Statistical Analysis of Financial Data With Examples In R

Statistical Analysis of Financial Data covers the use of statistical analysis and the methods of data science to model and analyze financial data. The first chapter is an overview of financial markets, describing the market operations and using exploratory data analysis to illustrate the nature of financial data. The software used to obtain the data for the examples in the first chapter and for all computations and to produce the graphs is R. However discussion of R is deferred to an appendix to the first chapter, where the basics of R, especially those most relevant in financial applications, are presented and illustrated. The appendix also describes how to use R to obtain current financial data from the internet. Chapter 2 describes the methods of exploratory data analysis, especially graphical methods, and illustrates them on real financial data. Chapter 3 covers probability distributions useful in financial analysis, especially heavy-tailed distributions, and describes methods of computer simulation of financial data. Chapter 4 covers basic methods of statistical inference, especially the use of linear models in analysis, and Chapter 5 describes methods of time series with special emphasis on models and methods applicable to analysis of financial data. Features * Covers statistical methods for analyzing models appropriate for financial data, especially models with outliers or heavy-tailed distributions. * Describes both the basics of R and advanced techniques useful in financial data analysis. * Driven by real, current financial data, not just stale data deposited on some static website. * Includes a large number of exercises, many requiring the use of open-source software to acquire real financial data from the internet and to analyze it.

1. The Nature of Financial Data 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 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 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. Statistical Models and Methods of Inference 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

James E. Gentle is University Professor Emeritus at George Mason University. He is a Fellow of the American Statistical Association (ASA) and of the American Association for the Advancement of Science. He is author of Random Number Generation and Monte Carlo Methods and Matrix Algebra.