# VAR with 12 lags and irf function

My VAR-model contains 8 variables and 12 lags (lags determined by the information criteria), and the frequency of the variables is monthly (140 observations). When i am analyzing the irf function, the graphs show movement of the response variables from the first period. My dilemma is from theoretical perspective: does the irf function show the response of the variables after the impact have occurs (after 12 months, even though on the axis it is period 1), or show the variable from the initial period of shock (which is by definition and is the logical answer). Then why there is response from the first period? The graphs are also not smooth, in some periods they show increase, in some decrease, and in others they vary around zero. Is this logical from practical perspective?

My VAR-model contains 8 variables and 12 lags (lags determined by the information criteria), and the frequency of the variables is monthly (140 observations).

You may want to consider a different VAR model as the current one is pretty big for the sample size you have. You are estimating $8 \times 12 = 96$ parameters (plus the intercept and the error variance) in each of the VAR equations on a sample size of just 140. Therefore, your estimation error is likely to be high and you are likely to overfit considerably. The selection of as many as 12 lags may be due to seasonality, since you are using monthly data. Consider either

1. seasonally adjusting the data before you select the lag order of the VAR model; or
2. using seasonal dummies as exogenous regressors in a VAR model of a lower lag order, or
3. using a VAR(12) model but restricting some of the lags to zero (e.g. keeping lags 1 and 12 without the lags 2 to 11 -- just an example).

This will allow to trade off some estimation variance for model bias, and hopefully you can get more precise estimates of model parameters in terms of mean squared error.

does the irf function show the response of the variables after the impact have occurs (after 12 months, even though on the axis it is period 1), or show the variable from the initial period of shock (which is by definition and is the logical answer). Then why there is response from the first period?

This is rather software specific, and it is hard to answer without seeing the actual IRF graph and/or the code used to generate it. Details of IRFs such as what the axis mean should be available in the software manual.

The graphs are also not smooth, in some periods they show increase, in some decrease, and in others they vary around zero. Is this logical from practical perspective?

It may happen in general; you could take a look at papers that use IRFs, e.g. some macroeconomic studies. You will see different patterns there. Whether the IRFs make sense in your case depends on what you are actually modelling.

P.S. If you update your post with more details and post a comment under my answer so that I am notified, I will try to update it accordingly.