SVNexus · Contagion
Diebold–Yilmaz connectedness
Also called: spillover index, connectedness index, DY index
The Diebold–Yilmaz index measures how much of each market's forecast-error variance comes from shocks to other markets, summarized as total connectedness.
Definition
The Diebold–Yilmaz framework (2009, 2012, 2014) measures connectedness between markets using variance decompositions from a vector autoregression. For each market it asks what share of its forecast-error variance, over a horizon, is due to shocks originating in other markets.
Summing those cross-market shares gives a total connectedness (spillover) index; the same table also gives directional and net measures for each market.
Intuition
If markets were isolated, each one's surprises would come only from its own shocks. In a connected system, a large part of every market's uncertainty is imported. The index turns that idea into one number and a matrix showing who transmits to whom.
Tracked over time with a rolling window, total connectedness tends to jump during crises, which makes it a compact gauge of systemic stress.
How it's calculated
Fit a VAR(p) to N series (returns or volatilities). Compute the H-step generalized forecast-error variance decomposition θij(H) (Pesaran–Shin), which does not depend on variable ordering, and normalize each row so it sums to one: θ̃ij = θij / Σj θij. Then:
Total: S(H) = 100 × Σi≠j θ̃ij(H) / N
From others to i: Si← = 100 × Σj≠i θ̃ij / N To others from i: S→i = 100 × Σj≠i θ̃ji / N
The net measure for market i is S→i − Si←: positive for net transmitters, negative for net receivers. Pairwise net spillovers come from θ̃ji − θ̃ij.
Example: in a three-market system, if 40% of market A's 10-day forecast-error variance comes from shocks to B and C, A's "from others" share is 40%, and its contribution to the total index is 40 / 3 ≈ 13.3 points. The total index is the average of the three markets' "from others" shares.
How to read it
Read total connectedness against its own history: a sustained rise well above its norm means shocks are spreading more widely. Use the directional table to see which markets drive the rise.
Results depend on the VAR lag order, horizon H and window length; report them and check robustness.
Common mistakes
- Using the original Cholesky decomposition without noting that results depend on the variable ordering.
- Comparing indices built from different horizons or windows.
- Reading transmission as a causal mechanism.
- Mixing returns and volatilities in one system without a reason.
- Over-reading small month-to-month changes in a rolling index, which partly reflect estimation noise.
In Saqrid
SVNexus measures total market connectedness and labels a stress regime when it runs well above its own history.
Open SVNexus.
Go deeper
Saqrid Institute lesson: Volatility Spillover (Diebold–Yilmaz). Lesson text is open to read without an account.