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Statistical Quantitative Methods in Finance.epub
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Statistical Quantitative Methods in Finance
Statistical methods are the cornerstone of many quantitative models. Their success derives from clear and concise mathematical formulation that suggests implementation details, along with their ability to be implemented and executed on ubiquitous, readily available computational hardware. Mathematical formulation of such models endows them with a virtue of intelligibility – practitioners can readily explain their features and acquire an intuitive understanding of how the models will behave when used with different kinds of data. For example, statisticians can readily explain the importance of uncorrelated error terms in ordinary least squares and what kinds of data and model characteristics may exacerbate the problem of correlated residuals in ordinary least squares (e.g., missing explanatory variables). This intuitive understanding aids in the deployment of statistical models to appropriate use cases, serves as a valuable verification method to ensure correct implementation, and enables modelers to explain model choice to statisticians and non-statisticians alike. In addition, they also serve as indispensable benchmarking tools for artificial intelligence models and are frequently deployed as components of advanced machine learning models. A comprehensive understanding of statistical models is foundational for both data science and machine learning disciplines.
This book explains statistical modeling using a range of applications drawn from the field of finance. It covers a wide swath of statistical modeling, beginning from ordinary least squares (OLS) and culminating in generalized method of moments (GMM) models used in econometrics. While the exegetical approach to describing statistical modeling adopted in this book begins with an explanation of the model followed by mathematical formulation, it is not obscured by excessive mathematics and notation. It includes practical applications drawn from the field of finance, along with hands-on code accessible online to illustrate the salient features of the model. Implementing code leverages libraries such as statsmodels, scipy, and sklearn. It also includes pseudo-code to aid explanation of code and models. By adopting a practical, hands-on focus while leveraging widely used, open source model implementations, this book enables readers to become experts at understanding statistical models, judiciously decide when to use a particular model, and effectively implement it using numerical libraries. It also enables the readers to write their own model implementations, though in most circumstances, use of widely adopted numerical libraries is preferred.
This book also provides a foundation for machine learning students to appreciate the statistical foundations of some of the most widely used machine learning algorithms, such as the naive Bayes method and the expectation-maximization (EM) algorithm. Readers inclined toward machine learning applications will find a rich variety of synergistic content between statistical methods and machine learning algorithms. This is particularly true for models such as random forests that are inspired by machine learning fundamentals such as decision trees and bagging and also derive some of their most attractive properties, such as robustness to overfitting, from statistical concepts like entropy, Gini impurity reduction, and ensemble learning. By delineating the statistical properties of random forests, along with demonstrating illustrative practical examples, this book provides a vista into their versatility. It showcases a good example where machine learning and statistics are being leveraged hand in hand to tackle complex problems that had been heretofore regarded as intractable using only statistical methods.
The book concludes with a chapter showcasing how statistical models can be used as benchmarking tools for machine learning algorithms.
Contents
1 Overview1
2 Linear Regression3
3 Generalized Linear Model41
4 Kernel Regression93
5 Dynamic Regime Switching Models111
6 Bayesian Methods157
7 Tobit Regression199
8 Random Forest219
9 Generalized Method of Moments241
10 Benchmarking Machine Learning Models253
Bibliography287
Index291
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