Statistical Analysis of Financial Data : With Examples In R book cover
1st Edition

Statistical Analysis of Financial Data
With Examples In R

ISBN 9781138599499
Published March 11, 2020 by CRC Press
666 Pages

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Book Description

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.

Table of Contents

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


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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