Glossary

Variance Decomposition

See Forecast-Error Variance Decomposition (FEVD). In the broader connectedness literature (Diebold and Yilmaz, 2014), variance decompositions from a VAR are interpreted as a network: each entry in the decomposition table represents a weighted, directed link showing what share ...

Definition

See Forecast-Error Variance Decomposition (FEVD). In the broader connectedness literature (Diebold and Yilmaz, 2014), variance decompositions from a VAR are interpreted as a network: each entry in the decomposition table represents a weighted, directed link showing what share of one variable's forecast-error variance is attributable to shocks from another.

Why It Matters

Variance decomposition answers a fundamental question in multivariate analysis: "What drives what, and by how much?" By breaking down each variable's forecast uncertainty into contributions from every other variable, it reveals the directional flow of shocks in a system — essential for understanding contagion in financial markets, policy transmission in macroeconomics, and systemic risk.

Example

In a three-variable VAR (GDP growth, interest rate, stock returns), variance decomposition shows that 60% of the forecast-error variance of stock returns at the 10-quarter horizon is attributable to interest-rate shocks, while only 15% comes from GDP shocks. This identifies interest-rate policy as the dominant driver of stock-market uncertainty.

Related Terms

Software Notes

  • SPSS: Not built-in; use the R plugin with the vars package
  • R: fevd() from the vars package; e.g., fevd(var_model, n.ahead = 10)
  • Stata: irf create after var estimation; irf table fevd to display decomposition