I want to study the impulse response function and the variance decomposition by fitting a VAR model. The lag length criteria gave me this result. What's the problem?
Based on the criteria (lowest AIC, lowest BIC, etc.), zero lag is preferred, which means a model with just an intercept but no lags. From such a model you will not be able to obtain impulse response functions, while variance decomposition will be trivial (none of the variables explains the variance). The selection of zero lag suggests that VAR might not be a good model for your data, so you might want to explore alternative models.
If zero lag presents mean there is no contribution of past value of the exogenous variable. So it is not a time series problem It is simple regression