This dissertation provides theoretical and practical guidance for the use of graphical models, a tool from machine learning and network theory, in financial econometrics and macroeconomic forecasting.

Chapter 1 gives a short introduction to the challenges, methods and findings studied in Chapter 2 to Chapter 4.

Chapter 2 studies a framework to estimate a high-dimensional inverse covariance (precision) matrix for a portfolio allocation problem. I integrate two competing streams of literature, graphical models and factor models, to develop a technique, Factor Graphical Lasso (FGL), that combines the benefits of both aforementioned approaches. I prove consistency of FGL for estimating precision matrix, portfolio weights and risk exposure for three formulations of the optimal portfolio allocation. FGL-based portfolios are shown to exhibit superior performance over several prominent competitors in the empirical application for the S&P500 constituents.

Chapter 3 develops a methodology to construct sparse portfolios in high dimensions. Motivated by a stylized fact that portfolios based on holding all assets fail to generate positive return during economic downturns, I hypothesize that holding sparse portfolios is the key to hedging during recessions. Given unrealistic assumptions imposed by the existing allocation techniques, I develop a strategy for constructing sparse portfolios that could be used as a hedging vehicle during economic downturns. I establish consistency properties of the optimal sparse allocations and provide guidance regarding the distribution of portfolio weights. I also examine the merit of sparse portfolios during different market scenarios and show their robustness to recession periods.

Motivated by the stylized fact that forecasters often use common sets of information and hence they tend to make common mistakes, Chapter 4 proposes a new approach to forecast combinations that separates unique errors from the common errors. I call the proposed algorithm Factor Graphical Model (FGM) and show that it overcomes the challenge of recovering the structure of precision matrix under the factor structure. I prove consistency of forecast combination weights and the Mean Squared Forecast Error estimated using FGM. An empirical application to forecasting macroeconomic series in big data environment demonstrates the merits of FGM.