Financial econometrics from basics to advanced modeling techniques by rachev mittnik and frank j fabozzi

ffirs.frm Page iii Wednesday, December 13, 2006 1:44 PM

Financial
Econometrics
From Basics to Advanced Modeling
Techniques

SVETLOZAR T. RACHEV
STEFAN MITTNIK
FRANK J. FABOZZI
SERGIO M. FOCARDI
ˇ ´
TEO JASIC

John Wiley & Sons, Inc.


ffirs.frm Page vi Wednesday, December 13, 2006 1:44 PM


ffirs.frm Page i Wednesday, December 13, 2006 1:44 PM

Financial
Econometrics


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THE FRANK J. FABOZZI SERIES
Fixed Income Securities, Second Edition by Frank J. Fabozzi

Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and
James A. Abate
Handbook of Global Fixed Income Calculations by Dragomir Krgin
Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi
Real Options and Option-Embedded Securities by William T. Moore
Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi
The Exchange-Traded Funds Manual by Gary L. Gastineau
Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by
Frank J. Fabozzi
Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu
Handbook of Alternative Assets by Mark J. P. Anson
The Exchange-Traded Funds Manual by Gary L. Gastineau
The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry
The Handbook of Financial Instruments edited by Frank J. Fabozzi
Collateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and
Frank J. Fabozzi
Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi
Investment Performance Measurement by Bruce J. Feibel
The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. Fabozzi
The Theory and Practice of Investment Management edited by Frank J. Fabozzi and
Harry M. Markowitz
Foundations of Economic Value Added: Second Edition by James L. Grant
Financial Management and Analysis: Second Edition by Frank J. Fabozzi and Pamela P. Peterson
Measuring and Controlling Interest Rate and Credit Risk: Second Edition by Frank J. Fabozzi,
Steven V. Mann, and Moorad Choudhry
Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by
Frank J. Fabozzi
The Handbook of European Fixed Income Securities edited by Frank J. Fabozzi and
Moorad Choudhry
The Handbook of European Structured Financial Products edited by Frank J. Fabozzi and

Moorad Choudhry
The Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi
and Frank J. Fabozzi
Short Selling: Strategies, Risks, and Rewards edited by Frank J. Fabozzi
The Real Estate Investment Handbook by G. Timothy Haight and Daniel Singer
Market Neutral Strategies edited by Bruce I. Jacobs and Kenneth N. Levy
Securities Finance: Securities Lending and Repurchase Agreements edited by Frank J. Fabozzi
and Steven V. Mann
Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn,
and Frank J. Fabozzi
Financial Modeling of the Equity Market: From CAPM to Cointegration by Frank J.
Fabozzi, Sergio M. Focardi, and Petter N. Kolm
Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by
Frank J. Fabozzi, Lionel Martellini, and Philippe Priaulet
Analysis of Financial Statements, Second Edition by Pamela P. Peterson and Frank J. Fabozzi
Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J.
Lucas, Laurie S. Goodman, and Frank J. Fabozzi
Handbook of Alternative Assets, Second Edition by Mark J. P. Anson
Introduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad Choudhry


ffirs.frm Page iii Wednesday, December 13, 2006 1:44 PM

Financial
Econometrics
From Basics to Advanced Modeling
Techniques

SVETLOZAR T. RACHEV
STEFAN MITTNIK

FRANK J. FABOZZI
SERGIO M. FOCARDI
ˇ ´
TEO JASIC

John Wiley & Sons, Inc.


ffirs.frm Page iv Wednesday, December 13, 2006 1:44 PM

Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in
any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright
Act, without either the prior written permission of the Publisher, or authorization through
payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at
www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201)
748-6011, fax (201) 748-6008, or online at />Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best
efforts in preparing this book, they make no representations or warranties with respect to the
accuracy or completeness of the contents of this book and specifically disclaim any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created
or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional
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visit our web site at www.wiley.com.

