| Abstract [eng] |
We study the assumption of sparse structures of the underlying signal in a high-dimensional linear regression context. The sparsity assumption is assessed from theoretical and practical sides. In the theoretical part the exact and asymptotic distributions for a suitably centered and normalized squared norm of the product between predictor matrix and outcome variable are derived. We deem that the derived results can be crucial for further advancements in construction of statistical testing for sparsity procedures and related work. This is explored further by performing a Monte Carlo simulation study under the assumption of approximate sparsity, demonstrating quick convergence towards the limiting distribution. In the empirical part of the dissertation the viability of assuming sparsity in macroeconomic data is inspected by performing a comprehensive pseudo-real-time short-term forecasting study, focusing on GDP expenditure components and comparing the performance of popular sparse and dense approaches. The empirical results suggest that in many analyzed cases the sparsity assumption holds. LASSO methods showed acceptable forecasting performance, outperforming the benchmark ARMA and factor models. Furthermore, a LASSO-PC method is proposed, combining both sparse and dense approaches, in some cases demonstrating further improvements in forecast accuracy. |
