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ISBN 10: 110843682X
ISBN 13: 978-1108436823
Author: Chris Brooks
A complete resource for finance students, this textbook presents the most common empirical approaches in finance in a comprehensive and well-illustrated manner that shows how econometrics is used in practice, and includes detailed case studies to explain how the techniques are used in relevant financial contexts. Maintaining the accessible prose and clear examples of previous editions, the new edition of this best-selling textbook provides support for the main industry-standard software packages, expands the coverage of introductory mathematical and statistical techniques into two chapters for students without prior econometrics knowledge, and includes a new chapter on advanced methods. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Online resources include extensive teacher and student support materials, including EViews, Stata, R, and Python software guides.
Introductory Econometrics for Finance 4th Table of contents:
1 Introduction and Mathematical Foundations
1.1 What is Econometrics?
1.2 Is Financial Econometrics Different from ‘Economic Econometrics’?
1.3 Steps Involved in Formulating an Econometric Model
1.4 Points to Consider When Reading Articles in Empirical Finance
1.5 Functions
1.5.1 Introduction to Functions
1.5.2 Straight Lines
1.5.3 Polynomial Functions
1.5.4 Powers of Numbers or of Variables
1.5.5 The Exponential Function
1.5.6 Logarithms
1.5.7 Inverse Functions
1.5.8 Sigma Notation
1.5.9 Pi Notation
1.5.10 Functions of More than one Variable
1.6 Differential Calculus
1.6.1 Differentiation: the Fundamentals
1.6.2 Derivatives of Products and Quotients
1.6.3 Higher Order Derivatives
1.6.4 Differentiation of Functions of Functions Using the Chain Rule
1.6.5 Partial Differentiation
1.6.6 Functions that Cannot be Differentiated
1.6.7 Derivatives in Use in Finance
1.6.8 Integration
1.7 Matrices
1.7.1 Operations with Matrices
1.7.2 The Rank of a Matrix
1.7.3 The Inverse of a Matrix
1.7.4 The Trace of a Matrix
1.7.5 The Eigenvalues of a Matrix
2 Statistical Foundations and Dealing with Data
2.1 Probability and Probability Distributions
2.1.1 The Central Limit Theorem
2.1.2 Other Statistical Distributions
2.2 A Note on Bayesian versus Classical Statistics
2.3 Descriptive Statistics
2.3.1 Measures of Central Tendency
2.3.2 Measures of Spread
2.3.3 Higher Moments
2.3.4 Measures of Association
2.3.5 An Example of How to Calculate Summary Statistics
2.3.6 Useful Algebra for Means, Variances and Covariances
2.4 Types of Data and Data Aggregation
2.4.1 Time-Series Data
2.4.2 Cross-Sectional Data
2.4.3 Panel Data
2.4.4 Continuous and Discrete Data
2.4.5 Cardinal, Ordinal and Nominal Numbers
2.5 Arithmetic and Geometric Series
2.6 Future Values and Present Values
2.6.1 Future Values
2.6.2 Present Value
2.6.3 Internal Rate of Return
2.7 Returns in Financial Modelling
2.7.1 Real versus Nominal Series and Deflating Nominal Series
2.8 Portfolio Theory Using Matrix Algebra
