Robust Inference in Financial Markets

Abstract

This thesis studies thick tails, found across financial markets, which present challenges for modern financial theory. Notably, traditional tools in financial econometrics deteriorate in the presence of thick-tailed predictors. The standard Koenker-Basset estimator of linear quantile regression is an example of a model with an unbounded influence function and is thus vulnerable to those predictors. To address thick tails, this thesis proposes a robust estimator of the linear quantile that is computable using existing software and has a bounded influence function, making it less vulnerable to non-Gaussian conditions frequently found in financial markets. Statistical properties of this estimator and empirical results when this estimator is used on market data are also described. Bounded influence functions are useful outside of purely financial econometric applications. This thesis connects the robust properties of the estimator developed to differential privacy, a mathematical privacy tool that protects individuals from identification under data analysis, and proposes differentially private and pseudo-private estimators. This estimator works well in comparison with existing private and pseudo-private regression methods, reducing noise under the same privacy budget constraints. Specifically, this paper presents three separate differentially private algorithms, and shows their utility in simulated experiments and real world data. In addition, this paper presents a pseudo-private algorithm for use in cases with small sample size where differential privacy is not feasible. Using the motivating example of Opportunity Atlas data, the estimator decreases noise significantly.