What the TDA gauge measures, in plain words. Take the last 60 trading days. Each day is a dot, positioned by how every market in the group moved that day — 12 markets means each dot lives in 12 dimensions. In a normal market those 60 dots form a shapeless fuzz: days don't relate to each other in any persistent way. When markets start moving in coordinated, repeating patterns — the kind of synchronised behaviour that builds before selloffs — the dot-cloud develops actual shape: loops and strands that persist. The TDA gauge is simply "how much shape does the cloud have right now", scored against the group's own last five years.
Direction: high = warning, low = normal. There is no good high reading.
| Verdict | What it means | What happened historically (next 60 days) |
|---|---|---|
| quiet | The cloud is shapeless — no unusual coordination. | Baseline odds: a >5% drawdown followed only ~17–20% of the time. Nothing to act on here. |
| watch | Structure building (above the 70th percentile), but below the audited alert line. | In-between zone — check the stress gauges more often. |
| alert | Heavy structure (>90th percentile) while turbulence still reads calm — coordination building under a quiet surface. This is the audited configuration. | A >5% drawdown followed 44–48% of the time (2–3× baseline) and volatility ran ~30% higher — expect a turbulent market even though today looks calm. |
| hot | Geometry hot, but turbulence is also elevated — the storm is already visible. | The stress gauges cover this case; geometry adds little once stress is overt. |
The commodities panel uses a different signal — hub concentration. The market tree below shows which markets are correlated to which; normally commodities trade on their own drivers (gold on rates, oil on supply). When the tree collapses so that everything connects through one hub, the group has become a single bet — and historically a >10% commodity drawdown followed 44% of the time vs 15% from distributed readings. Same direction: high concentration = warning.
Tree length (bottom chart) is context, not a signal: shorter = markets more correlated = less diversification inside the group. Its information overlaps the absorption ratio, so we don't issue verdicts from it.
All the odds above come from the audit on this page — ~12 independent episodes over 16 years, so treat them as odds-shifters, not certainties. One sentence to take away: high geometry reading + calm surface = the historical setup for rough markets; everything else here is context.
We don't add indicators because they're fashionable — every tool has to beat the incumbents somewhere, out loud. The original audit ran on 9 markets; when the board expanded to 20 in July 2026, the whole study was re-run on the full 18-market cross-asset panel against the site's existing fragility gauges, Turbulence and the Absorption Ratio. Trailing percentiles only, no look-ahead, results published win or lose. The per-class views above use the same machinery; the audited evidence below is from the cross-asset panels.
| Episode | Depth | TDA 60d before | TDA 20d before | Turbulence 20d before | Absorption 20d before |
|---|---|---|---|---|---|
| 2015–16 global | −23% | p45 | p83 | p83 | p17 |
| 2018 | −13% | p17 | p34 | p22 | p20 |
| COVID 2020 | −28% | p77 | p0 | p27 | p55 |
| 2022 | −15% | p67 | p66 | p70 | p24 |
Episodic, not universal: the TDA gauge built into 2015–16 and flickered before COVID; nothing warned before 2018 — which is exactly why this page sits alongside Systemic Risk rather than replacing it.
The decisive test, per panel: when a group's headline signal is hot (>90th percentile) while that group's Turbulence reads calm (<70th) — the configuration the incumbents call safe — what actually happened over the next 60 days?
| Panel · signal | P(>5% dd) hot | quiet | P(>10% dd) hot | quiet | Fwd 60d vol hot | quiet |
|---|---|---|---|---|---|---|
| Equities · TDA | 44% | 20% | 16% | 6% | 12.3% | 9.6% |
| Cross-asset · TDA | 48% | 17% | 11% | 5% | 11.1% | 8.1% |
| Commodities · hub concentration | 67% | 39% | 44% | 15% | — | — |
Those three pairs are the page's headline verdicts — each panel shows only the signal that passed its own audit. The failures are listed too: commodity TDA carries no drawdown information (hot and quiet readings led to identical outcomes); equity hub concentration is mildly inverted; tree tightness everywhere overlaps the absorption ratio and is shown as structure only.
A retraction. An earlier version of this page reported cross-asset hub concentration preceding ~2× worse drawdowns. After a calendar data-quality fix (mixed Sun–Thu/Mon–Fri trading weeks had been deleting whole days from the panel), that result does not replicate and is withdrawn. The hub-collapse signal is real only within commodities. We leave this note here because silently deleting findings is how quant marketing works, and this page isn't that.
A handful of episodes is still a small sample — a conservative block bootstrap puts these spreads at p≈0.10–0.16, so treat them as odds-shifters, not certainties. Parameters follow the literature (60-day windows per Gidea & Katz; 90-day correlations per the MST literature) with no optimisation. These are environment measures: they say a group's geometry is deforming, not that a crash is scheduled. Treat readings as a prompt to check the regime board and stress gauges, never as a standalone signal.
TDA landscape norm. For each asset class, each day, we take the trailing 60 daily return vectors of the group's markets — a cloud of 60 points — and compute its Vietoris–Rips persistent homology (H1: loops). The persistence landscape's L1 norm summarises how much robust geometric structure the cloud contains. Markets are scaled once by full-sample volatility so no single asset dominates; day-to-day volatility structure is deliberately preserved — it is part of the signal. Smoothed over 10 days; dials show the trailing 5-year percentile within the group's own history. After Gidea & Katz (2018), "Topological data analysis of financial time series: Landscapes of crashes."
Market tree. From each group's trailing 90-day correlation matrix we build Mantegna's distance d = √(2(1−ρ)) and extract the minimum spanning tree — the shortest network connecting the group's markets. Its mean edge length contracts when correlations rise; its shape shows which markets carry the connections; its collapse toward a single hub is the configuration the audit flags. After Mantegna (1999) and Onnela et al. (2003).
Groups: Equities (12 indices), Commodities (gold, silver, WTI, copper), Cross-asset (all 18 — adds US 10Y Treasuries and the Dollar Index; interpret with care, since safe-haven flows read as unification there). Crypto is excluded: 24/7 calendars distort a daily-close panel. Rates and FX are too few for their own tree. All series precomputed in the daily pipeline. Educational, not investment advice — see the Disclaimer.