2.8.1 The Mean–Variance Efficient Frontier in Excel
3 A Brief Overview of the Classical Linear Regression Model
3.1 What is a Regression Model?
3.2 Regression versus Correlation
3.3 Simple Regression
3.3.1 What are [hat(alpha)] and [hat(beta)] Used For?
3.4 Some Further Terminology
3.4.1 The Data Generating Process, the Population Regression Function and the Sample Regression Func
3.4.2 Linearity and Possible Forms for the Regression Function
3.4.3 Estimator or Estimate?
3.5 The Assumptions Underlying the Classical Linear Regression Model
3.6 Properties of the OLS Estimator
3.6.1 Consistency
3.6.2 Unbiasedness
3.6.3 Efficiency
3.6.4 More on Unbiasedness and Efficiency
3.7 Precision and Standard Errors
3.7.1 Estimating the Variance of the Error Term (σ[sup(2)])
3.7.2 Some Comments on the Standard Error Estimators
3.8 An Introduction to Statistical Inference
3.8.1 Hypothesis Testing: Some Concepts
3.8.2 The Probability Distribution of the Least Squares Estimators
3.8.3 A Note on the t and the Normal Distributions
3.8.4 The Test of Significance Approach (Box 3.5)
3.8.5 The Confidence Interval Approach to Hypothesis Testing (Box 3.6)
3.8.6 The Test of Significance and Confidence Interval Approaches Always Give the Same Conclusion
3.8.7 Some More Terminology
3.8.8 Classifying the Errors That Can be Made Using Hypothesis Tests
3.9 A Special Type of Hypothesis Test: The t-ratio
3.10 An Example of a Simple t-test of a Theory in Finance: Can US Mutual Funds Beat the Market?
3.11 Can UK Unit Trust Managers Beat the Market?
3.12 The Overreaction Hypothesis and the UK Stock Market
3.12.1 Motivation
3.12.2 Methodology
3.12.3 Conclusions
3.13 The Exact Significance Level
Appendix 3.1 Mathematical Derivations of CLRM Results
3A.1 Derivation of the OLS Coefficient Estimator in the Bivariate Case
3A.2 Derivation of the OLS Standard Error Estimators for the Intercept and Slope in the Bivariate Ca
4 Further Development and Analysis of the Classical Linear Regression Model
4.1 Generalising the Simple Model to Multiple Linear Regression
4.2 The Constant Term
4.3 How are the Parameters (the Elements of the β Vector) Calculated in the Generalised Case?
4.4 Testing Multiple Hypotheses: The F-test
4.4.1 The Relationship Between the t- and the F-Distributions
4.4.2 Determining the Number of Restrictions, m
4.4.3 Hypotheses that Cannot be Tested with Either an F- or a t-Test
4.4.4 A Note on Sample Sizes and Asymptotic Theory
4.5 Data Mining and the True Size of the Test
4.6 Qualitative Variables
4.7 Goodness of Fit Statistics
4.7.1 R[sup(2)]
4.7.2 Problems with R[sup(2)] as a Goodness of Fit Measure
4.7.3 Adjusted R[sup(2)]
4.8 Hedonic Pricing Models
4.9 Tests of Non-Nested Hypotheses
4.10 Quantile Regression
4.10.1 Background and Motivation
4.10.2 Estimation of Quantile Functions
4.10.3 An Application of Quantile Regression: Evaluating Fund Performance
Appendix 4.1 Mathematical Derivations of CLRM Results
Appendix 4.2 A Brief Introduction to Factor Models and Principal Components Analysis
