Lagged values in a LASSO regression

Hi all,

While working on the statistics for my thesis, I became confused while building up my model.

I am currently working on a forecasting model with the use of a LASSO regression. The model is build as follows: the unemployment rate is the dependent variable and as exogenous variables I have the autoregressive terms and three additional indices.

My problem now lays with the lagged values in my model. At first I thought that I could just add for each of the variables 12 lagged values, since a LASSO regression just gives them a coefficient of zero if they are not significant. But that seemed illogical and based on nothing. So then I looked further, and since I have a limited amount of observations (around 200) I thought about using the AICc. Therefore, I made different models by always adding a lagged value of a variable (stepwise every variable) until it had the lowest value. In the end this lead to 8 lagged values of the autoregressive terms, 4 lagged values of the first index, 2 lagged values of the 2nd index and 1 lagged value of the 3th index.

When putting this in R and letting the LASSO regression run again with those specific lags for the variables, this lead once again to coefficients of zero. Which leads to my question if my way of working is correct or if I made a mistake along the way?

Thanks in advance!