Vector Autoregression (VAR) is a statistical method used for modeling the dynamic interdependencies among multiple time series variables. Unlike traditional regression models that focus on the relationship between one dependent variable and several independent variables, VAR simultaneously considers several variables as both predictors and outcomes. This makes VAR particularly useful for capturing the complex interactions and feedback mechanisms within a system.

In VAR, a system of equations is constructed, where each equation represents the behavior of one variable as a linear function of its past values and the past values of all other variables in the system. The model assumes that each variable in the system has a dynamic relationship with the lagged values of all variables, allowing for a more comprehensive understanding of how changes in one variable affect others over time.

Estimating a VAR model involves determining the optimal lag length and estimating coefficients through methods like the least squares approach. Once the model is estimated, it can be used for various purposes, such as forecasting, impulse response analysis, and variance decomposition.

VAR is widely applied in economics, finance, and other fields where the interactions between multiple time series variables are of interest. Granger causality tests, impulse response functions, and forecast error variance decomposition are common tools used to analyze the results of a VAR model, providing insights into the dynamic relationships and response patterns within the system. Overall, VAR is a valuable tool for understanding and predicting the behavior of interconnected time series variables.