannot be fully offset by strength in another.	Fiscal and public debt risk · Climate physical hazard · Water security risk · Health security risk · Socio-economic vulnerability · Energy security risk · Infrastructure fragility · Cyber risk · Lack of coping capacity
mazziotta pareto	Mean adjusted by the spread across components (non-compensatory): unbalanced profiles read as riskier than balanced ones with the same mean.	Financial stability risk · Food insecurity risk · Conflict risk
arithmetic	Weighted arithmetic mean: full compensation, used where components are substitutes.	External dependence risk · Climate transition exposure · Environmental pressure · Displacement pressure · Governance weakness · Technology concentration risk
geometric complement	Complement of the geometric mean of complements: any single high exposure lifts the index, as for multi-hazard exposure.	Multi-hazard exposure
product	Product of normalised components: risk exists only where all components are present, as for space-weather exposure.	Space-weather exposure

FIG 4 · Simulator: aggregate fiscal and public debt risk on your numbers

Components (0 to 10)

Public debt burden sub-index · w 23.0

Financing pressure sub-index · w 25.0

Debt composition risk sub-index · w 1.57.0

Budget rigidity and revenue weakness sub-index · w 14.0

Fiscal position sub-index · w 16.0

Contingent liability sub-index · w 13.0

External vulnerability sub-index · w 0.55.0

Aggregation

Weight uncertainty ±%25

Mix aggregation alternatives (0 or 1)1

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runs in your browser

Contribution of each component (leave one out)

Simulator: the index's published aggregation run on numbers you set, with 1,000 draws over weights and aggregation. The slider positions are starting points for the explainer, not NXS-GRX values.

09Missing data

No data is not zero

Imputation happens only at the indicator layer and is always flagged: dimension mean, indicator median or multiple imputation, as each definition declares. Each composite caps the share of its weight that may rest on modelled or imputed inputs and withholds its value below its coverage minimum. Coverage is published as a vector per country and indicator, never as a single complete flag; fragile and small-island states are where gaps cluster, so their coverage is shown first.

10Status

Status and value states

Glyph	Status	Means
●	OBSERVED	Measured directly and published by the source
□	REPORTED	Reported or declared by a publisher, not independently measured
◆	ESTIMATED	Estimated or modelled by a stated method
▲	INFERRED	Inferred from related signals
◇	FORECAST	Probabilistic statement about a future period
◈	SIMULATED	Output of a simulation or stochastic event set
○	SCENARIO	Conditional on a named scenario, not a prediction
◎	EXPERT INPUT	Structured expert judgement

Value state	Means
`PUBLISHED`	Released in an edition with interval, class and sources
`NO_DATA`	No admitted input; not a zero
`INSUFFICIENT_EVIDENCE`	Coverage below the method minimum; value withheld
`WITHHELD`	An input's licence or the public-safe screen does not admit public display; counted
`DEGRADED`	Published with a stated quality limitation

11Instrument

Pulse

Question

What has changed since the last structural cut?

Cadence

Weekly nowcast, event-driven between releases

Method

Mixed-frequency dynamic factor model over admitted event streams (multi-hazard alerts, Earth observation, conflict events, prices, shipping, market stress), expressed as a standardised anomaly against each country's own history.

Outputs

Pulse anomaly by domain
Signals for review with their sources
Threshold crossings for subscribers

Status of outputs

OBSERVEDINFERRED

Pulse publishes with the first edition. Weekly anomalies by country and domain will appear here as a timeline, each signal with its sources and status.

12Instrument

Outlook

Question

How likely are defined adverse outcomes over a stated horizon?

Cadence

Monthly, horizons of 1, 3, 12 and 36 months

Method

Calibrated probabilistic ensembles (statistical, machine learning and structured expert elicitation) for defined events: conflict onset and escalation, acute food insecurity phase shifts, debt distress signals, disaster losses, displacement surges. Verified with Brier skill, reliability diagrams, ROC and CRPS against outcomes.

Outputs

Event probabilities with credible intervals
Forecast verification scorecards
Back-test record per model version

Status of outputs

FORECAST

FIG 7 · Explainer: how forecasts are verified

Event base rate0.15

Signal strength1.4

Over- or under-confidence (1 = calibrated)1

Bias (log-odds)0

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runs in your browser

Explainer: 3,000 synthetic forecasts and outcomes from your settings, scored the way every Outlook model version is scored: reliability diagram, Brier score, skill against climatology and ROC area.

13Instrument

Pathways

Question

How does risk move under alternative futures to 2030, 2050 and 2100?

Cadence

Each annual edition

Method

Pillar and domain values projected under SSP × warming-level combinations and central-bank-network transition scenario families (used as labelled scenario structures), with demographic, urbanisation, governance and conflict pathways; fan charts, not point paths.

Outputs

Fan charts per domain and pillar
Scenario cascades
Adaptation and transition levers

Status of outputs

SCENARIOSIMULATED

FIG 8 · Explorer: a pathway fan chart to 2100

Starting index4

Drift per decade0.35

Volatility per decade0.45

Shock chance per decade %10

Shock size1

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runs in your browser

Explorer: 2,000 paths from your drift, volatility and shock settings, shown as a fan chart (50% and 90% bands, median line) against the class bounds. Pathways editions project each domain under named scenario families; this explainer uses no scenario data.

14Instrument

Tail

Question

What does the rare, severe end of the distribution look like?

Cadence

Each annual edition, event-updated

Method

Event loss tables and year loss tables, exceedance-probability curves, probable maximum loss at 1-in-100 and 1-in-250, expected shortfall, compound-event copulas and a register of low-probability, high-impact and global catastrophic risks.

