Machine Learning in Finance: Estimation, Inference and Financial Applications for Correlated Data

Abstract

Modern technologies have generated big data at an unprecedented scale and speed, which has spurred remarkable progress in high-dimensional statistical research and o ers alternative solutions to some prominent nancial research questions facing the \curse of dimensionality". This thesis endeavors to utilize some newly developed statistical methods to address the \curse of dimensionality" in nancial research, while providing new perspectives on the economic and nancial implications. For instance, Chapter One of this thesis addresses the \factor zoo enigma" while taking account of high correlations observed between factors. I introduce a newly developed machine learning method to dissect this chaotic factor zoo: the OWL estimator, which is not only e cient in dimension reduction but also robust with correlated variables. Chapter Two extends the econometric theory of the OWL estimator I derived in Chapter One, and mainly concerns the underlying statistical properties of the OWL estimator under less restrictive conditions. Furthermore, I utilize the nodewise LASSO technique to identify and quantify the bias in the OWL estimator and I propose the de-biased OWL estimator before deriving its asymptotic normality property. Chapter Three employs the OWL shrinkage method in the portfolio optimization problems, to exploit contemporaneous relations between stocks. I also develop a exible algorithm which can incorporate bespoke constraints on portfolio weights should investors have any prior information on individual stocks. This thesis covers a broad range of research areas spanning between empirical asset pricing and econometric inferences. It contributes to the literature concerning high-dimensional statistics, with an emphasis on the LASSO-type estimators, while taking account of correlated variables. It also contributes to the empirical asset pricing literature: this thesis sheds light on new perspectives of the \factor zoo enigma", where the importance of factor correlations is highlighted. It also enriches the literature pertaining to portfolio optimization problems. The OWL shrinkage method o ers an extension to the existing LASSO shrinkage method while further exploiting stocks' contemporaneous relations.