By Gary Koop

Contents
Preface ix
Chapter 1 Introduction 1
Organization of the book 3
Useful background 4
Appendix 1.1: Concepts in mathematics used in this book 4
Chapter 2 Basic data handling 9
Types of financial data 9
Obtaining data 15
Working with data: graphical methods 16
Working with data: descriptive statistics 21
Expected values and variances 24
Chapter summary 26
Appendix 2.1: Index numbers 27
Appendix 2.2: Advanced descriptive statistics 30
Chapter 3 Correlation 33
Understanding correlation 33
Understanding why variables are correlated 39
Understanding correlation through XY-plots 40
Correlation between several variables 44
Covariances and population correlations 45
Chapter summary 47
Appendix 3.1: Mathematical details 47
Chapter 4 An introduction to simple regression 49
Regression as a best fitting line 50
Interpreting OLS estimates 53
Fitted values and R2: measuring the fit of a regression model 55
Nonlinearity in regression 61
Chapter summary 64
Appendix 4.1: Mathematical details 65
Chapter 5 Statistical aspects of regression 69
Which factors affect the accuracy of the estimate bˆ? 70
Calculating a confidence interval for b 73
Testing whether b =0 79
Hypothesis testing involving R2: the F-statistic 84
Chapter summary 86
Appendix 5.1: Using statistical tables for testing whether
b =0 87
Chapter 6 Multiple regression 91
Regression as a best fitting line 93
Ordinary least squares estimation of the multiple
regression model 93
Statistical aspects of multiple regression 94
Interpreting OLS estimates 95
Pitfalls of using simple regression in a multiple
regression context 98
Omitted variables bias 100
Multicollinearity 102
Chapter summary 105
Appendix 6.1: Mathematical interpretation of
regression coefficients 105
Chapter 7 Regression with dummy variables 109
Simple regression with a dummy variable 112
Multiple regression with dummy variables 114
Multiple regression with both dummy and non-dummy
explanatory variables 116
Interacting dummy and non-dummy variables 120
What if the dependent variable is a dummy? 121
Chapter summary 122
Chapter 8 Regression with lagged explanatory variables 123
Aside on lagged variables 125
Aside on notation 127
vi Contents
Selection of lag order 132
Chapter summary 135
Chapter 9 Univariate time series analysis 137
The autocorrelation function 140
The autoregressive model for univariate time series 144
Nonstationary versus stationary time series 146
Extensions of the AR(1) model 149
Testing in the AR( p) with deterministic trend model 152
Chapter summary 158
Appendix 9.1: Mathematical intuition for the AR(1) model 159
Chapter 10 Regression with time series variables 161
Time series regression when X and Y are stationary 162
Time series regression when Y and X have unit roots:
spurious regression 167
Time series regression when Y and X have unit roots:
cointegration 167
Time series regression when Y and X are cointegrated:
the error correction model 174
Time series regression when Y and X have unit roots
but are not cointegrated 177
Chapter summary 179
Chapter 11 Regression with time series variables with
several equations 183
Granger causality 184
Vector autoregressions 190
Chapter summary 203
Appendix 11.1: Hypothesis tests involving more than
one coefficient 204
Appendix 11.2: Variance decompositions 207
Chapter 12 Financial volatility 211
Volatility in asset prices: Introduction 212
Autoregressive conditional heteroskedasticity (ARCH) 217
Chapter summary 222
Appendix A Writing an empirical project 223
Description of a typical empirical project 223
General considerations 225
Appendix B Data directory 227
Index 231
Contents vii