5 Classical Linear Regression Model Assumptions and Diagnostic Tests
5.1 Introduction
5.2 Statistical Distributions for Diagnostic Tests
5.3 Assumption (1): E(u[sub(t)])=0
5.4 Assumption (2): var(u[sub(t)]) = σ[sup(2)] < ∞
5.4.1 Detection of Heteroscedasticity
5.4.2 Consequences of Using OLS in the Presence of Heteroscedasticity
5.4.3 Dealing with Heteroscedasticity
5.5 Assumption (3): cov(u[sub(i)],u[sub(j)]) = 0 for i [neq] j
5.5.1 The Concept of a Lagged Value
5.5.2 Graphical Tests for Autocorrelation
5.5.3 Detecting Autocorrelation: The Durbin–Watson Test
5.5.4 Conditions Which Must be Fulfilled for DW to be a Valid Test
5.5.5 Another Test for Autocorrelation: The Breusch–Godfrey Test
5.5.6 Consequences of Ignoring Autocorrelation if it is Present
5.5.7 Dealing with Autocorrelation
5.5.8 Dynamic Models
5.5.9 Why Might Lags be Required in a Regression?
5.5.10 The Long-Run Static Equilibrium Solution
5.5.11 Problems with Adding Lagged Regressors to ‘Cure’ Autocorrelation
5.5.12 Autocorrelation in Cross-Sectional Data
5.6 Assumption (4): The x[sub(t)] are Non-Stochastic
5.7 Assumption (5): The Disturbances are Normally Distributed
5.7.1 Testing for Departures from Normality
5.7.2 What Should be Done if Evidence of Non-Normality is Found?
5.8 Multicollinearity
5.8.1 Measuring Near Multicollinearity
5.8.2 Problems if Near Multicollinearity is Present but Ignored
5.8.3 Solutions to the Problem of Multicollinearity
5.9 Adopting the Wrong Functional Form
5.9.1 What if the Functional Form is Found to be Inappropriate?
5.10 Omission of an Important Variable
5.11 Inclusion of an Irrelevant Variable
5.12 Parameter Stability Tests
5.12.1 The Chow Test
5.12.2 The Predictive Failure Test
5.12.3 Backward versus Forward Predictive Failure Tests
5.12.4 How Can the Appropriate Sub-Parts to Use be Decided?
5.12.5 The QLR Test
5.12.6 Stability Tests Based on Recursive Estimation
5.13 Measurement Errors
5.13.1 Measurement Error in the Explanatory Variable(s)
5.13.2 Measurement Error in the Explained Variable
5.14 A Strategy for Constructing Econometric Models and a Discussion of Model-Building Philosophies
5.15 Determinants of Sovereign Credit Ratings
5.15.1 Background
5.15.2 Data
5.15.3 Interpreting the Models
5.15.4 The Relationship Between Ratings and Yields
5.15.5 What Determines How the Market Reacts to Ratings Announcements?
5.15.6 Conclusions
6 Univariate Time-Series Modelling and Forecasting
6.1 Introduction
6.2 Some Notation and Concepts
6.2.1 A Strictly Stationary Process
6.2.2 A Weakly Stationary Process
6.2.3 A White Noise Process
6.3 Moving Average Processes
6.4 Autoregressive Processes
6.4.1 The Stationarity Condition
6.4.2 Wold’s Decomposition Theorem
6.5 The Partial Autocorrelation Function
6.5.1 The Invertibility Condition
6.6 ARMA Processes
6.6.1 Sample acf and pacf Plots for Standard Processes
6.7 Building ARMA Models: The Box–Jenkins Approach
6.7.1 Information Criteria for ARMA Model Selection
6.7.2 Which Criterion Should be Preferred if they Suggest Different Model Orders?
6.7.3 ARIMA Modelling
6.8 Examples of Time-Series Modelling in Finance
6.8.1 Covered and Uncovered Interest Parity
6.8.2 Covered Interest Parity
6.8.3 Uncovered Interest Parity
6.9 Exponential Smoothing
6.10 Forecasting in Econometrics
6.10.1 Why Forecast?
6.10.2 The Difference Between In-Sample and Out-of-Sample Forecasts
6.10.3 Some More Terminology: One-Step-Ahead versus Multi-Step-Ahead Forecasts and Rolling versus Re
6.10.4 Forecasting with Time-Series versus Structural Models
6.10.5 Forecasting with ARMA Models
6.10.6 Forecasting the Future Value of an MA(q) Process
6.10.7 Forecasting the Future Value of an AR(p) Process
6.10.8 Determining Whether a Forecast is Accurate or Not
6.10.9 Statistical versus Financial or Economic Loss Functions
