Forex Partial-Correlation Network Report

About this report

This report tracks a statistical network built from the returns of 7 FX pairs (EUR/USD, GBP/USD, USD/JPY, USD/CHF, USD/CAD, AUD/USD, NZD/USD) — the forex-network-seven-majors network. For each date, every pair of currencies is checked for a direct relationship with every other pair — the result is a graph where nodes are currency pairs and edges are the relationships that date's data actually supports. The measurements below are what the rest of this report is built from:

Partial correlation

How strongly two pairs move together after netting out the influence of the other 6 — it isolates a direct relationship from one that only shows up because both pairs are being pushed around by some third pair they share.

Reading it: the sign tells you the direction of co-movement — positive means the two pairs tend to move the same way, negative means opposite. The magnitude tells you how strong that link is: values near zero are real but weak (the model kept the edge, but only just), while values approaching the plots' saturation ceiling (|0.6|) are about as strong as this dataset tends to produce. A pair with no edge at all isn't "weak" — the model found no direct link once the other five pairs are accounted for, often because both are only related through a shared driver (commonly a broad dollar move).

Granger causality

A test for whether one pair's past values help predict another pair's future values, beyond what that pair's own history already explains. It's used to give each edge a direction — which pair tends to move first.

Reading it: a direction means real statistical evidence of a lead-lag relationship, not just "these move together." Treat a bidirected result (both directions significant) with a little extra skepticism — fast, simultaneous reactions to shared news can produce that pattern even without a genuine two-way feedback loop. And a single day's direction is a noisy read on its own; it's worth checking whether it's held up over the last few days (see "Most recent direction changes" below) rather than trusting one date in isolation.

Density

The fraction of all possible pairings among these 7 pairs (21 total) that have an active edge on a given date — a rough gauge of how broadly interconnected the market is that day.

Reading it: rising density usually means the pairs are becoming more interconnected — often a sign of market stress or a single dominant macro theme (a broad risk-on/risk-off move, a shared dollar driver) crowding out pair-specific behavior. Falling density usually means pairs are behaving more independently — a calmer market, or one where pair-specific news is driving prices instead of a shared theme.

Mean absolute partial correlation

The average strength of that date's active edges, as opposed to how many there are. Density and this measure can move in opposite directions — e.g. more pairs becoming linked while each individual link gets weaker.

Reading it: a day with many weak edges (high density, low mean |partial corr|) is a different regime from a day with a few very strong ones (low density, high mean |partial corr|) — the first looks like broad, mild co-movement across the network; the second looks like a small cluster of pairs reacting intensely to the same thing. Read this measurement alongside density, not by itself.

Direction

Each edge is labeled i->j or j->i (one pair leads the other), i<->j (bidirected — both directions found significant), or undirected (the pairs are linked, but no lead-lag relationship was significant either way).

Reading it: a change from one state to another (see the direction-changes table below) is worth asking "what changed?" — a new edge often means a new shared driver, a lost edge often means one pair had idiosyncratic news that broke the prior co-movement, and swapped leadership (i->j to j->i) is worth checking against which currency's news calendar was actually active that day. The single biggest caveat: a lone, one-day flip is more likely statistical noise than a real regime change — Granger tests sitting near the FDR significance boundary can flicker in and out from one window to the next just from sampling noise. Trust a flip once it persists across a few consecutive dates, not the moment it first appears.

For more on the project behind this report, read the blog post Our Heroine Wiretaps Seven Currency Pairs; the source code that produced it is on GitHub.