Glossary

VAR (Vector Autoregression)

A multivariate time-series model in which each variable is regressed on its own lags and the lags of every other variable in the system. VARs are foundational in macroeconomic forecasting, monetary-policy analysis, and financial-connectedness research.

Definition

Why It Matters

VAR models impose minimal a priori restrictions on the dynamic interactions among variables, letting the data reveal the relationships rather than imposing potentially incorrect structural assumptions. This flexibility makes VARs the workhorse of macroeconomic time-series analysis. They serve as the basis for impulse response functions, forecast-error variance decompositions, and Granger causality tests. However, VARs estimated in levels can produce unreliable results when variables contain unit roots, making prior unit-root and cointegration testing essential.

Example

A three-variable VAR(2) model for the Turkish economy includes GDP growth, CPI inflation, and the policy interest rate. Each variable is regressed on two lags of all three variables. The model is estimated by seemingly unrelated regression (SUR), and impulse response functions show that a monetary-policy shock reduces inflation with a two-quarter lag while temporarily depressing output.

Related Terms

Software Notes

SPSS: Use Analyze > Forecasting > VAR for basic VAR estimation, though functionality is limited compared to R and Stata.
R: Use VAR() from the vars package for estimation, causality() for Granger causality, irf() for impulse responses, and fevd() for forecast-error variance decomposition. Lag selection uses VARselect().
Stata: Use var for VAR estimation, vargranger for Granger causality, irf create and irf graph for impulse responses, and fevd for variance decomposition. Use varsoc for lag-order selection.