High-dimensional quantile regression and forecast combination

The first introduces a high-dimensional threshold quantile model for investigating the relationship between public debt and GDP growth. From theoretical perspectives, our paper makes three contributions to existing literature: first, we generalize the Lasso and adaptive Lasso method to time series context. Second, we introduce high-dimensional threshold quantile model and show that under mixing and sparse conditions, the proposed Lasso estimators can consistently estimate regression coefficients irrespective of the identification of the tipping point. Furthermore, when tipping point is identified, the threshold estimator achieves the super-consistency rate. Third, we show that adaptive Lasso simultaneously achieves optimal consistency rate and validate the tipping point effects even when the number of covariates is much larger than sample size.;The second chapter contributes to the growing debate on the relationship between GDP growth rate and publice debt and provides crucial insights for the current debate on tipping point effects in the debt-growth nexus stirred by Reinhart and Rogoff (2010a). Our empirical contributions are fourfold. First, we confirm the estimated 90% tipping point under median cross-country regression. Second, once we allow for the debt-growth nexus to be country-specific, the estimated tipping point thresholds are much lower than 90% for most economies. The thresholds wildly range between 10% to 100% across countries. That is to say, the public debt could start influencing economic growth under moderate debt level. Third, the tipping point effects are more common in developing countries than developed countries. For developed countries, the pattern of tipping point effects is relatively prominent on the upper-tail of the growth distribution; whereas the threshold effects are widespread on entire GDP growth distribution for developing countries. Lastly, we identify country-specific channels whereby the public debt affects economic growth. Channels for the impacts of public debt in developing countries are monetary policies, government spending, and capital investment; while demox graphic factors and the infrastructure investment are eminent transmissions for developed countries.;In third chapter, we propose a new forecast combination method which selects the forecast weights by minimizing Shibata criterion. The advantages of the proposed method are twofold. The estimator is asymptotically optimal in the sense of achieving the lowest possible one-step-ahead mean-squared prediction error for same-realization autoregressions. The Monte Carlo simulation results show that the proposed method has low out-of-sample mean-square prediction error.