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Let s say I have a big VAR model with many variables. Then I run the model. How can I know which variables I should keep or get rid of if I want to ameliorate my model ?

What if my model has so many variables I can't remove it one variable after the other ? How to select the variables ?

Thank you

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I don't know a lot about VAR, but model selection is well-developed in the context of OLS and should be analogously applicable to VAR.

LASSO is the most commonly used method of model selection. The premise is to penalize choice of a non-zero coefficient for a variable. The variable only receives a nonzero coefficient if doing so reduces the sum of squared residuals in a meaningful manner.

The LASSO method also biases coefficients toward 0. To overcome this, there is a common two-step method of (1) estimating with LASSO to observe which variables have nonzero coefficients and (2) estimating the regular (non-LASSO) model while only restricting to coefficients chosen in the first step.

Belloni and Chernozhukov (2013) is a citation for this two-step approach.

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