1st Edition

Statistical Analysis of Financial Data With Examples In R

By James Gentle Copyright 2020
    666 Pages
    by CRC Press

    666 Pages
    by CRC Press

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    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.


    * 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



      Time Scales and Data Aggregation

      Financial Assets and Markets

      Markets and Regulatory Agencies


      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



      Multivariate Data

      The Normal Distribution

      Q-Q Plots


      Other Statistical Measures


      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


      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



      Density Plots

      Bivariate Data

      Q-Q Plots

      Graphics in R

      Notes and Further Reading


    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


      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


    4.       Statistical Models and Methods of Inference


      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


      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


    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


              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



    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.

    "The book is very well written, and fills an important need for an up-to-date textbook about statistical techniques applied to finance. The book explains the theory behind the statistical techniques very well, with good detail. The mathematical notation is appealing and elegant."
    ~Jerzy Pawlowski, New York University Tandon School of Engineering

    "I thoroughly enjoyed reading the first two chapters of the book. Often, the first couple of chapters of a book provide a "boilerplate" discussion of the characteristics of the data and R. Here, the first two chapters are very well developed, to the point that they provide a good general resource to readers approaching the analysis of financial data from several different perspectives. For example, students in statistics usually approach the entire analysis of time series having in mind the potential application to the analysis of financial data, but they know nothing about the characteristics of the data and the financial markets...Just like the previous chapters, I broadly enjoyed reading this chapter. Prof. Gentle explains the topics clearly and often uses simulations to convey the intuition. That's also the way I like to teach these concepts and I think it enhances understanding among economics and finance students. I also commend the way he discusses the lag and difference operators and how they are implemented in R. He devotes quite some space to them, and I believe that is good as many texts go over these concepts too quickly for many students. Likewise, the discussion of the AR(I)MA models is very detailed and clear.
    ~Jan Annaert, University of Antwerp and Antwerp Management School