Basics of Financial Econometrics

FRANK J. FABOZZI is Professor of Finance at EDHEC Business School and Editor of the Journal of Portfolio Management. SERGIO M. FOCARDI is Visiting Professor of Finance at Stony Brook University and a founding partner of the Paris-based consulting firm The Intertek Group. SVETLOZAR T. RACHEV is Professor of Finance, College of Business and Center for Finance, Stony Brook University, and Chief-Scientist with FinAnalytica. BALA G. ARSHANAPALLI is the Gallagher-Mills Chair of Business and Economics at Indiana University Northwest.

• Preface xiii Acknowledgments xviiAbout the Authors xixChapter 1 Introduction 1Financial Econometrics at Work 2The Data Generating Process 5Applications of Financial Econometrics to Investment Management 6Key Points 10Chapter 2 Simple Linear Regression 13The Role of Correlation 13Regression Model: Linear Functional Relationship between Two Variables 14Distributional Assumptions of the Regression Model 16Estimating the Regression Model 18Goodness-of-Fit of the Model 22Two Applications in Finance 25Linear Regression of a Nonlinear Relationship 36Key Points 38CHAPTER 3 Multiple Linear Regression 41The Multiple Linear Regression Model 42Assumptions of the Multiple Linear Regression Model 43Estimation of the Model Parameters 43Designing the Model 45Diagnostic Check and Model Significance 46Applications to Finance 51Key Points 79chapter 4 Building and Testing a Multiple Linear Regression Model 81The Problem of Multicollinearity 81Model Building Techniques 84Testing the Assumptions of the Multiple Linear Regression Model 88Key Points 100CHAPTER 5 Introduction to Time Series Analysis 103What Is a Time Series? 103Decomposition of Time Series 104Representation of Time Series with Difference Equations 108Application: The Price Process 109Key Points 113chapter 6 Regression Models with Categorical Variables 115Independent Categorical Variables 116Dependent Categorical Variables 137Key Points 140Chapter 7 Quantile Regressions 143Limitations of Classical Regression Analysis 144Parameter Estimation 144Quantile Regression Process 146Applications of Quantile Regressions in Finance 148Key Points 155CHAPTER 8 Robust Regressions 157Robust Estimators of Regressions 158Illustration: Robustness of theCorporate Bond Yield Spread Model 161Robust Estimation of Covariance and Correlation Matrices 166Applications 168Key Points 170Chapter 9 Autoregressive Moving Average Models 171Autoregressive Models 172Moving Average Models 176Autoregressive Moving Average Models 178ARMA Modeling to Forecast S&P 500 Weekly Index Returns 181Vector Autoregressive Models 188Key Points 189Chapter 10 Cointegration 191Stationary and Nonstationary Variables and Cointegration 192Testing for Cointegration 196Key Points 211chapter 11 Autoregressive Heteroscedasticity Model and Its Variants 213Estimating and Forecasting Volatility 214ARCH Behavior 215GARCH Model 223What Do ARCH/GARCH Models Represent? 226Univariate Extensions of GARCH Modeling 226Estimates of ARCH/GARCH Models 229Application of GARCH Models to Option Pricing 230Multivariate Extensions of ARCH/GARCH Modeling 231Key Points 233Chapter 12 Factor Analysis and Principal Components Analysis 235Assumptions of Linear Regression 236Basic Concepts of Factor Models 237Assumptions and Categorization of Factor Models 240Similarities and Differences between Factor Models and Linear Regression 241Properties of Factor Models 242Estimation of Factor Models 244Principal Components Analysis 251Differences between Factor Analysis and PCA 259Approximate (Large) Factor Models 261Approximate Factor Models and PCA 263Key Points 264Chapter 13 Model Estimation 265Statistical Estimation and Testing 265Estimation Methods 267Least-Squares Estimation Method 268The Maximum Likelihood Estimation Method 278Instrumental Variables 283Method of Moments 284The M-Estimation Method and M-Estimators 289Key Points 289CHAPTER 14 Model Selection 291Physics and Economics: Two Ways of Making Science 291Model Complexity and Sample Size 293Data Snooping 296Survivorship Biases and Other Sample Defects 297Model Risk 300Model Selection in a Nutshell 301Key Points 303Chapter 15 Formulating and Implementing Investment Strategies Using Financial Econometrics 305The Quantitative Research Process 307Investment Strategy Process 314Key Points 318Appendix A Descriptive Statistics 321Basic Data Analysis 321Measures of Location and Spread 328Multivariate Variables and Distributions 332Appendix B Continuous Probability Distributions Commonly Used in Financial Econometrics 343Normal Distribution 344Chi-Square Distribution 347Student’s t-Distribution 349F-Distribution 352α-Stable Distribution 353Appendix C Inferential Statistics 359Point Estimators 359Confidence Intervals 369Hypothesis Testing 372Appendix D Fundamentals of Matrix Algebra 385Vectors and Matrices Defined 385Square Matrices 387Determinants 388Systems of Linear Equations 389Linear Independence and Rank 391Vector and Matrix Operations 391Eigenvalues and Eigenvectors 396APPENDIX E Model Selection Criterion: AIC and BIC 399Akaike Information Criterion 400Bayesian Information Criterion 402Appendix F Robust Statistics 405Robust Statistics Defined 405Qualitative and Quantitative Robustness 406Resistant Estimators 406M-Estimators 408The Least Median of Squares Estimator 408The Least Trimmed of Squares Estimator 409Robust Estimators of the Center 409Robust Estimators of the Spread 410Illustration of Robust Statistics 410Index 413