The number of penalty parameters as well as the depth of the penalty grid are left to user input. The number of penalty parameters is generally inconsequential; glmnet uses 50 by default, but we have not found any substantial improvements in considering more than 10.
However, the choice for the depth of the penalty grid can affect forecasting performance. By default, the penalty grid starts at the smallest value in which all model coefficients should theoretically be zero and then uses a bisection approach to find a tighter, data-specific bound from which it decrements in log-linear increments according to the user's specification.
BigVAR provides some diagnostic procedures to help best determine penalty grid depth. Plotting a BigVAR.results object displays the in-sample MSFEs of all penalty parameters, highlighting that selected by rolling cross-validation with a green vertical line. It is preferable that the selected penalty parameter is in the middle of the grid of values. If it is at the edge, it is possible that forecasts can be improved with a deeper grid. However, setting the grid too deep will increase computation time, as smaller penalty values require a more iterations for our algorithms to converge.