Financial econometrics is a quest for models that describe financial time series such as prices, returns, interest rates, and exchange rates. In Financial Econometrics, readers will be introduced to this growing discipline and the concepts and theories associated with it, including background material on probability theory and statistics. The experienced author team uses real-world data where possible and brings in the results of published research provided by investment banking firms and journals. Financial Econometrics clearly explains the techniques presented and provides illustrative examples for the topics discussed.

Svetlozar T. Rachev, PhD (Karlsruhe, Germany) is currently Chair-Professor at the University of Karlsruhe. Stefan Mittnik, PhD (Munich, Germany) is Professor of Financial Econometrics at the University of Munich. Frank J. Fabozzi, PhD, CFA, CFP (New Hope, PA) is an adjunct professor of Finance at Yale University’s School of Management. Sergio M. Focardi (Paris, France) is a founding partner of the Paris-based consulting firm The Intertek Group. Teo Jasic, PhD, (Frankfurt, Germany) is a senior manager with a leading international management consultancy firm in Frankfurt.

From the Back Cover
Financial econometrics combines mathematical and statistical theory and techniques to understand and solve problems in financial economics. Modeling and forecasting financial time series, such as prices, returns, interest rates, financial ratios, and defaults, are important parts of this field.

In Financial Econometrics, you'll be introduced to this growing discipline and the concepts associated with it—from background material on probability theory and statistics to information regarding the properties of specific models and their estimation procedures.

With this book as your guide, you'll become familiar with:

• Autoregressive conditional heteroskedasticity (ARCH) and GARCH modeling
• Principal components analysis (PCA) and factor analysis
• Stable processes and ARMA and GARCH models with fat-tailed errors
• Robust estimation methods
• Vector autoregressive and cointegrated processes, including advanced estimation methods for cointegrated systems
• And much more

The experienced author team of Svetlozar Rachev, Stefan Mittnik, Frank Fabozzi, Sergio Focardi, and Teo Jasic not only presents you with an abundant amount of information on financial econometrics, but they also walk you through a wide array of examples to solidify your understanding of the issues discussed.

Filled with in-depth insights and expert advice, Financial Econometrics provides comprehensive coverage of this discipline and clear explanations of how the models associated with it fit into today's investment management process.

Contents
Preface xi
Abbreviations and Acronyms xv
About the Authors xix
CHAPTER 1
Financial Econometrics: Scope and Methods 1
The Data Generating Process 3
Financial Econometrics at Work 7
Time Horizon of Models 10
Applications 12
Appendix: Investment Management Process 16
Concepts Explained in this Chapter (in order of presentation) 22
CHAPTER 2
Review of Probability and Statistics 25
Concepts of Probability 25
Principles of Estimation 58
Bayesian Modeling 69
Appendix A: Information Structures 72
Appendix B: Filtration 74
Concepts Explained in this Chapter (in order of presentation) 75
CHAPTER 3
Regression Analysis: Theory and Estimation 79
The Concept of Dependence 79
Regressions and Linear Models 85
Estimation of Linear Regressions 90
Sampling Distributions of Regressions 96
Determining the Explanatory Power of a Regression 97
Using Regression Analysis in Finance 99
Stepwise Regression 114
Nonnormality and Autocorrelation of the Residuals 121
Pitfalls of Regressions 123
Concepts Explained in this Chapter (in order of presentation) 125
CHAPTER 4
Selected Topics in Regression Analysis 127
Categorical and Dummy Variables in Regression Models 127
Constrained Least Squares 151
The Method of Moments and its Generalizations 163
Concepts Explained in this Chapter (in order of presentation) 167
CHAPTER 5
Regression Applications in Finance 169
Applications to the Investment Management Process 169
A Test of Strong-Form Pricing Efficiency 174
Tests of the CAPM 175
Using the CAPM to Evaluate Manager Performance: The Jensen Measure 179
Evidence for Multifactor Models 180
Benchmark Selection: Sharpe Benchmarks 184
Return-Based Style Analysis for Hedge Funds 186
Hedge Fund Survival 191
Bond Portfolio Applications 192
Concepts Explained in this Chapter (in order of presentation) 199
CHAPTER 6
Modeling Univariate Time Series 201
Difference Equations 201
Terminology and Definitions 207
Stationarity and Invertibility of ARMA Processes 214
Linear Processes 219
Identification Tools 223
Concepts Explained in this Chapter (in order of presentation) 239
CHAPTER 7
Approaches to ARIMA Modeling and Forecasting 241
Overview of Box-Jenkins Procedure 242
Identification of Degree of Differencing 244
Identification of Lag Orders 250
Model Estimation 253
Diagnostic Checking 262
Forecasting 271
Concepts Explained in this Chapter (in order of presentation) 277
CHAPTER 8
Autoregressive Conditional Heteroskedastic Models 279
ARCH Process 280
GARCH Process 284
Estimation of the GARCH Models 289
Stationary ARMA-GARCH Models 293
Lagrange Multiplier Test 294
Variants of the GARCH Model 298
GARCH Model with Student’s
t-Distributed Innovations 299
Multivariate GARCH Formulations 314
Appendix: Analysis of the Properties of the GARCH(1,1) Model 316
Concepts Explained in this Chapter (in order of presentation) 319
CHAPTER 9
Vector Autoregressive Models I 321
VAR Models Defined 321
Stationary Autoregressive Distributed Lag Models 334
Vector Autoregressive Moving Average Models 335
Forecasting with VAR Models 338
Appendix: Eigenvectors and Eigenvalues 339
Concepts Explained in this Chapter (in order of presentation) 341
CHAPTER 10
Vector Autoregressive Models II 343
Estimation of Stable VAR Models 343
Estimating the Number of Lags 357
Autocorrelation and Distributional Properties of Residuals 359
VAR Illustration 360
Concepts Explained in this Chapter (in order of presentation) 372
CHAPTER 11
Cointegration and State Space Models 373
Cointegration 373
Error Correction Models 381
Theory and Methods of Estimation of Nonstationary VAR Models 385
State-Space Models 398
Concepts Explained in this Chapter (in order of presentation) 404
CHAPTER 12
Robust Estimation 407
Robust Statistics 407
Robust Estimators of Regressions 417
Illustration: Robustness of the Corporate Bond Yield Spread Model 421
Concepts Explained in this Chapter (in order of presentation) 428
CHAPTER 13
Principal Components Analysis and Factor Analysis 429
Factor Models 429
Principal Components Analysis 436
Factor Analysis 450
PCA and Factor Analysis Compared 461
Concepts Explained in this Chapter (in order of presentation) 464
CHAPTER 14
Heavy-Tailed and Stable Distributions in Financial Econometrics 465
Basic Facts and Definitions of Stable Distributions 468
Properties of Stable Distributions 475
Estimation of the Parameters of the Stable Distribution 479
Applications to German Stock Data 485
Appendix: Comparing Probability Distributions 487
Concepts Explained in this Chapter (in order of presentation) 494
CHAPTER 15
ARMA and ARCH Models with Infinite-Variance Innovations 495
Infinite Variance Autoregressive Processes 495
Stable GARCH Models 501
Estimation for the Stable GARCH Model 507
Prediction of Conditional Densities 513
Concepts Explained in this Chapter (in order of presentation) 516
APPENDIX
Monthly Returns for 20 Stocks: December 2000–November 2005 517
INDEX 525