Vector Autoregression

What is Vector Autoregression (VAR)? VAR Explained

Vector Autoregression (VAR) is a time series model used to analyze the dynamic relationship between multiple variables. It is an extension of the autoregressive (AR) model, which models the relationship between a single variable and its lagged values.

In VAR, instead of modeling a single variable, we consider a system of multiple variables. The VAR model captures the interdependencies among these variables and allows for the analysis of their mutual interactions over time.

The VAR model assumes that each variable in the system is a linear combination of its own lagged values and the lagged values of the other variables in the system. The order of the VAR model, denoted as p, represents the number of lagged terms used in the model. For example, a VAR(2) model uses the values of the variables up to two time steps in the past.

The parameters of the VAR model are estimated using various estimation techniques, such as least squares or maximum likelihood estimation. The estimated coefficients represent the strength and direction of the relationships between the variables in the system.

Once the VAR model is estimated, it can be used for various purposes, including forecasting, impulse response analysis, and variance decomposition. Forecasting involves using the estimated model to make predictions about the future values of the variables. Impulse response analysis measures the dynamic response of the variables to a shock in one of the variables. Variance decomposition analyzes the contribution of each variable to the total variation in the system.

VAR models are widely used in econometrics, finance, and other fields where the relationships between multiple time series variables need to be studied. They provide a flexible framework for capturing the dynamics and interdependencies among variables, allowing for more comprehensive and insightful analysis of time series data.