ISBN-13 978-0-471-78450-0
ISBN-10 0-471-78450-8

Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1


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STR
To my children Boryana and Vladimir
SM
To Erika and Alissa
FJF
To my son Francesco Alfonso
SMF
To my parents
TJ
To my parents


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Contents

Preface
Abbreviations and Acronyms
About the Authors

xi
xv
xix

CHAPTER 1
Financial Econometrics: Scope and Methods
The Data Generating Process
Financial Econometrics at Work
Time Horizon of Models
Applications
Appendix: Investment Management Process
Concepts Explained in this Chapter (in order of presentation)

1
3
7
10
12
16
22

CHAPTER 2
Review of Probability and Statistics
Concepts of Probability
Principles of Estimation

Bayesian Modeling
Appendix A: Information Structures
Appendix B: Filtration
Concepts Explained in this Chapter (in order of presentation)

25
25
58
69
72
74
75

CHAPTER 3
Regression Analysis: Theory and Estimation
The Concept of Dependence
Regressions and Linear Models
Estimation of Linear Regressions
Sampling Distributions of Regressions
Determining the Explanatory Power of a Regression
Using Regression Analysis in Finance
Stepwise Regression
Nonnormality and Autocorrelation of the Residuals
Pitfalls of Regressions
Concepts Explained in this Chapter (in order of presentation)

79
79
85
90

96
97
99
114
121
123
125

vii


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viii

Contents

CHAPTER 4
Selected Topics in Regression Analysis
Categorical and Dummy Variables in Regression Models
Constrained Least Squares
The Method of Moments and its Generalizations
Concepts Explained in this Chapter (in order of presentation)

127
127
151
163
167

CHAPTER 5
Regression Applications in Finance
Applications to the Investment Management Process
A Test of Strong-Form Pricing Efficiency
Tests of the CAPM
Using the CAPM to Evaluate Manager Performance: The Jensen Measure
Evidence for Multifactor Models
Benchmark Selection: Sharpe Benchmarks
Return-Based Style Analysis for Hedge Funds
Hedge Fund Survival
Bond Portfolio Applications
Concepts Explained in this Chapter (in order of presentation)

169
169
174
175
179
180
184
186
191
192
199

CHAPTER 6
Modeling Univariate Time Series
Difference Equations
Terminology and Definitions
Stationarity and Invertibility of ARMA Processes

Linear Processes
Identification Tools
Concepts Explained in this Chapter (in order of presentation)

201
201
207
214
219
223
239

CHAPTER 7
Approaches to ARIMA Modeling and Forecasting
Overview of Box-Jenkins Procedure
Identification of Degree of Differencing
Identification of Lag Orders
Model Estimation
Diagnostic Checking
Forecasting
Concepts Explained in this Chapter (in order of presentation)

241
242
244
250
253
262
271
277

CHAPTER 8
Autoregressive Conditional Heteroskedastic Models
ARCH Process
GARCH Process
Estimation of the GARCH Models
Stationary ARMA-GARCH Models

279
280
284
289
293


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Contents

Lagrange Multiplier Test
Variants of the GARCH Model
GARCH Model with Student’s t-Distributed Innovations
Multivariate GARCH Formulations
Appendix: Analysis of the Properties of the GARCH(1,1) Model
Concepts Explained in this Chapter (in order of presentation)

ix
294
298
299

314
316
319

CHAPTER 9
Vector Autoregressive Models I
VAR Models Defined
Stationary Autoregressive Distributed Lag Models
Vector Autoregressive Moving Average Models
Forecasting with VAR Models
Appendix: Eigenvectors and Eigenvalues
Concepts Explained in this Chapter (in order of presentation)

321
321
334
335
338
339
341

CHAPTER 10
Vector Autoregressive Models II
Estimation of Stable VAR Models
Estimating the Number of Lags
Autocorrelation and Distributional Properties of Residuals
VAR Illustration
Concepts Explained in this Chapter (in order of presentation)