6.10.10 Finance Theory and Time-Series Analysis
7 Multivariate Models
7.1 Motivations
7.2 Simultaneous Equations Bias
7.3 So how can Simultaneous Equations Models be Validly Estimated?
7.4 Can the Original Coefficients be Retrieved from the πs?
7.4.1 What Determines Whether an Equation is Identified or Not?
7.4.2 Statement of the Order Condition
7.5 Simultaneous Equations in Finance
7.6 A Definition of Exogeneity
7.6.1 Tests for Exogeneity
7.7 Triangular Systems
7.8 Estimation Procedures for Simultaneous Equations Systems
7.8.1 Indirect Least Squares (ILS)
7.8.2 Estimation of Just Identified and Overidentified Systems using 2SLS
7.8.3 Instrumental Variables
7.8.4 What Happens if IV or 2SLS are Used Unnecessarily?
7.8.5 Other Estimation Techniques
7.9 An Application of a Simultaneous Equations Approach to Modelling Bid–Ask Spreads and Trading A
7.9.1 Introduction
7.9.2 The Data
7.9.3 How Might the Option Price/Trading Volume and the Bid–Ask Spread be Related?
7.9.4 The Influence of Tick-Size Rules on Spreads
7.9.5 The Models and Results
7.9.6 Conclusions
7.10 Vector Autoregressive Models
7.10.1 Advantages of VAR Modelling
7.10.2 Problems with VARs
7.10.3 Choosing the Optimal Lag Length for a VAR
7.10.4 Rules of Thumb for VAR Lag Length Selection
7.10.5 Cross-Equation Restrictions for VAR Lag Length Selection
7.10.6 Information Criteria for VAR Lag Length Selection
7.11 Does the VAR Include Contemporaneous Terms?
7.12 Block Significance and Causality Tests
7.12.1 Restricted VARs
7.13 VARs with Exogenous Variables
7.14 Impulse Responses and Variance Decompositions
7.15 VAR Model Example: The Interaction Between Property Returns and the Macroeconomy
7.15.1 Background, Data and Variables
7.15.2 Methodology
7.15.3 Results
7.15.4 Conclusions
7.16 A Couple of Final Points on VARs
8 Modelling Long-Run Relationships in Finance
8.1 Stationarity and Unit Root Testing
8.1.1 Why are Tests for Non-Stationarity Necessary?
8.1.2 Two Types of Non-Stationarity
8.1.3 Some More Definitions and Terminology
8.1.4 Testing for a Unit Root
8.1.5 Testing for Higher Orders of Integration
8.1.6 Phillips–Perron (PP) Tests
8.1.7 Criticisms of Dickey–Fuller- and Phillips–Perron-Type Tests
8.2 Tests for Unit Roots in the Presence of Structural Breaks
8.2.1 Motivation
8.2.2 The Perron (1989) Procedure
8.2.3 An Example: Testing for Unit Roots in EuroSterling Interest Rates
8.2.4 Seasonal Unit Roots
8.3 Cointegration
8.3.1 Definition of Cointegration (Engle and Granger, 1987)
8.3.2 Examples of Possible Cointegrating Relationships in Finance
8.4 Equilibrium Correction or Error Correction Models
8.5 Testing for Cointegration in Regression: A Residuals-Based Approach
8.6 Methods of Parameter Estimation in Cointegrated Systems
8.6.1 The Engle–Granger 2-Step Method
8.6.2 The Engle and Yoo 3-Step Method
8.7 Lead–Lag Relationships Between Spot and Futures Markets
8.7.1 Background
8.7.2 Forecasting Spot Returns
8.7.3 Conclusions
8.8 Testing for and Estimating Cointegration in Systems Using the Johansen Technique based on VARs
8.8.1 Tests for Cointegration with Mixed Orders of Integration
8.8.2 Hypothesis Testing using Johansen
8.9 Purchasing Power Parity
8.10 Cointegration Between International Bond Markets
8.10.1 Cointegration Between International Bond Markets: A Univariate Approach
8.10.2 Cointegration Between International Bond Markets: A Multivariate Approach
8.10.3 Cointegration in International Bond Markets: Conclusions
8.11 Testing the Expectations Hypothesis of the Term Structure of Interest Rates
9 Modelling Volatility and Correlation
9.1 Motivations: An Excursion into Non-Linearity Land
9.1.1 Types of Non-Linear Models
9.1.2 Testing for Non-Linearity
9.1.3 Chaos in Financial Markets
9.1.4 Neural Network Models
9.2 Models for Volatility
9.3 Historical Volatility
