Estimation and Inference for High Dimensional Time Series Data Models

The thesis introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. Oracle inequalities are established for the sparse group LASSO (sg-LASSO) estimator within a framework that allows for the mixing processes and recognizes that the financial data and the macroeconomic data may have heavier than exponential tails. The inferential theory for the sg-LASSO in the high-dimensional setting is developed. The debiased central limit theorem is established for low-dimensional groups of regression coefficients and the HAC estimator of the long-run variance based on the sg-LASSO residuals is studied. This leads to valid time-series inference for individual regression coefficients as well as low-dimensional groups, including Granger causality tests. Lastly, the thesis extends the structured machine learning regressions for prediction and inference to panel data consisting of series sampled at different frequencies. Several empirical applications of prediction and Granger causality are provided for macroeconomic and financial data, including textual analysis based data.