343

343
357
359
360
372

CHAPTER 11
Cointegration and State Space Models
Cointegration
Error Correction Models
Theory and Methods of Estimation of Nonstationary VAR Models
State-Space Models
Concepts Explained in this Chapter (in order of presentation)

373
373
381
385
398
404

CHAPTER 12
Robust Estimation
Robust Statistics
Robust Estimators of Regressions
Illustration: Robustness of the Corporate Bond Yield Spread Model
Concepts Explained in this Chapter (in order of presentation)

407
407

417
421
428

CHAPTER 13
Principal Components Analysis and Factor Analysis
Factor Models
Principal Components Analysis
Factor Analysis

429
429
436
450


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x

Contents

PCA and Factor Analysis Compared
Concepts Explained in this Chapter (in order of presentation)

461
464

CHAPTER 14
Heavy-Tailed and Stable Distributions in Financial Econometrics

Basic Facts and Definitions of Stable Distributions
Properties of Stable Distributions
Estimation of the Parameters of the Stable Distribution
Applications to German Stock Data
Appendix: Comparing Probability Distributions
Concepts Explained in this Chapter (in order of presentation)

465
468
475
479
485
487
494

CHAPTER 15
ARMA and ARCH Models with Infinite-Variance Innovations
Infinite Variance Autoregressive Processes
Stable GARCH Models
Estimation for the Stable GARCH Model
Prediction of Conditional Densities
Concepts Explained in this Chapter (in order of presentation)

495
495
501
507
513
516

APPENDIX
Monthly Returns for 20 Stocks: December 2000–November 2005

517

INDEX

525


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Preface

his book is intended to provide a modern, up-to-date presentation of
financial econometrics. It was written for students in finance and practitioners in the financial services sector.
Initially and primarily used in the derivative business, mathematical
models have progressively conquered all areas of risk management and
are now widely used also in portfolio construction. The choice of topics
and walk-through examples in this book reflect the current use of modeling in all areas of investment management.
Financial econometrics is the science of modeling and forecasting
financial time series. The development of financial econometrics was
made possible by three fundamental enabling factors: (1) the availability
of data at any desired frequency, including at the transaction level; (2)
the availability of powerful desktop computers and the requisite IT
infrastructure at an affordable cost; and (3) the availability of off-theshelf econometric software. The combination of these three factors put
advanced econometrics within the reach of most financial firms.
But purely theoretical developments have also greatly increased the
power of financial econometrics. The theory of autoregressive and moving average processes reached maturity in the 1970s with the development of a complete analytical toolbox by Box and Jenkins. Multivariate
extensions followed soon after; and the fundamental concepts of cointegration and of ARCH/GARCH modeling were introduced by Engle and

Granger in the 1980s. Starting with the fundamental work of Benoit
Mandelbrot in the 1960s, empirical studies established firmly that
returns are not normally distributed and might exhibit “fat tails,” leading to a renewed interest in distributional aspects and in models that
might generate fat tails and stable distributions.
This book updates the presentation of these topics. It begins with
the basics of econometrics and works its way through the most recent
theoretical results as regards the properties of models and their estimation procedures. It discusses tests and estimation methods from the
point of view of a user of modern econometric software—although we
have not endorsed any software.

T

x


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xi

Preface

A distinguishing feature of this book is the wide use of walkthrough examples in finance to explain the concepts that modelers and
those that use model results encounter in their professional life. In particular, our objective is to show how to interpret the results obtained
through econometric packages. The reader will find all the important
concepts in this book—from stepwise regression to cointegration and
the econometrics of stable distributions—illustrated with examples
based on real-world data. The walk-through examples provided can be
repeated by the reader, using any of the more popular econometric
packages available and data of the reader’s choice.
Here is a roadmap to the book. In Chapter 1, we informally introduce the concepts and methods of financial econometrics and outline

