Lagged values in a Lasso regression 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!
 A: You are comparing LASSO and subset selection. It is not quite clear how you tune the penalty intensity of LASSO$\color{red}{^*}$, while for subset selection you use AICc as the criterion.
It seems you are only considering nested models in subset selection. E.g. you select between models with lags $\{1\}$, $\{1, 2\}$ or $\{1, 2, 3\}$ but not $\{2\}$ $\{3\}$, $\{1, 3\}$  or $\{2, 3\}$. This may or may not make sense depending on the application. Meanwhile, when using LASSO you consider any combination of variables; you do not use some sort of hierarchical penalty where a coefficient can be set to zero only if all of the subsequent coefficients are set to zero, given some ordering of variables. It can very well be this difference that is driving your results. If one of the nonnested combinations tends to work best, LASSO will select it and this will "contradict" the nested subset selection. 
Another difference between LASSO and subset selection is that LASSO will shrink some of the coefficients part of the way towards zero, in contrast to unpenalized models in the subset selection. This may yield improved performance and result in different variables with nonzero coefficients in LASSO vs. subset selection even if you consider nonnested as well as nested models there.
I would not do LASSO on the model from subset selection based on AICc. I would either use LASSO as is or subset selection. Regarding the choice of the maximum lag length in LASSO, you could use subject-matter knowledge (perhaps macroeconomic theory). Consider how distant past is still relevant. If there are seasonal patterns, you could add as many lags as there are seasons.
$\color{red}{^*}$Typically, the penalty intensity of LASSO is tuned via cross validation. It is also possible to use information criteria such as AICc instead; I have seen it done in some papers. The rationale behind the latter choice is that AICc, AIC and leave-one-out cross validation are asymptotically equivalent. AICc is a convenient alternative when cross validation is problematic, e.g. in time series analysis that you are dealing with.
