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Vector Auto-Regressions (VAR)
This is a model that is used to predict several time series variables with one model. It is an improved or extended univariate autoregressive model where the values lagged in all k series occur as regressors. Vector auto-regression model on the other hand regresses a time series variables’ vector on the variables’ lagged vectors. VAR has a structure that supports joint test restrictions on more than two equations.
In Bayesian modeling, a posterior probability is the updated likelihood of a phenomenon happening after considering new information. The analyst uses the Bayesian theorem to revise the initial probability. In simple terms, we can define this type of probability as the chance of situation A happening given that situation B has already happened. The posterior probability is applied in a myriad of fields including medicine and finance to update the decision originally made before the new evidence was found.
Vector Error Correction Models
Vector error correction models are applied after the researcher has identified the long-run association between the variables. These models determine the direction taken by the causality between the variables. Vector error correction models can be used for variables that have a cointegration relationship. A vector error correction model can also be likened to a restricted vector auto-regression that has been curated to work with a nonstationary and cointegrated series.