how modeling fits into the investment management process. In Chapter
2, we summarize the basic statistical concepts that are used throughout
the book.
Chapters 3 to 5 are devoted to regression analysis. We present different regression models and their estimation methods. In particular, we discuss a number of real-world applications of regression analysis as walkthrough examples. Among the walk-through examples presented are:
■ Computing and analyzing the characteristic line of common stocks and
■
■
■
■
■
■
■
■
■
■

mutual funds
Computing the empirical duration of common stocks
Predicting the Treasury yield
Predicting corporate bond yield spread
Testing the characteristic line in different market environments
Curve fitting to obtain the spot rate curve with the spline method
Tests of market efficiency and tests of CAPM
Evaluating manager performance
Selecting benchmarks
Style analysis of hedge-funds
Rich-cheap analysis of bonds

Chapter 6 introduces the basic concepts of time series analysis.
Chapter 7 discusses the properties and estimation methods of univariate

autoregressive moving average models. Chapter 8 is an up-to-date presentation of ARCH/GARCH modeling with walk-through examples. We
illustrate the concepts discussed, analyzing the properties of returns of
the DAX stock index and of selected stock return processes.
Chapters 9 through 11 introduce autoregressive vector processes
and cointegrated processes, including advanced estimation methods for
cointegrated systems. Both processes are illustrated with real-world
examples. Vector autoregressive (VAR) analysis is illustrated by fitting a


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Preface

xii

VAR model to three real-world stock indexes; a cointegration analysis is
also performed on the same three indexes.
Chapter 12 covers robust estimation. With the broad diffusion of
modeling, interest in robust estimation methods has grown: Robust estimation is used to make results more robust. The concepts of robust statistics are introduced and a detailed analysis of robust regressions is
performed and illustrated with many examples. We provide a robust
analysis of the returns of a Japanese stock and show the results of
applying robust methods to some of the regression examples discussed
in previous chapters.
Chapter 13 discusses Principal Components Analysis (PCA) and Factor Analysis, both now widely used in risk management and in equity and
bond portfolio construction. We illustrate the application of both techniques on a portfolio of selected U.S. stocks and show an application of
PCA to bond portfolio management, to control interest rate risk.
Chapters 14 and 15 introduce stable processes and autoregressive
moving average (ARMA) and GARCH models with fat-tailed errors. We
illustrate the concepts discussed with an example in currency modeling
and equity return modeling.

We thank several individuals for their assistance in various aspects
of this project:
■ Christian Menn for allowing us to use material from the book he coau-

■

■
■
■

■
■
■
■

thored with Svetlozar Rachev and Frank Fabozzi to create the appendix to Chapter 14.
Robert Scott of the Bank for International Settlements for providing
data for the illustration on predicting the 10-year Treasury yield in
Chapter 3 and the data and regression results for the illustration on the
use of the spline method in Chapter 4.
Raman Vardharaj of The Guardian for the mutual fund data and
regression results for the characteristic line in Chapter 3.
Katharina Schüller for proofreading several chapters.
Anna Chernobai of Syracuse University and Douglas Martin of the
University of Washington and Finanalytica for their review of Chapter
12 (Robust Estimation).
Stoyan Stoyanov for reviewing several chapters.
Markus Hoechstoetter for the illustration in Chapter 14.
Martin Fridson and Greg Braylovskiy for the corporate bond spread
data used for the illustration in Chapter 4.

David Wright of Northern Illinois University for the data to compute
the equity durations in Chapter 3.


