Statistical Quantitative Methods in Finance: From Theory to Quantitative Portfolio Management

About the Author
About the Technical Reviewer
Preface
Contents
Introduction
1 Overview
2 Linear Regression
	2.1 Solving OLS
		2.1.1 Loss Function
		2.1.2 Variance of OLS Estimator
		2.1.3 Gauss-Markov Assumptions
		2.1.4 BLUE: Best Linear Unbiased Estimator
		2.1.5 Residuals: Standardized and Studentized
		2.1.6 Influential Points
	2.2 Normal Equations
	2.3 QR Factorization
		2.3.1 Householder Transformation
			Code Explanation
		2.3.2 Givens Rotation
		2.3.3 Gram-Schmidt Orthogonalization
			Code Explanation
	2.4 Singular Value Decomposition
	2.5 Maximum Likelihood
	2.6 Confidence Intervals
		2.6.1 Heteroskedasticity Consistent Standard Errors
		2.6.2 HAC Consistent Standard Errors
	2.7 Regularization
	2.8 Goodness of Fit
		2.8.1 Coefficient of Determination, R2
		2.8.2 Adjusted R2
		2.8.3 Pseudo R2
		2.8.4 Information Criterion
		2.8.5 Wald Test
		2.8.6 LM Test
	2.9 Diagnostic Measures
	2.10 Cointegration and Error Correction Model
		2.10.1 Spurious Regression
		2.10.2 ADF Test
		2.10.3 Cointegration
		2.10.4 Error Correction Model
	2.11 Instrumental Variables
3 Generalized Linear Model
	3.1 Score Equations
	3.2 Exponential Family of Probability Distributions
		3.2.1 Normal Distribution
			Application
			Code Explanation
		3.2.2 Poisson Distribution
			Application
			Code Explanation
		3.2.3 Binomial Distribution
			Application
			Code Explanation
		3.2.4 Gamma Distribution
			Application
			Code Explanation
		3.2.5 Inverse Gamma Distribution
		3.2.6 Multinomial Distribution
			Application
			Code Explanation
	3.3 Maximum Likelihood
	3.4 Binary Data
4 Kernel Regression
	4.1 Nadaraya-Watson Kernel Regression
	4.2 Application
		Code Explanation
5 Dynamic Regime Switching Models
	5.1 Model Formulation
	5.2 Model Estimation Using Maximum Likelihood
	5.3 Dynamic Transition Probabilities
	5.4 EM Algorithm
		5.4.1 K-Means Algorithm
			Code Explanation
		5.4.2 Gaussian Mixture Model
			Code Explanation
	5.5 Estimating Dynamic Transition Probabilities
	5.6 Application
		5.6.1 Taylor Rule
			Code Explanation
			Time-Varying Transition Probabilities
			Code Explanation
		5.6.2 Phillips Curve
			Code Explanation
6 Bayesian Methods
	6.1 Application
		6.1.1 Model Fitting
		6.1.2 Inference
		6.1.3 Hypothesis Testing
			Code Explanation
	6.2 Bayesian Linear Regression
		6.2.1 Application
			Code Explanation
		6.2.2 Conjugate Priors
	6.3 Bayesian Kernel Regression
	6.4 Bayesian Generalized Linear Regression
		6.4.1 Laplace Approximation
		6.4.2 Markov Chain Monte Carlo Method
			Importance Sampling
			Metropolis-Hastings Algorithm
			Gibbs Sampling
		6.4.3 Application
	6.5 Kalman Filter
7 Tobit Regression
	7.1 Problem Formulation
	7.2 Marginal Effects
	7.3 Tobit-I Implementation
	7.4 Heteroskedasticity in Tobit-I Model
	7.5 Tobit-II Model
		7.5.1 Fitting Heckman Two-Step Model
8 Random Forest
	8.1 Strength and Correlation of Trees
	8.2 Building a Random Forest
	8.3 Performance Metrics and Error Estimates
	8.4 Other Applications of Random Forests
	8.5 Financial Applications
		8.5.1 Marketing a Banking Product
9 Generalized Method of Moments
	9.1 GMM for Linear Equations
	9.2 GMM for Non-linear Equations
	9.3 Hansen J Test
	9.4 Application
		9.4.1 Code Explanation
10 Benchmarking Machine Learning Models
	10.1 Predicting Asset Returns
		10.1.1 Code Explanation
	10.2 Word2Vec
		10.2.1 Code Explanation
	10.3 Glove
		10.3.1 Code Explanation
	10.4 Regression Using Random Forest
		10.4.1 Code Explanation
Bibliography
Index