VAR model: many parameters, but short time series We are wondering how many degrees of freedom are sensible in a model and if there is a rule of thumb.
We have a time series of 57 periods, with 4 endogenous variables and 3 exogenous variables in a VAR model. Preferably, we would like to use a lag length of 4 (since our data is quarterly). 
We were wondering if that is sensible.
 A: If you use 4 lags of both the endogenous and the exogenous variables, that is likely too many. You will have as many as $4 \times (4 + 3) + 1 = 29$ variables ($+1$ due to the intercept) per equation to be estimated using only 57 data points. You will likely end up with large standard errors and unstable point estimates. This will be bad regardless whether you will use the model for hypothesis testing (you will have low power) or forecasting (you will have high variance). 
You could perhaps keep lag 1 and lag 4 (but skip lags 2, 3) and see if the model residuals look alright. Alternatively, you could use Bayesian VAR (BVAR) or perhaps regularized VAR instead. However, regularization normally requires finding the shrinkage parameter from the data (e.g. using cross validation), and that again becomes a problem in small samples.
A: I agree with the abovementioned answer. The data points you need should be at least equal to the total number of parameters. So if B is the number of exogenous variables, M the endogenous and p the model order then you will need at least MxMxp+BxMxp data points. However if u have noise and other issues you need 5 to 10 times more than that. Instead of using cross validation, you can use model order selection criteria like BIC and AIC. Thus you dont have to break your dataset into more segments. Could you plz also clarify what you mean exactly with 57 periods? You mean data points right?
