Statistical Analysis of Financial Data in S-Plus

Contents
Part I Data Exploration, Estimation And Simulation
1 Univariate Exploratory Data Analysis
1.1 Data, Random Variables and Their Distributions
1.1.1 The PCS Data
1.1.2 The S&P 500 Index and Financial Returns
1.1.3 Random Variables and Their Distributions
1.1.4 Examples of Probability Distribution Families
1.2 First Exploratory Data Analysis Tools
1.2.1 Random Samples
1.2.2 Histograms
1.3 More Nonparametric Density Estimation
1.3.1 Kernel Density Estimation
1.3.2 Comparison with the Histogram
1.3.3 S&P Daily Returns
1.3.4 Importance of the Choice of the Bandwidth
1.4 Quantiles and Q-Q Plots
1.4.1 Understanding the Meaning of Q-Q Plots
1.4.2 Value at Risk and Expected Shortfall
1.5 Estimation from Empirical Data
1.5.1 The Empirical Distribution Function
1.5.2 Order Statistics
1.5.3 Empirical Q-Q Plots
1.6 Random Generators and Monte Carlo Samples
1.7 Extremes and Heavy Tail Distributions
1.7.1 S&P Daily Returns, Once More
1.7.2 The Example of the PCS Index
1.7.3 The Example of the Weekly S&P Returns
Problems
Notes & Complements 2 Multivariate Data Exploration
2.1 Multivariate Data and First Measure of Dependence
2.1.1 Density Estimation
2.1.2 The Correlation Coefficient
2.2 The Multivariate Normal Distribution
2.2.1 Simulation of Random Samples
2.2.2 The Bivariate Case
2.2.3 A Simulation Example
2.2.4 Let’s Have Some Coffee
2.2.5 Is the Joint Distribution Normal?
2.3 Marginals and More Measures of Dependence
2.3.1 Estimation of the Coffee Log-Return Distributions
2.3.2 More Measures of Dependence
2.4 Copulas and Random Simulations
2.4.1 Copulas
2.4.2 First Examples of Copula Families
2.4.3 Copulas and General Bivariate Distributions
2.4.4 Fitting Copulas
2.4.5 Monte Carlo Simulations with Copulas
2.4.6 A Risk Management Example
2.5Principal Component Analysis
2.5.1 Identification of the Principal Components of a Data Set
2.5.2 PCA with S-Plus
2.5.3 Effective Dimension of the Space of Yield Curves
2.5.4 Swap Rate Curves
Appendix 1: Calculus with Random Vectors and Matrices
Appendix 2: Families of Copulas
Problems
Notes & Complements Part II Regression
3 Parametric Regression
3.1 Simple Linear Regression
3.1.1 Getting the Data
3.1.2 First Plots
3.1.3 Regression Set-up
3.1.4 Simple Linear Regression
3.1.5 Cost Minimizations
3.1.6 Regression as a Minimization Problem
3.2 Regression for Prediction & Sensitivities
3.2.1 Prediction
3.2.2 Introductory Discussion of Sensitivity and Robustness
3.2.3 Comparing L2 and L1 Regressions
3.2.4 Taking Another Look at the Coffee Data
3.3 Smoothing versus Distribution Theory
3.3.1 Regression and Conditional Expectation
3.3.2 Maximum Likelihood Approach
3.4 Multiple Regression
3.4.1 Notation
3.4.2 The S-Plus Function lm
3.4.3 R2 as a Regression Diagnostic
3.5 Matrix Formulation and Linear Models
3.5.1 Linear Models
3.5.2 Least Squares (Linear) Regression Revisited
3.5.3 First Extensions
3.5.4 Testing the CAPM
3.6 Polynomial Regression
3.6.1 Polynomial Regression as a Linear Model
3.6.2 Example of S-Plus Commands
3.6.3 Important Remark
3.6.4 Prediction with Polynomial Regression
3.6.5 Choice of the Degree p
3.7 Nonlinear Regression
3.8 Term Structure of Interest Rates: A Crash Course
3.9 Parametric Yield Curve Estimation
3.9.1 Estimation Procedures
3.9.2 Practical Implementation
3.9.3 S-Plus Experiments
3.9.4 Concluding Remarks
Appendix: Cautionary Notes on Some S-Plus Idiosyncracies
Problems
Notes & Complements 4 Local & Nonparametric Regression
4.1 Review of the Regression Setup
4.2 Natural Splines as Local Smoothers
4.3 Non