9.4 Implied Volatility Models
9.5 Exponentially Weighted Moving Average Models
9.6 Autoregressive Volatility Models
9.7 Autoregressive Conditionally Heteroscedastic (ARCH) Models
9.7.1 Another Way of Expressing ARCH Models
9.7.2 Non-Negativity Constraints
9.7.3 Testing for ‘ARCH Effects’
9.7.4 Limitations of ARCH(q) Models
9.8 Generalised ARCH (GARCH) Models
9.8.1 The Unconditional Variance Under a GARCH Specification
9.9 Estimation of ARCH/GARCH Models
9.9.1 Parameter Estimation Using Maximum Likelihood
9.9.2 Non-Normality and Maximum Likelihood
9.10 Extensions to the Basic GARCH Model
9.11 Asymmetric GARCH Models
9.12 The GJR model
9.13 The EGARCH Model
9.14 Tests for Asymmetries in Volatility
9.14.1 News Impact Curves
9.15 GARCH-in-Mean
9.16 Uses of GARCH-Type Models Including Volatility Forecasting
9.17 Testing Non-Linear Restrictions or Testing Hypotheses About Non-Linear Models
9.17.1 Likelihood Ratio Tests
9.18 Volatility Forecasting: Some Examples and Results from the Literature
9.19 Stochastic Volatility Models Revisited
9.19.1 Higher Moment Models
9.19.2 Tail Models
9.20 Forecasting Covariances and Correlations
9.21 Covariance Modelling and Forecasting in Finance: Some Examples
9.21.1 The Estimation of Conditional Betas
9.21.2 Dynamic Hedge Ratios
9.22 Simple Covariance Models
9.22.1 Historical Covariance and Correlation
9.22.2 Implied Covariance Models
9.22.3 Exponentially Weighted Moving Average Model for Covariances
9.23 Multivariate GARCH Models
9.23.1 The VECH model
9.23.2 The Diagonal VECH Model
9.23.3 The BEKK model
9.23.4 Model Estimation for Multivariate GARCH
9.24 Direct Correlation Models
9.24.1 The Constant Correlation Model
9.24.2 The Dynamic Conditional Correlation Model
9.25 Extensions to the Basic Multivariate GARCH Model
9.25.1 Asymmetric Multivariate GARCH
9.25.2 Alternative Distributional Assumptions
9.26 A Multivariate GARCH Model for the CAPM with Time-Varying Covariances
9.27 Estimating a Time-Varying Hedge Ratio for FTSE Stock Index Returns
9.27.1 Background
9.27.2 Notation
9.27.3 Data and Results
9.28 Multivariate Stochastic Volatility Models
Appendix 9.1 Parameter Estimation Using Maximum Likelihood
10 Switching and State Space Models
10.1 Motivations
10.1.1 What Might Cause One-Off Fundamental Changes in the Properties of a Series?
10.2 Seasonalities in Financial Markets: Introduction and Literature Review
10.3 Modelling Seasonality in Financial Data
10.3.1 Slope Dummy Variables
10.3.2 Interactive Dummy Variables
10.4 Estimating Simple Piecewise Linear Functions
10.5 Markov Switching Models
10.5.1 Fundamentals of Markov Switching Models
10.6 A Markov Switching Model for the Real Exchange Rate
10.7 A Markov Switching Model for the Gilt–Equity Yield Ratio
10.8 Threshold Autoregressive Models
10.9 Estimation of Threshold Autoregressive Models
10.9.1 Threshold Model Order (Lag Length) Determination
10.9.2 Determining the Delay Parameter, d
10.10 Specification Tests in the Context of Markov Switching and Threshold Autoregressive Models: A
10.11 A SETAR Model for the French franc–German mark Exchange Rate
10.12 Threshold Models and the Dynamics of the FTSE 100 Index and Index Futures Markets
10.13 A Note on Regime Switching Models and Forecasting Accuracy
10.14 State Space Models and the Kalman Filter
10.14.1 Introduction to the State Space Formulation
10.14.2 Parameter Estimation for State Space Models
10.14.3 Example: Time-Varying Beta Estimation
10.14.4 Further Reading on State Space Models
11 Panel Data
11.1 Introduction: What Are Panel Techniques and Why are They Used?
11.2 What Panel Techniques Are Available?
11.3 The Fixed Effects Model
11.4 Time-Fixed Effects Models
11.5 Investigating Banking Competition Using a Fixed Effects Model
11.6 The Random Effects Model
