Vector Autoregression (VAR) Model
Vector Autoregression Model · Also known as: vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).
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When to use it
Use VAR when you have several continuous time series that influence one another and you want to model their joint dynamics or forecast them together, with a reasonably long sample (at least about 60 observations). It assumes the series are stationary, that an appropriate lag length has been chosen via AIC or BIC, and that the residuals show no remaining autocorrelation. It is not appropriate for non-stationary series without differencing or cointegration handling, or for short samples where the number of variables times lags inflates the parameter count.
Strengths & limitations
- Treats all series symmetrically, capturing mutual causality and feedback without pre-assigning cause and effect.
- Supports joint forecasting and dynamic analysis (impulse responses, variance decomposition) across the whole system.
- Each equation is a straightforward least-squares regression, so estimation is simple once the lag length is fixed.
- Requires stationary series; on non-stationary data the coefficients are inconsistent and differencing or a cointegration check is needed first.
- The parameter count grows with the number of variables times the lag length, so short samples risk over-parameterisation.
- Coefficients are hard to interpret individually; analysis usually relies on impulse responses and variance decompositions instead.
Frequently asked
How does VAR differ from ARIMA?
ARIMA models a single time series from its own past, while VAR models several series together so that each variable depends on the recent history of every variable in the system. VAR is the right choice when the series influence one another; ARIMA suffices when you only need to forecast one series on its own.
How do I choose the lag length p?
Select p with an information criterion such as AIC or BIC, fitting the model at several lag lengths and keeping the one that the criterion favours. Too few lags leave residual autocorrelation; too many inflate the parameter count.
What if my series are not stationary?
VAR coefficients are inconsistent on non-stationary series. First difference the data to make it stationary, or test for cointegration — when the series are cointegrated, a Vector Error Correction Model (VECM) captures both the short-run dynamics and the long-run equilibrium.
Why is my sample too small for VAR?
The number of parameters scales with the number of variables multiplied by the lag length, so a system with several variables and a few lags can demand many coefficients. With fewer than about 60 observations this leads to over-parameterisation, and a more parsimonious model such as ARIMA may be more reliable.
Sources
- Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer. DOI: 10.1007/978-3-540-27752-1 ↗
How to cite this page
ScholarGate. (2026, June 1). Vector Autoregression Model. ScholarGate. https://scholargate.app/en/econometrics/var-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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