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## Book Description

Taking a data-driven approach, A Course on Statistics for Finance presents statistical methods for financial investment analysis. The author introduces regression analysis, time series analysis, and multivariate analysis step by step using models and methods from finance.

The book begins with a review of basic statistics, including descriptive statistics, kinds of variables, and types of data sets. It then discusses regression analysis in general terms and in terms of financial investment models, such as the capital asset pricing model and the Fama/French model. It also describes mean-variance portfolio analysis and concludes with a focus on time series analysis.

Providing the connection between elementary statistics courses and quantitative finance courses, this text helps both existing and future quants improve their data analysis skills and better understand the modeling process.

1. Preliminaries
2. Preface
4. Part I Introductory Concepts and Definitions
1. Chapter 1 Review of Basic Statistics
1. 1.1 What Is Statistics?
1. 1.1.1 Data Are Observations
2. 1.1.2 Statistics Descriptions; Statistics Methods
3. 1.1.3 Origins of Data
4. 1.1.4 Philosophy of Data and Information
2. 1.2 Characterizing Data
1. 1.2.1 Types of Data
2. 1.2.2 Raw Data versus Derived Data
3. 1.3 Measures of Central Tendency
1. 1.3.1 Mode
2. 1.3.2 Measuring the Center of a Set of Numbers
3. 1.3.3 Other Kinds of Averages
4. 1.3.4 Section Exercises
4. 1.4 Measures of Variability
2. 1.4.2 Distance-Based Measures of Spread
5. 1.5 Higher Moments
6. 1.6 Summarizing Distributions
7. 1.7 Bivariate Data
1. 1.7.1 Covariance and Correlation
2. 1.7.2 Covariance of a Bivariate Distribution
8. 1.8 Three Variables
9. 1.9 Two-Way Tables
1. 1.9.1 Two-Way Tables of Counts
2. 1.9.2 Turnover Tables
3. 1.9.3 Seasonal Data
10. 1.10 Summary
11. 1.11 Chapter Exercises
12. 1.12 Bibliography
2. Chapter 2 Stock Price Series and Rates of Return
1. 2.1 Introduction
1. 2.1.1 Price Series
2. 2.1.2 Rates of Return
3. 2.1.3 Review of Mean, Variance, and Standard Deviation
2. 2.2 Ratios of Mean and Standard Deviation
3. 2.3 Value-at-Risk
4. 2.4 Distributions for RORs
5. 2.5 Summary
6. 2.6 Chapter Exercises
7. 2.7 Bibliography
3. Chapter 3 Several Stocks and Their Rates of Return
1. 3.1 Introduction
2. 3.2 Review of Covariance and Correlation
3. 3.3 Two Stocks
4. 3.4 Three Stocks
5. 3.5 m Stocks
6. 3.6 Summary
7. 3.7 Chapter Exercises
8. 3.8 Bibliography
5. Part II Regression
1. Chapter 4 Simple Linear Regression; CAPM and Beta
1. 4.1 Introduction
2. 4.2 Simple Linear Regression
3. 4.3 Estimation
1. 4.3.1 Method of Least Squares
2. 4.3.2 Maximum Likelihood Estimator under the Assumption of Normality*
3. 4.3.3 A Heuristic Approach
4. 4.3.4 Means and Variances of Estimators
5. 4.3.5 Estimating the Error Variance
4. 4.4 Inference Concerning the Slope
5. 4.5 Testing Equality of Slopes of Two Lines through the Origin
6. 4.6 Linear Parametric Functions
7. 4.7 Variances Dependent upon X *
8. 4.8 A Financial Application: CAPM and “Beta”
9. 4.9 Slope and Intercept
10. 4.10 Appendix 4A: Optimality of the Least Squares Estimator
11. 4.11 Summary
12. 4.12 Chapter Exercises
13. 4.13 Bibliography
2. Chapter 5 Multiple Regression and Market Models
1. 5.1 Multiple Regression Models