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xiii

Preface

Svetlozar Rachev’s research was supported by grants from the Division of Mathematical, Life and Physical Sciences, College of Letters and
Science, University of California, Santa Barbara, and the Deutschen Forschungsgemeinschaft. Stefan Mittnik’s research was supported by the
Deutsche Forschungsgemeinschaft (SFB 368) and the Institut für Quantitative Finanzanalyse (IQF) in Kiel, Germany.
Svetlozar T. Rachev
Stefan Mittnik
Frank J. Fabozzi
Sergio M. Focardi
ˇ ´
Teo Jasic


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Abbreviations and Acronyms

a.a. almost always
ABS asset-backed securities
ACF autocorrelation function
ACovF autocovariance function
ADF augmented Dickey-Fuller (test)

AD-statistic Anderson-Darling distance statistic
a.e. almost everywhere
AIC Akaike information criterion
AICC Corrected Akaike information criterion
ALM asset-liability management
APT arbitrage pricing theory
AR autoregressive
ARCH autoregressive conditional heteroskedastic
ARDL autoregressive distributed lag
ARIMA autoregressive integrated moving average
ARMA autoregressive moving average
ARMAX autoregressive moving average with exogenous variables
a.s. almost surely
BD breakdown (as in BD bound/point)
BHHH Berndt, Hall, Hall, and Hausmann (algorithm)
BIC Bayesian information criterion
BIS Bank of International Settlements
BLUE best linear unbiased estimator
cap capitalization
CAPM capital asset pricing model
CCA canonical correlation analysis
CD certificate of deposit
CLF concentrated likelihood function
CLT central limit theorem

xv


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xvi

Abbreviations and Acronyms

DA domain of attraction
DAX Deutscher Aktinenindex (German blue chip stock index)
DGP data generating process
DJIA Dow Jones Industrial Average
DF Dickey-Fuller
DS difference stationary
EBIT earnings before interest and taxes
EGARCH exponential generalized autoregressive conditional heteroskedastic
EGB2 exponential generalized beta distribution of the second kind
EBITDA earnings before interest, taxes, depreciation, and amortization
ECM error correction model
FA factor analysis
FARIMA fractional autoregressive integrated moving average
FFT fast Fourier transform
FIEGARCH fractionally integrated exponential generalized autoregressive conditional heteroskedastic
FIGARCH fractionally integrated generalized autoregressive conditional
heteroskedastic
FPE final prediction error
FRC Frank Russell Company
GAAP generally accepted accounting principles
GARCH generalized autoregressive conditional heteroskedastic
GED generalized exponential distribution
GLS generalized least squares
GCLT generalized central limit theorem
GM General Motors
GNP gross national product

HFD high-frequency data
HFR Hedge Fund Research Company
IBM International Business Machines
IC information criterion/criteria
IC influence curve
IF influence function
IGARCH integrated generalized autoregressive conditional heteroskedastic
IID independent and identically distributed
IMA infinite moving average
IQR interquartile range


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Abbreviations and Acronyms

xvii

IR information ratio
IV instrumental variables (as in IV methods)
IVAR infinite variance autoregressive model
KD-statistic Kolmogorov distance statistic
L lag operator
LAD least absolute deviation
LCCA level canonical correlation analysis
LF likelihood function
LM Lagrange multipliers (as in LM test/statistics)
LMedS least median of squares (as in LMedS estimator)
LMGARCH long-memory generalized autoregressive conditional heteroskedastic
LRD long-range dependent

LS least squares (as in LS estimators)
LSE least squares estimator
LTS least trimmed of squares (as in LTS estimator)
MA moving average
MAD median absolute deviation
MAE mean absolute error
MAPE mean absolute percentage error
MBS mortgage-backed securities
MeanAD mean absolute deviation
Med median
ML maximum likelihood
MLE maximum likelihood estimator
MM method of moments
MSCI Morgan Stanley Composite Index
MSE mean squared error
OAS option-adjusted spread (as in OAS duration)
OLS ordinary least squares
PACF partial autocorrelation function
PC principal components
PCA principal components analysis
PDE partial differential equation
pdf probability density function
PMLE pseudo-maximum likelihood estimator
QMLE quasi-maximum likelihood estimator


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xviii

Abbreviations and Acronyms

RLS reweighted least squares
RMSE root mean squared error
ROI return on investment
S&P Standard & Poor
SACF (or SACovF) sample autocorrelation function
SPACF sample partial autocorrelation function
ss self similar (as in ss-process)
SSB BIG Index Salomon Smith Barney Broad Investment Grade Index
TS trend stationary
VAR vector autoregressive
VaR value at risk
VARMA vector autoregressive moving average
VDE vector difference equation
VECH multivariate GARCH model
YW Yule-Walker (in Yule-Walker equations)


