Consider, again, the monthly macroeconomic data set of Problem 1. Apply Group Lasso by letting

(a) lagged predictors of CPIAUCSL as group 1, and

(b) predictors of other variables with the same lag form a group.

Data From Problem 1:

The dependent variable of interest is the inflation, consumer price index all items, which is CPIAUCSL. The predictors consist of the first 6 lagged values of all 122 variables available. Perform a Lasso linear regression analysis on the data, including coefficient profile plot and the CV plot. Use CV to select the optimal penalty parameter. Plot the resulting estimated coefficients \(\hat{\beta}_{i}\) of the Lasso regression.