Machine learning techniques have been increasingly adopted in economics and finance for forecasting, policy evaluation, and structural modeling. Despite their empirical success, a key question remains: can machine learning methods—originally developed for tasks in computer science—effectively address the unique challenges posed by economic data, such as weak signals, cross-sectional dependence, and temporal dependence? This dissertation explores the theoretical foundations and empirical relevance of modern machine learning methods in econometric applications. Chapter I examines the performance of several popular machine learning estimators in high-dimensional regressions with low signal-to-noise ratios. We show that Ridge regression and ℓ2-regularized neural networks can effectively exploit weak and possibly nonlinear signals, while Lasso may fail to outperform a zero benchmark due to its reliance on sparsity. Both theoretical analysis and empirical studies across multiple economic datasets highlight that signal weakness, rather than lack of sparsity, may be the main bottleneck in prediction. Chapter II develops non-asymptotic guarantees for deep autoencoders within a highdimensional nonlinear factor model. We show that autoencoders can consistently recover latent structures, with approximation errors diminishing as dimensionality and sample size increase. These results justify the use of autoencoders in tasks such as asset return prediction and structured matrix completion for causal analysis. Chapter III studies the application of Recurrent Neural Networks (RNNs) in modeling nonlinear time series. Under a nonlinear autoregressive and moving-average model with exogenous variables, we establish finite-sample error bounds for RNN-based predictions. These bounds reveal the role of function smoothness, input dimensionality, and process dependence in shaping prediction accuracy. Our analysis shows that RNNs are particularly effective in capturing nonlinear dynamics in noise, offering advantages over traditional nonparametric methods. Together, these essays contribute to a deeper understanding of the conditions under which machine learning methods are both theoretically sound and practically useful for econometric modeling and economic prediction.