VectorAutoregressionModellen

Vector Autoregression, often abbreviated as VAR, is a statistical model used in time series analysis. It's an extension of the univariate autoregression model to multivariate time series. Instead of predicting a single time series based on its own past values, a VAR model predicts each time series in a system based on the past values of all time series in that system. This allows for the capture of interdependencies and dynamic relationships between multiple variables over time.

A VAR model is characterized by its order, denoted by 'p', which represents the number of past lags of all variables included in the model. The general form of a VAR(p) model involves a system of equations where each variable at a given time point is a linear combination of its own past values and the past values of all other variables in the system, up to 'p' periods ago, plus an error term.

VAR models are widely used in econometrics and finance to forecast multiple related economic indicators, analyze the impact of shocks on different series, and understand causality between time series. The estimation of VAR models typically involves ordinary least squares (OLS) for each equation. Model selection, such as determining the optimal lag order 'p', can be done using information criteria like AIC or BIC. Diagnostic checks are crucial to ensure the model adequately captures the data's dynamics and that the residuals are well-behaved.