Essays on the application of sparse penalized regressions in time series: meta-analysis, theory, and empirical applications

The present Thesis investigates the use of penalized regressions in the context of large time series, with a special focus on those that address the curse of dimensionality by providing variable selection, i.e. sparse penalized regressions. It consists of three essays that aim to address this topic in depth. In particular, each essay deals with a different problem linked to this topic, and for this reason, each of them employs a different scientific methodology. The first essay proposes a meta-analysis to empirically identify in which contexts the penalized regressions forecasts contribute significantly to the contemporary forecasting literature. The second essay characterizes the impact of serial dependence of covariates on the non-asymptotic estimation error bound of penalized regressions. Moreover, this essay proposes a new approach to improve the estimation performance of penalized regressions in a time series context. Finally, the third essay examines the performance of the proposed methodology through a theoretical analysis, an extensive simulation study, and an empirical application on real data.