11.7 Panel Data Application to Credit Stability of Banks in Central and Eastern Europe
11.8 Panel Unit Root and Cointegration Tests
11.8.1 Background and Motivation
11.8.2 Tests with Common Alternative Hypotheses
11.8.3 Panel Unit Root Tests with Heterogeneous Processes
11.8.4 Panel Stationarity Tests
11.8.5 Allowing for Cross-Sectional Heterogeneity
11.8.6 Panel Cointegration
11.8.7 An Illustration of the Use of Panel unit Root and Cointegration Tests: The Link Between Finan
11.9 Further Feading
12 Limited Dependent Variable Models
12.1 Introduction and Motivation
12.2 The Linear Probability Model
12.3 The Logit Model
12.4 Using a Logit to Test the Pecking Order Hypothesis
12.5 The Probit Model
12.6 Choosing Between the Logit and Probit Models
12.7 Estimation of Limited Dependent Variable Models
12.8 Goodness of Fit Measures for Linear Dependent Variable Models
12.9 Multinomial Linear Dependent Variables
12.10 The Pecking Order Hypothesis Revisited: The Choice Between Financing Methods
12.11 Ordered Response Linear Dependent Variables Models
12.12 Are Unsolicited Credit Ratings Biased Downwards? An Ordered Probit Analysis
12.13 Censored and Truncated Dependent Variables
12.13.1 Censored Dependent Variable Models
12.13.2 Truncated Dependent Variable Models
Appendix 12.1 The Maximum Likelihood Estimator for Logit and Probit Models
13 Simulation Methods
13.1 Motivations
13.2 Monte Carlo Simulations
13.3 Variance Reduction Techniques
13.3.1 Antithetic Variates
13.3.2 Control Variates
13.3.3 Random Number Re-Usage Across Experiments
13.4 Bootstrapping
13.4.1 An Example of Bootstrapping in a Regression Context
13.4.2 Situations where the Bootstrap will be Ineffective
13.5 Random Number Generation
13.6 Disadvantages of the Simulation Approach to Econometric or Financial Problem Solving
13.7 An example of Monte Carlo Simulation in Econometrics: Deriving a Set of Critical Values for a D
13.8 An Example of how to Simulate the Price of a Financial Option
13.8.1 Simulating the Price of a Financial Option Using a Fat-Tailed Underlying Process
13.8.2 Simulating the Price of an Asian Option
13.9 An Example of Bootstrapping to Calculate Capital Risk Requirements
13.9.1 Financial Motivation
14 Additional Econometric Techniques for Financial Research
14.1 Event Studies
14.1.1 Some Notation and a Description of the Basic Approach
14.1.2 Cross-Sectional Regressions
14.1.3 Complications When Conducting Event Studies and Their Resolution
14.1.4 Conducting an Event Study Using Excel
14.2 Tests of the CAPM and the Fama–French Methodology
14.2.1 Testing the CAPM
14.2.2 Asset Pricing Tests: the Fama–French Approach
14.3 Extreme Value Theory
14.3.1 Extreme Value Theory: An Introduction
14.3.2 The Block Maximum Approach
14.3.3 The Peaks Over Threshold Approach
14.3.4 Parameter Estimation for Extreme Value Distributions
14.3.5 Introduction to Value at Risk
14.3.6 Some Final Further Issues in Implementing Extreme Value Theory
14.3.7 An Application of Extreme Value Theory to VaR Estimation
14.3.8 Additional Further Reading on Extreme Value Theory
14.4 The Generalised Method of Moments
14.4.1 Introduction to the Method of Moments
14.4.2 The Generalised Method of Moments
14.4.3 GMM in the Asset Pricing Context
14.4.4 A GMM Application to the Link Between Financial Markets and Economic Growth
14.4.5 Additional Further Reading
15 Conducting Empirical Research or Doing a Project or Dissertation in Finance
15.1 What is an Empirical Research Project and What is it For?
15.2 Selecting the Topic
15.3 Sponsored or Independent Research?
15.4 The Research Proposal
15.5 Working Papers and Literature on the Internet
15.6 Getting the Data
15.7 Choice of Computer Software
15.8 Methodology
15.9 How Might the Finished Project Look?
15.10 Presentational Issues
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