Vector Autoregression (VAR)

Vector autoregression (VAR) is a multivariate time-series model in which each variable is regressed on its own lagged values and the lagged values of every other variable in the system.

벡터자기회귀(VAR)는 각 변수를 자신의 과거값과 체계 내 다른 모든 변수의 과거값에 회귀시키는 다변량 시계열 모형입니다.

How do I model how several time series influence each other over time?

여러 시계열이 시간에 따라 서로 어떻게 영향을 주는지 어떻게 모형화하나요?

A vector autoregression treats several time series as jointly determined, regressing each on lags of all the variables, and is used for Granger causality tests, impulse response analysis, and forecasting. It fits stationary or differenced series, while cointegrated nonstationary series call for a vector error correction model.

When to use Vector Autoregression (VAR)

• Two or more interrelated economic or business time series
• Testing whether past values of one series help predict another (Granger causality)
• Tracing the dynamic response of variables to a shock with impulse response functions

When to use something else

• Nonstationary series that are cointegrated: use a vector error correction model (VECM)
• One outcome with predictors that are not affected by it: use ARIMAX or a distributed lag regression

Assumptions and requirements

• Stationary variables, or appropriately differenced
• Lag order chosen with AIC, BIC, or similar criteria
• No remaining residual autocorrelation
• Enough observations relative to the number of parameters

What the analysis reports

• Lag selection criteria
• Coefficient estimates for each equation
• Granger causality tests
• Impulse response functions with confidence bands
• Forecast error variance decomposition

How to report it

A VAR([p]) model, with lag order selected by [criterion], indicated that [variable X] Granger-caused [variable Y], χ²([df]) = [value], p = [value].

Related methods

• Vector Error Correction Model (VECM)
• ARIMA
• Granger Causality Test

Run Vector Autoregression (VAR) on Quorant