Vector autoregression (VAR), a statistical method widely employed in time series analysis and econometrics, serves to model the intricate relationships among multiple time series variables. Unlike univariate autoregressive models that focus solely on predicting a single variable based on its own past values, VAR models consider the interdependencies among various variables.
The process of VAR modeling unfolds in several key steps, encompassing the specification and estimation of the VAR model, ongoing model evaluation and refinement through inferences, prediction, and analysis of the model’s structure. Least squares methods are applied for estimating VAR models, with the model’s order, represented by the lag parameter ‘p,’ determining the number of past observations considered. Selecting an appropriate lag order is a critical phase in VAR modeling, often achieved through metrics like the Bayesian Information Criterion (BIC) or the Akaike Information Criterion (AIC).
VAR models find extensive application in fields such as macroeconomics and finance, where the interactions among multiple time series variables are of interest. Additionally, in cases where cointegration among time series variables is identified, VAR models serve as the foundation for more intricate models like Vector Error Correction Models (VECM). Cointegration implies long-term relationships between variables, and VECM facilitates the modeling of both short-term dynamics and long-term equilibrium.