Statistical Analysis of Financial Data: With Examples In R

1. The Nature of Financial Data

1. Financial Time Series

   Autocorrelations

   Stationarity

   Time Scales and Data Aggregation

   Financial Assets and Markets

   Markets and Regulatory Agencies

   Interest

   Returns on Assets

   Stock Prices; Fair Market Value

   Splits, Dividends, and Return of Capital

   Indexes and "the Market"

   Derivative Assets

   Short Positions

   Portfolios of Assets: Diversification and Hedging

   Frequency Distributions of Returns

   Location and Scale

   Skewness

   Kurtosis

   Multivariate Data

   The Normal Distribution

   Q-Q Plots

   Outliers

   Other Statistical Measures

   Volatility

   The Time Series of Returns

   Measuring Volatility: Historical and Implied

   Volatility Indexes: The VIX

   The Curve of Implied Volatility

   Risk Assessment and Management

   Market Dynamics

   Stylized Facts about Financial Data

   Notes and Further Reading

   Exercises and Questions for Review

   Appendix A: Accessing and Analyzing Financial Data in R

   A R Basics

   A Data Repositories and Inputting Data into R

   A Time Series and Financial Data in R

   A Data Cleansing

   Notes, Comments, and Further Reading on R

   Exercises in R

2. Exploratory Financial Data Analysis

1. Data Reduction

   Simple Summary Statistics

   Centering and Standardizing Data

   Simple Summary Statistics for Multivariate Data

   Transformations

   Identifying Outlying Observations

   The Empirical Cumulative Distribution Function

   Nonparametric Probability Density Estimation

   Binned Data

   Kernel Density Estimator

   Multivariate Kernel Density Estimator

   Graphical Methods in Exploratory Analysis

   Time Series Plots

   Histograms

   Boxplots

   Density Plots

   Bivariate Data

   Q-Q Plots

   Graphics in R

   Notes and Further Reading

   Exercises

3. Probability Distributions in Models of Observable Events

1. Random Variables and Probability Distributions

   Discrete Random Variables

   Continuous Random Variables

   Multivariate Distributions

   Measures of Association in Multivariate Distributions

   Copulas

   Transformations of Multivariate Random Variables

   Distributions of Order Statistics

   Asymptotic Distributions; The Central Limit Theorem

   The Tails of Probability Distributions

   Sequences of Random Variables; Stochastic Processes

   Diffusion of Stock Prices and Pricing of Options

   Some Useful Probability Distributions

   Discrete Distributions

   Continuous Distributions

   Multivariate Distributions

   General Families of Distributions Useful in Modeling

   Constructing Multivariate Distributions

   Modeling of Data-Generating Processes

   R Functions for Probability Distributions

   Simulating Observations of a Random Variable

   Uniform Random Numbers

   Generating Nonuniform Random Numbers

   Simulating Data in R

   Notes and Further Reading

   Exercises

4. St atistical Models and Methods of Inference

1. Models

   Fitting Statistical Models

   Measuring and Partitioning Observed Variation

   Linear Models

   Nonlinear Variance-Stabilizing Transformations

   Parametric and Nonparametric Models

   Bayesian Models

   Models for Time Series

   Criteria and Methods for Statistical Modeling

   Estimators and Their Properties

   Methods of Statistical Modeling

   Optimization in Statistical Modeling; Least Squares and Other Applications

   The General Optimization Problem

   Least Squares

   Maximum Likelihood

   R Functions for Optimization

   Statistical Inference

   Confidence Intervals

   Testing Statistical Hypotheses

   Prediction

   Inference in Bayesian Models

   Resampling Methods; The Bootstrap

   Robust Statistical Methods

   Estimation of the Tail Index

   Estimation of VaR and Expected Shortfall

   Models of Relationships among Variables

   Principal Components

   Regression Models

   Linear Regression Models

   Linear Regression Models: The Regressors

   Linear Regression Models: Individual Observations and Residuals

   Linear Regression Models: An Example

   Nonlinear Models

   Specifying Models in R

   Assessing the Adequacy of Models

   Goodness-of-Fit Tests; Tests for Normality

   Cross Validation

   Model Selection and Model Complexity

   Notes and Further Reading

   Exercises

5. Discrete Time Series Models and Analysis

Basic Linear Operations

The Backshift Operator

The Difference Operator

The Integration Operator

Summation of an Infinite Geometric Series

Linear Difference Equations

Trends and Detrending

Cycles and Seasonal Adjustment

Analysis of Discrete Time Series Models

Stationarity

Sample Autocovariance and Autocorrelation Functions; Estimators

Statistical Inference in Stationary Time Series

Autoregressive and Moving Average Models

Moving Average Models; MA(q)

Autoregressive Models; AR(p)

The Partial Autocorrelation Function (PACF)

ARMA and ARIMA Models

Simulation of ARMA and ARIMA Models

Statistical Inference in ARMA and ARIMA Models

Selection of Orders in ARIMA Models

Forecasting in ARIMA Models

Analysis of ARMA and ARIMA Models in R

Robustness of ARMA Procedures; Innovations with Heavy Tails

Financial Data

Linear Regression with ARMA Errors

Conditional Heteroscedasticity

ARCH Models

GARCH Models and Extensions

Unit Roots and Cointegration

Spurious Correlations; The Distribution of the Correlation Coefficient

Unit Roots

Cointegrated Processes

Notes and Further Reading

Exercises