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About the Authors

Svetlozar (Zari) T. Rachev completed his Ph.D. Degree in 1979 from
Moscow State (Lomonosov) University, and his Doctor of Science Degree
in 1986 from Steklov Mathematical Institute in Moscow. Currently he is
Chair-Professor in Statistics, Econometrics and Mathematical Finance at
the University of Karlsruhe in the School of Economics and Business
Engineering. He is also Professor Emeritus at the University of California,
Santa Barbara in the Department of Statistics and Applied Probability. He

has published seven monographs, eight handbooks and special-edited volumes, and over 250 research articles. Professor Rachev is cofounder of
Bravo Risk Management Group specializing in financial risk-management
software. Bravo Group was recently acquired by FinAnalytica for which
he currently serves as Chief-Scientist.
Stefan Mittnik studied at the Technical University Berlin, Germany, the
University of Sussex, England, and at Washington University in St. Louis,
where he received his doctorate degree in economics. He is now Professor of Financial Econometrics at the University of Munich, Germany,
and research director at the Ifo Institute for Economic Research in
Munich. Prior to joining the University of Munich he taught at SUNYStony Brook, New York, the University of Kiel, Germany, and held several visiting positions, including that of Fulbright Distinguished Chair at
Washington University in St. Louis. His research focuses on financial
econometrics, risk management, and portfolio optimization. In addition
to purely academic interests, Professor Mittnik directs the risk management program at the Center for Financial Studies in Frankfurt, Germany,
and is co-founder of the Institut für Quantitative Finanzanalyse (IQF) in
Kiel, where he now chairs the scientific advisory board.
Frank J. Fabozzi is an Adjunct Professor of Finance and Becton Fellow in
the School of Management at Yale University. Prior to joining the Yale faculty, he was a Visiting Professor of Finance in the Sloan School at MIT.
Professor Fabozzi is a Fellow of the International Center for Finance at
Yale University and on the Advisory Council for the Department of Oper-

xix


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xx

About the Authors

ations Research and Financial Engineering at Princeton University. He is
the editor of The Journal of Portfolio Management and an associate editor

of the The Journal of Fixed Income. He earned a doctorate in economics
from the City University of New York in 1972. In 2002 Professor Fabozzi
was inducted into the Fixed Income Analysts Society’s Hall of Fame. He
earned the designation of Chartered Financial Analyst and Certified Public
Accountant. He has authored and edited numerous books in finance.
Sergio Focardi is a partner of The Intertek Group and a member of the
Editorial Board of the Journal of Portfolio Management. He is the (co-)
author of numerous articles and books on financial modeling and risk
management, including the CFA Institute’s recent monograph Trends in
Quantitative Finance (co-authors Fabozzi and Kolm) and the award-winning books Financial Modeling of the Equity Market (co-authors Fabozzi
and Kolm, Wiley) and The Mathematics of Financial Modeling and
Investment Management (co-author Fabozzi, Wiley). Mr. Focardi has
implemented long-short portfolio construction applications based on
dynamic factor analysis and conducts research in the econometrics of
large equity portfolios and the modeling of regime changes. He holds a
degree in Electronic Engineering from the University of Genoa and a postgraduate degree in Communications from the Galileo Ferraris Electrotechnical Institute (Turin).
ˇ ´ earned his doctorate (Dr.rer.pol.) in economics from the UniverTeo Jasic
sity of Karlsruhe in 2006. He also holds an MSc degree from the National
University of Singapore and a Dipl.-Ing. degree from the University of
Zagreb. Currently, he is a Postdoctoral Research Fellow at the Chair of
Statistics, Econometrics and Mathematical Finance at the University of
Karlsruhe in the School of Economics and Business Engineering. He is
also a senior manager in Financial & Risk Management Group of a leading
international management consultancy firm in Frankfurt, Germany. His
current professional and research interests are in the areas of asset manageˇ ´ has published
ment, risk management, and financial forecasting. Dr. Jasic
more than a dozen research papers in internationally refereed journals.


