Forecast Error Variance Decomposition (FEVD)
Also known as: Variance Decomposition, Error Variance Decomposition, VD Analysis, Varyans Ayrıştırması
Forecast Error Variance Decomposition (FEVD) is a multivariate time series technique used within Vector Autoregression (VAR) frameworks to quantify what proportion of the forecast error variance of each variable is attributable to shocks from every other variable in the system. It is widely used by econometricians, macroeconomists, and financial researchers to assess the relative importance of different structural disturbances in driving short-run and long-run fluctuations across interconnected economic series.
Key highlights
- Provides an intuitive percentage-based measure of shock importance that is easy to communicate to non-technical audiences
- Works naturally within the standard VAR framework, requiring no additional structural assumptions beyond shock identification
- Allows comparison of shock contributions across multiple forecast horizons, distinguishing short-run from long-run drivers
- Complements impulse response functions by offering a magnitude-based rather than path-based view of dynamic relationships
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
FEVD is appropriate when working with a stationary or cointegrated multivariate time series system estimated as a VAR or SVAR, and the goal is to understand the relative contribution of different shocks to forecast uncertainty over time. It is most informative when applied alongside impulse response analysis. Key assumptions include correct VAR lag order, valid identification of structural shocks (e.g., via Cholesky or sign restrictions), and system stationarity or proper differencing. It is less suitable for very small samples where VAR estimates are imprecise. Alternatives include historical decomposition for actual episodes and structural FAVAR models for large systems.
Strengths & limitations
- Provides an intuitive percentage-based measure of shock importance that is easy to communicate to non-technical audiences
- Works naturally within the standard VAR framework, requiring no additional structural assumptions beyond shock identification
- Allows comparison of shock contributions across multiple forecast horizons, distinguishing short-run from long-run drivers
- Complements impulse response functions by offering a magnitude-based rather than path-based view of dynamic relationships
- Results depend critically on the chosen shock identification scheme; Cholesky ordering imposes arbitrary causal priority among variables
- Requires a correctly specified VAR, including appropriate lag length and inclusion of all relevant variables, to avoid misleading variance shares
- Assumes linearity and parameter stability across the sample period, which may not hold during structural breaks or regime changes
- Variance shares can be sensitive to the stationarity treatment; ignoring cointegration may distort long-horizon decompositions
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
Does the ordering of variables in a Cholesky decomposition affect FEVD results?
Yes, substantially. Cholesky decomposition assigns all contemporaneous covariance to the first variable in the ordering, so placing a variable first grants it a larger share of explained variance at short horizons. Researchers should either justify the ordering on economic grounds, test sensitivity by trying alternative orderings, or use sign restrictions or external instruments for more robust structural identification.
How do I interpret a FEVD share of, say, 30% at horizon 8?
It means that 30% of the variance of the 8-step-ahead forecast error for the variable of interest is attributable to the identified shock in question, under the chosen identification scheme. The remaining 70% is explained by all other shocks in the system combined. Higher shares indicate that the shock is a more important source of forecast uncertainty at that horizon.
Should I report FEVD at one horizon or multiple horizons?
Reporting across multiple horizons is strongly recommended because the pattern of variance shares often changes substantially over time. Short horizons reveal which shocks dominate immediate fluctuations, while long horizons uncover the structural drivers of persistent movements. Presenting a table or plot covering horizons from 1 to 20 or 24 periods is standard practice in applied macroeconomics.
Sources
- 1.Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.ISBN 978-3-540-40172-8
You have read it. What now?
Cite this page
ScholarGate. (2026, June 2). FEVD. ScholarGate. https://scholargate.app/econometrics/forecast-error-variance-decomposition