2. 5.2 Market Models
3. 5.3 Models with Numerical and Dummy Explanatory Variables
1. 5.3.1 Two-Group Models
2. 5.3.2 Other Market Models
4. 5.4 Model Building
1. 5.4.1 Principle of Parsimony
2. 5.4.2 Model-Selection Criteria
3. 5.4.3 Testing a Reduced Model against a Full Model
4. 5.4.4 Comparing Several Models
5. 5.4.5 Combining Results from Several Models
5. 5.5 Chapter Summary
6. 5.6 Chapter Exercises
7. 5.7 Bibliography
6. Part III Portfolio Analysis
1. Chapter 6 Mean-Variance Portfolio Analysis
1. 6.1 Introduction
2. 6.2 Two Stocks
1. 6.2.1 Mean
2. 6.2.2 Variance
3. 6.2.3 Covariance and Correlation
4. 6.2.4 Portfolio Variance
5. 6.2.5 Minimum Variance Portfolio
3. 6.3 Three Stocks
4. 6.4 m Stocks
5. 6.5 m Stocks and a Risk-Free Asset
6. 6.6 Value-at-Risk
7. 6.7 Selling Short
8. 6.8 Market Models and Beta
9. 6.9 Summary
10. 6.10 Chapter Exercises
11. 6.11 Appendix 6A: Some Results in Terms of Vectors and Matrices (Optional)*
1. 6.11.1 Variates
2. 6.11.2 Vector Differentiation
3. 6.11.3 Section Exercises
12. 6.12 Appendix 6B: Some Results for the Family of Normal Distributions
13. 6.13 Bibliography
2. Chapter 7 Utility-Based Portfolio Analysis
1. 7.1 Introduction
2. 7.2 Single-Criterion Analysis
3. 7.3 Summary
4. 7.4 Chapter Exercises
5. 7.5 Bibliography
7. Part IV Time Series Analysis
1. Chapter 8 Introduction to Time Series Analysis
1. 8.1 Introduction
2. 8.2 Control Charts
3. 8.3 Moving Averages
1. 8.3.1 Running Median
2. 8.3.2 Various Moving Averages
3. 8.3.3 Exponentially Weighted Moving Averages
4. 8.3.4 Using a Moving Average for Prediction
4. 8.4 Need for Modeling
5. 8.5 Trend, Seasonality, and Randomness
6. 8.6 Models with Lagged Variables
7. 8.7 Moving-Average Models
8. 8.8 Identification of ARIMA Models
1. 8.8.1 Pre-Processing
2. 8.8.2 ARIMA Parameters p, d, q
3. 8.8.3 Autocorrelation Function; Partial Autocorrelation Function
9. 8.9 Seasonal Data
10. 8.10 Dynamic Regression Models
11. 8.11 Simultaneous Equations Models
12. 8.12 Appendix 8A: Growth Rates and Rates of Return
13. 8.13 Appendix 8B: Prediction after Data Transformation
14. 8.14 Appendix 8C: Representation of Time Series
1. 8.14.1 Operators
2. 8.14.2 White Noise
3. 8.14.3 Stationarity
4. 8.14.4 AR
5. 8.14.5 MA
6. 8.14.6 ARMA
15. 8.15 Summary
16. 8.16 Chapter Exercises
17. 8.17 Bibliography
2. Chapter 9 Regime Switching Models
1. 9.1 Introduction
2. 9.2 Bull and Bear Markets
1. 9.2.1 Definitions of Bull and Bear Markets
2. 9.2.2 Regressions on Bull3
3. 9.2.3 Other Models for Bull/Bear
4. 9.2.4 Bull and Bear Portfolios
3. 9.3 Summary
4. 9.4 Chapter Exercises
5. 9.5 Bibliography
8. Appendix A Vectors and Matrices
1. A.1 Introduction
2. A.2 Vectors
3. A.3 Matrices
1. A.3.1 Entries of a Matrix
2. A.3.2 Transpose of a Matrix
3. A.3.3 Matrix Multiplication
4. A.3.4 Section Exercises
5. A.3.5 Identity Matrix
6. A.3.6 Inverse
7. A.3.7 Determinant
4. A.4 Vector Differentiation
5. A.5 Paths
7. A.7 Eigensystem
8. A.8 Transformation to Uncorrelated Variables
9. A.9 Statistical Distance
10. A.10 Appendix Exercises
11. A.11 Bibliography
9. Appendix B Normal Distributions
1. B.1 Some Results for Univariate Normal Distributions
2. B.2 Family of Multivariate Normal Distributions
3. B.3 Role of D-Square
4. B.4 Bivariate Normal Distributions
5. B.5 Other Multivariate Distributions
6. B.6 Summary
7. B.7 Appendix B Exercises
8. B.8 Bibliography