Glossary

R: Forecast-error variance decomposition from a VAR

A tool from VAR analysis that breaks down the forecast-error variance of each variable into the proportions attributable to shocks from each variable in the system. FEVD reveals the relative importance of different shocks over various horizons.

title: FEVD (Forecast-Error Variance Decomposition)

slug: fevd

Definition

Why It Matters

Policy analysis and risk management require understanding not just whether variables move together, but which shocks drive those movements. FEVD quantifies the contribution of each structural shock to the uncertainty in each variable's forecasts. This allows analysts to identify dominant sources of fluctuation — for example, whether oil price shocks or monetary policy shocks explain more of the variation in inflation — and to trace how these contributions evolve from short to long horizons.

Example

A three-variable VAR models GDP growth, inflation, and the interest rate. At the one-quarter horizon, GDP's own shock explains 90% of its forecast-error variance, but at the 12-quarter horizon, interest rate shocks account for 40%. This pattern suggests that monetary policy has delayed but substantial effects on output, a finding that directly informs the pacing of policy interventions.

```r

library(vars)

var_fit <- VAR(data, p = 4, type = "const")

fevd_result <- fevd(var_fit, n.ahead = 20)

plot(fevd_result)

```

Related Terms

Software Notes

R: Use vars::fevd() for reduced-form FEVD; svars package for structural FEVD after identification. Stata: Use irf create after var to compute and graph FEVD. Python: Use statsmodels.tsa.vector_ar.VAR with the fevd() method; results can be plotted and summarized over custom horizons.