Volatility Spillovers & Connectedness Services
Markets do not move in isolation—shocks in one spread to others, and the structure of that transmission shifts over time and across horizons. Spillover and connectedness analysis measures who transmits risk to whom and by how much; wavelet methods reveal how co-movement differs between the short and long run. MAS Research delivers both.
Volatility spillover and connectedness analysis measures how shocks and volatility transmit across markets or assets—quantifying who are the net transmitters and receivers of risk, and how connected the system is overall. The Diebold–Yilmaz framework (built on variance decompositions) is standard, and wavelet methods add a time-frequency view, showing how co-movement differs across short- and long-run horizons.
What spillover and connectedness analysis does
Financial markets are interconnected: a shock to one market—an equity index, a currency, an oil price—does not stay contained but transmits to others, sometimes amplifying into system-wide stress. Understanding this transmission is central to questions of contagion, systemic risk, hedging, and diversification. Spillover and connectedness analysis quantifies it: not just whether markets move together, but who transmits to whom, in which direction, and by how much.
The dominant framework is Diebold–Yilmaz connectedness, built on the forecast-error variance decomposition of a vector autoregression. It produces a connectedness “table” and a set of intuitive measures: a total connectedness index summarising how interlinked the system is; directional spillovers (how much each market transmits to, and receives from, all others); and net spillovers identifying each market as a net transmitter or net receiver of shocks. Estimated over rolling windows, these measures reveal how connectedness—and systemic risk—rises and falls over time, typically spiking in crises.
Wavelets: the time-frequency view
Connectedness answers “who and how much” over time, but there is a second dimension: horizon. Two markets might be tightly linked for short-term traders yet loosely coupled over the long run, or vice versa. Standard time-series methods blur these together. Wavelet analysis decomposes a series by frequency as well as time, so relationships can be examined separately at short, medium, and long horizons—revealing structure that a single aggregate correlation hides.
Wavelet coherence extends this to pairs of series, showing where in time and at which frequencies two markets co-move, how strong that co-movement is, and which leads which. It is especially powerful for questions about whether a relationship is a short-run trading phenomenon or a long-run fundamental link, and how that changes around crises. We use the Diebold–Yilmaz and wavelet approaches as complementary lenses—connectedness for the network of transmission over time, wavelets for how co-movement varies across horizons—choosing and combining them to fit the question.
Two complementary lenses on transmission
| Diebold–Yilmaz connectedness | Wavelet analysis | |
|---|---|---|
| Answers | Who transmits risk to whom, and how much? | How does co-movement differ by horizon? |
| Built on | VAR variance decompositions | Time-frequency decomposition |
| Key outputs | Total, directional & net spillovers | Wavelet power & coherence (lead/lag) |
| Time dimension | Rolling windows over time | Time and frequency jointly |
| Best for | Networks of transmission, systemic risk | Short- vs long-run co-movement |
Doing connectedness & wavelet analysis credibly
Connectedness analysis inherits the requirements of the VAR it is built on: stationarity of the inputs (returns or volatilities), sensible lag selection, and a stable system. A key practical choice is the use of generalized variance decompositions, which—unlike a Cholesky decomposition—do not depend on the ordering of the variables, removing an arbitrary assumption that would otherwise affect the results. The rolling-window length is also consequential: too short and the measures are noisy, too long and they smooth over the very dynamics of interest, so the choice is made deliberately and its sensitivity checked.
Wavelet analysis has its own care points: the choice of wavelet, the treatment of edge effects (the “cone of influence,” outside which estimates are unreliable), and the significance assessment of coherence. We report results only within the reliable region and test significance appropriately rather than reading patterns into noise. Across both methods, the honest framing matters: connectedness and coherence describe statistical transmission and co-movement—directional, lead–lag, and net-flow measures—which is strong evidence of linkage and influence, but is interpreted as transmission within the system rather than as proof of a structural causal mechanism. We state the inputs, the decomposition and window choices, and the diagnostics in full.
The window and the decomposition choice shape the results. Generalized variance decompositions avoid arbitrary variable ordering; the rolling-window length trades noise against smoothing. For wavelets, results are read only within the cone of influence. These choices are made deliberately and their sensitivity reported—not left at defaults.
Software
We deliver connectedness and wavelet analysis in established, reproducible tools—R (frequencyConnectedness, vars, WaveletComp, biwavelet) and MATLAB/Python—with generalized decompositions, rolling-window estimation, directional and net spillover measures, wavelet power and coherence with significance testing, and clear network and heatmap visualisations, all with versioned code.
How we deliver a spillover / connectedness study
This work sits within our wider financial-econometrics practice—so the decomposition is ordering-robust, the window is justified, and transmission is interpreted honestly.
We start from the set of markets or assets and the question—static network, time-varying connectedness, or horizon-specific co-movement. We prepare the inputs (returns or volatility measures), fit the underlying VAR with sensible lags, and compute connectedness with generalized decompositions over appropriate rolling windows; or, for horizon questions, run wavelet power and coherence analysis within the reliable region.
Reporting sets out the inputs and model, the decomposition and window choices, the total/directional/net spillover measures (or wavelet coherence results), robustness to those choices, and clear visualisations—so the transmission structure can be read and trusted.
You receive the connectedness measures (total index, directional and net spillovers, net transmitter/receiver identification) and/or wavelet coherence results, the time-varying dynamics, network and heatmap visualisations, robustness checks on window and decomposition, and reproducible analytical code and analysis-ready files (where appropriate and permitted).
Spillovers & connectedness across finance research
Transmission and co-movement questions run throughout finance and financial economics—so these methods apply across the field.
Systemic Risk & Contagion
Measuring how risk transmits across banks, markets, or countries, and how connectedness spikes in crises—a core systemic-risk application.
Energy & Commodity Markets
Spillovers between oil, gas, commodities, and financial markets, and how they co-move across horizons—a heavy user of both methods.
Portfolio & Hedging
Understanding transmission and horizon-specific co-movement to inform diversification and hedging decisions.
Currency & International Markets
Cross-market and cross-country volatility transmission in FX and international equity markets.
Cryptocurrency & Digital Assets
Connectedness within crypto and between crypto and traditional markets—an active, fast-growing area.
Green & Sustainable Finance
Spillovers between green assets, conventional markets, and energy—how clean and traditional finance interconnect.
Spillovers & connectedness: common questions
Studying risk transmission across markets?
Whether the question is who transmits systemic risk to whom, or how co-movement differs between the short and long run, we deliver connectedness and wavelet analysis—ordering-robust, horizon-aware, and reported with the robustness these methods demand.