c01-FinEconoScope Page 1 Thursday, October 26, 2006 1:57 PM

CHAPTER

1

Financial Econometrics:
Scope and Methods

inancial econometrics is the econometrics of financial markets. It is a
quest for models that describe financial time series such as prices,
returns, interest rates, financial ratios, defaults, and so on. The economic equivalent of the laws of physics, econometrics represents the
quantitative, mathematical laws of economics. The development of a
quantitative, mathematical approach to economics started at the end of
the 19th century, in a period of great enthusiasm for the achievements of
science and technology.
The World Exhibition held in Paris in 1889 testifies to the faith of
that period in science and technology. The key attraction of the exhibition—the Eiffel Tower—was conceived by Gustave Eiffel, an architect
and engineer who had already earned a reputation building large metal
structures such as the 94-foot-high wrought-iron square skeleton that
supports the Statue of Liberty.1 With its 300-meter-high iron structure,
Eiffel’s tower was not only the tallest building of its time but also a

F

1

Eiffel was a shrewd businessman as well as an accomplished engineer. When he
learned that the funding for the 1889 World Exhibition tower would cover only
one fourth of the cost, he struck a deal with the French government: He would raise
the requisite funds in return for the right to exploit the tower commercially for 20

years. The deal made him wealthy. In the first year alone, revenues covered the entire cost of the project! Despite his sense of business, Eiffel’s career was destroyed
by the financial scandal surrounding the building of the Panama Canal, for which
his firm was a major contractor. Though later cleared of accusations of corruption,
Eiffel abandoned his business activities and devoted the last 30 years of his life to
research.

1


c01-FinEconoScope Page 2 Thursday, October 26, 2006 1:57 PM

2

FINANCIAL ECONOMETRICS

monument to applied mathematics. To ensure that the tower would
withstand strong winds, Eiffel wrote an integral equation to determine
the tower’s shape.2
The notion that mathematics is the language of nature dates back
2,000 years to the ancient Greeks and was forcefully expressed by Galileo. In his book Il saggiatore (The Assayer), published in 1623, Galileo
wrote (translation by one of the authors of this book):
[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it
is written. It is written in the language of mathematics; the
letters are triangles, circles, and other geometrical figures,
without which it is humanly impossible to comprehend a
single word.
It was only when Newton published his Principia some 60 years later
(1687) that this idea took its modern form. In introducing the concept
of instantaneous rate of change3 and formulating mechanics as laws that
link variables and their rates of change, Newton made the basic leap

forward on which all modern physical sciences are based. Linking variables to their rate of change is the principle of differential equations. Its
importance can hardly be overestimated. Since Newton, differential
equations have progressively conquered basically all the fields of the
physical sciences, including mechanics, thermodynamics, electromagnetism, relativity, and quantum mechanics.
During the 19th century, physics based on differential equations
revolutionized technology. It was translated into steam and electrical
engines, the production and transmission of electrical power, the transmission of electrical signals, the chemical transformation of substances,
and the ability to build ships, trains, and large buildings and bridges. It

2
The design principles employed by Eiffel have been used in virtually every subsequent tall building. Eiffel’s equation,

1
--2

H

∫x f ( x )

2

dx – c ( H – x ) =

H

∫x xw ( x )f ( x ) dx

states that the torque from the wind on any part of the Tower from a given height to
the top is equal to the torque of the weight of this same part.
3

The instantaneous rate of change, “derivative” in mathematical terminology, is one
of the basic concepts of calculus. Calculus was discovered independently by Newton
and Leibniz, who were to clash bitterly in claiming priority in the discovery.