Outputs

Exceedance curves and return-period losses where loss can be modelled
Protection-gap readings
Catastrophic and frontier risk register

Status of outputs

SIMULATEDMODELLED

FIG 9 · Explorer: exceedance, return-period loss and the protection gap

Frequency and severity

Events per year (Poisson)1.2

Median event loss20

Severity spread (lognormal σ)1.4

One risk-transfer layer

Attachment per event60

Limit per event240

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runs in your browser

Explorer: 20,000 simulated years from your frequency and severity settings; the exceedance curve, average annual loss, 1-in-100 and 1-in-250 annual losses, expected shortfall, and how one layer splits loss into retained, transferred and gap. Units are yours; nothing here is a modelled loss for any place.

15Instrument

Coupling

Question

Where does risk travel across systems and borders?

Cadence

Each annual edition, quarterly network refresh

Method

Typed multi-layer dependency network (trade and input–output, finance and debt, energy, food trade, infrastructure and digital links); contagion estimated with DebtRank, Eisenberg–Noe clearing and threshold cascades; systemic importance and exposure scores per country and system.

Outputs

Systemic coupling score S
Coupled composite beside standalone
Transmission paths with status and references

Status of outputs

ESTIMATEDSIMULATED

FIG 10 · Expected direct couplings between systems (row affects column)

	WAT	ENE	FOO	HLT	BIO	FIN	TRD	INF	DIG	SEC
Water
Energy
Food
Health
Biodiversity
Finance
Trade
Infrastructure
Digital
Security

Weak expected couplingModerate expected couplingStrong expected coupling

Schematic: the couplings the Coupling instrument expects to estimate. Strengths here are expectations from the literature the edition will cite, not estimates; each becomes ◆ ESTIMATED with its method and references in an edition.

FIG 11 · Simulator: how a shock cascades across systems

Shock enters at

Shock size0.8

Coupling strength0.7

Failure threshold0.5

Buffers and redundancy0.2

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runs in your browser

Simulator: a threshold cascade on a schematic network of systems. Edge strengths are expected couplings (weak, moderate, strong), not estimates; the shock, coupling, threshold and buffers are yours. NXS-GRX estimates couplings per edition before any coupled value is published.

16Instrument

Perception

Question

Where does perceived risk differ from measured risk?

Cadence

Annual expert and public survey waves

Method

Structured expert elicitation and public risk surveys, published as their own dimension with a perception-versus-measured gap per domain; never blended into the composite.

Outputs

Perceived severity by domain and horizon
Perception gap
Respondent coverage statement

Status of outputs

EXPERT INPUTREPORTED

Perception publishes with the first survey wave. Perceived severity by domain and horizon, with the perception gap against measured values.

17Geography

Six geographic levels

G0GlobalThe global series aggregates country values population- and exposure-weighted and reads the global systems directly.G1Country195 country profiles: the 193 UN member states and the 2 UN observer states.G2First administrative level (ADM1)Where boundaries and inputs admit; boundary versions are recorded.G3Second administrative level and below (ADM2+)Selected indicators and hazard layers.G4Cities and functional areasCities, river basins, coasts, corridors and islands.G5Hexagonal grid (H3)Resolution 4 to 7 for national views, finer for local layers; one fabric for hazard, exposure and capacity.

18Validation

Validation in public

Back-testing of Structural and Outlook values against realised outcomes

Back-testing of Structural and Outlook values against realised outcomes: disaster mortality and losses, acute food insecurity phases, conflict onset and fatalities, debt distress episodes, displacement

Forecast verification with Brier skill score

Forecast verification with Brier skill score, reliability diagrams, ROC area and CRPS, published per model version

Independent statistical audit of each major methodology version (correlation structure

Independent statistical audit of each major methodology version (correlation structure, coherence, uncertainty and rank stability)

Golden-value tests for every kernel with hand derivations

Golden-value tests for every kernel with hand derivations, so a value can be recomputed by anyone

Country right of reply and public correction log

19Revisions

Revisions and corrections

Methodology carries a semantic version; a change that breaks comparability is back-cast where inputs allow, and a correction propagates to every dependent value with a public log entry.

DraftComputedEvidence boundReviewedApproved for releasePublishedCorrectedSuperseded

20Reproducibility

Recompute any value

Each release publishes definitions, method versions, code paths, random seeds and content digests; every kernel is tested against hand-derived golden values.

Indicator Standard: 451 indicators · 106 composites · 501 crosswalks
Hazard Standard: 14 domains · 120 families · 905 hazards · 281 HIPs 2025 hazards
model registry: 670 methods in 23 fabrics
Snapshot: saeedvaladbaygi/nexus-foundry@31a753f769a9b3262945d0a07888a960bd9c9ee2

One grammar, seven instruments

Eight principles

A family of indices, not one monolithic score

Classes with intervals, never league tables

No data is not zero

Every value resolves to its source

Measured, modelled and perceived are kept apart

Systemic by construction

Licence-gated and reproducible

Information, not authority

Source to profile

Pillars and domain indices

HTE · Hazard and threat exposure

VUL · Human and systems vulnerability

MSF · Macro-financial and structural fragility

LCC · Lack of coping and adaptive capacity

Composite and coupled composite

Classes and intervals, never league tables

Ten construction steps

One edition, run as a workflow

Five aggregation shapes

No data is not zero

Status and value states

Pulse

Outlook

Pathways

Tail

Coupling

Perception

Six geographic levels

Validation in public

Back-testing of Structural and Outlook values against realised outcomes

Forecast verification with Brier skill score

Independent statistical audit of each major methodology version (correlation structure

Golden-value tests for every kernel with hand derivations

Country right of reply and public correction log

Revisions and corrections

Recompute any value

Disagree with a method?

Status

What NXS-GRX is not

Institutions and sources