Contents
List of figures ix
List of tables x
Acknowledgements xii
Preface xiv
1 Stochastic processes and financial data generating processes 1
1.1. Introduction 1
1.2. Stochastic processes and their properties 5
1.3. The behaviour of financial variables and beyond 8
2 Commonly applied statistical distributions and their relevance 15
2.1. Normal distributions 15
2.2. χ2-distributions 23
2.3. t-distributions 25
2.4. F-distributions 28
3 Overview of estimation methods 30
3.1. Basic OLS procedures 30
3.2. Basic ML procedures 32
3.3. Estimation when iid is violated 33
3.4. General residual distributions in time series and
cross-section modelling 35
3.5. MM and GMM approaches 40
4 Unit roots, cointegration and other comovements in time series 45
4.1. Unit roots and testing for unit roots 45
4.2. Cointegration 49
4.3. Common trends and common cycles 51
4.4. Examples and cases 53
4.5. Empirical literature 58

5 Time-varying volatility models: GARCH and stochastic
volatility 66
5.1. ARCH and GARCH and their variations 66
5.2. Multivariate GARCH 70
5.3. Stochastic volatility 74
5.4. Examples and cases 75
5.5. Empirical literature 82
6 Shock persistence and impulse response analysis 89
6.1. Univariate persistence measures 90
6.2. Multivariate persistence measures 92
6.3. Impulse response analysis and variance decomposition 95
6.4. Non-orthogonal cross-effect impulse response analysis 98
6.5. Examples and cases 99
6.6. Empirical literature 108
7 Modelling regime shifts: Markov switching models 113
7.1. Markov chains 113
7.2. Estimation 114
7.3. Smoothing 117
7.4. Time-varying transition probabilities 119
7.5. Examples and cases 120
7.6. Empirical literature 126
8 Present value models and tests for rationality
and market efficiency 131
8.1. The basic present value model and its time series
characteristics 131
8.2. The VAR representation 133
8.3. The present value model in logarithms with time-varying
discount rates 136
8.4. The VAR representation for the present value model in the
log-linear form 138
8.5. Variance decomposition 139
8.6. Examples and cases 140
8.7. Empirical literature 147
9 State space models and the Kalman filter 151
9.1. State space expression 151
9.2. Kalman filter algorithms 152
9.3. Time-varying coefficient models 153
9.4. State space models of commonly used time
series processes 154

9.5. Examples and cases 158
9.6. Empirical literature 164
10 Frequency domain analysis of time series 168
10.1. The Fourier transform and spectra 168
10.2. Multivariate spectra, phases and coherence 172
10.3. Frequency domain representations of commonly used time
series processes 173
10.4. Frequency domain analysis of the patterns of violation of
white noise conditions 175
10.5. Examples and cases 182
10.6. Empirical literature 194
11 Limited dependent variables and discrete choice models 198
11.1. Probit and logit formulations 199
11.2. Multinomial logit models and multinomial logistic
regression 202
11.3. Ordered probit and logit 205
11.4. Marginal effects 207
11.5. Examples and cases 210
11.6. Empirical literature 220
12 Limited dependent variables and truncated and censored
samples 226
12.1. Truncated and censored data analysis 226
12.2. The Tobit model 230
12.3. Generalisation of the Tobit model: Heckman and
Cragg 233
12.4. Examples and cases 234
12.5. Empirical literature 242
13 Panel data analysis 249
13.1. Structure and organisation of panel data sets 250
13.2. Fixed effects vs. random effects models 252
13.3. Random parameter models 260
13.4. Dynamic panel data analysis 264
13.5. Examples and cases 269
13.6. Empirical literature 278
14 Research tools and sources of information 289
14.1. Financial economics and econometrics literature
on the Internet 289

14.2. Econometric software packages for financial and economic
data analysis 291
14.3. Learned societies and professional associations 294
14.4. Organisations and institutions 299
Index 313