Penalized Convex Estimation in Dynamic Location-Scale models

This paper introduces a two-step procedure for convex penalized estimation in dynamic location-scale models. The method uses a consistent, non-sparse first-step estimator to construct a convex Weighted Least Squares (WLS) optimization problem compatible with the Least Absolute Shrinkage and Selection Operator (LASSO), addressing challenges associated with non-convexity and enabling efficient, sparse estimation. The consistency and asymptotic distribution of the estimator are established, with finite-sample performance evaluated through Monte Carlo simulations. The method's practical utility is demonstrated through an application to electricity prices in France, Belgium, the Netherlands, and Switzerland, effectively capturing seasonal patterns and external covariates while ensuring model sparsity.