The PCA is intended to convert covariates to linearly uncorrelated. On the opposite VAR model captures the linear interdependencies among covariates. Will then the PCA transformation improve VAR model or there is risk of decreasing its predictive power?
Best Answer
$$ pca: X=ST $$ $$ VAR: S_t=phi S_{t-1}+epsilon_t=hat{S_t}+epsilon_t $$ $$ Forecasting: hat{X}_t=hat{S}_tT=phi S_{t-1}T=phi X_{t-1} T^{-1}T=phi X_{t-1} $$ Couple of thoughts:
1) Performing PCA on your dependent variables won't change the predictive power, as shown above
2) if you do PCA on some set of exogenous variables (not shown above), it may give you better insight on whether all variables included in the set of exogenous variables provide predictive power, which is something you might consider doing for model selection… But it would have no affect on the predictive power on the model (it'd be equivalent to transforming your betas), so there's no reason to do it if your purpose is to strengthen your model.