Empirical likelihood approach for high-dimensional moment restrictions with dependent data

Abstract: Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a unified framework, with high-dimensional parameters identified by moment conditions. As the number of parameters and moment conditions may surpass the sample size, we propose adding a double penalty to the empirical likelihood criterion to induce sparsity and facilitate dimension reduction. Notably, we utilize a marginal empirical likelihood approach despite temporal dependence in the data. Under regularity conditions, we provide asymptotic guarantees for our method, making it an attractive option for estimating large-scale multivariate time series models. We demonstrate the versatility of our procedure through extensive Monte Carlo simulations and three empirical applications, including analyses of US sectoral inflation rates, fiscal multipliers, and volatility spillover in China's banking sector.