Again, consider the monthly macroeconomic data set of Problem 1. Apply boosting to the problem with subcommands \(\mathrm{n}\). trees \(=10000\) and shrinkage \(=0.001\).

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.