Financial Econometrics
Methods and models
Peijie Wang

2003
193pages

Detailed contents
1 Stochastic processes and financial time series 1
1.1 Introduction 1
1.2 Stochastic processes and their properties 3
1.2.1 Martingales 4
1.2.2 Random walks 4
1.2.3 Gaussian white noise processes 4
1.2.4 Poisson processes 5
1.2.5 Markov processes 6
1.2.6 Wiener processes 6
1.2.7 Stationarity and ergodicity 6
1.3 The behaviour and valuation of security prices 7
1.3.1 Generalised Wiener processes 7
1.3.2 Ito processes 8
1.3.3 Ito’s lemma 8
1.3.4 Geometric Wiener processes and financial variable
behaviour in the short term and long run 9
1.3.5 Valuation of derivative securities and beyond 11
References 12



2 Unit roots, cointegration and other comovements in time series 14
2.1 Unit roots and testing for unit roots 14
2.1.1 Dickey and Fuller 16
2.1.2 Phillips and Perron 16
2.1.3 Kwiatkowski, Phillips, Schmidt and Shin 17
2.1.4 Panel unit root tests 17
2.2 Cointegration 18
2.3 Common trends and common cycles 20
2.4 Examples and cases 22
2.5 Empirical literature 27
Questions and problems 30
References 32


3 Time-varying volatility models – GARCH and
stochastic volatility 35
3.1 ARCH and GARCH and their variations 35
3.1.1 ARCH and GARCH models 35
3.1.2 Variations of the ARCH/GARCH model 37
3.2 Multivariate GARCH 39
3.2.1 Constant correlation 39
3.2.2 Full parameterisation 40
3.2.3 Positive definite parameterisation 40
3.3 Stochastic volatility 43
3.4 Examples and cases 44
3.5 Empirical literature 50
Questions and problems 54
References 54



4 Shock persistence and impulse response analysis 58
4.1 Univariate persistence measures 59
4.2 Multivariate persistence 61
4.3 Impulse response analysis and variance decomposition 64
4.4 Non-orthogonal cross-effect impulse response analysis 67
4.5 Examples and cases 68
4.6 Empirical literature 76
Questions and problems 79
References 80


5 Modelling regime shifts: Markov switching models 82
5.1 Markov chains 82
5.2 Estimation 83
5.3 Smoothing 86
5.4 Time-varying transition probabilities 88
5.5 Examples and cases 89
5.6 Empirical literature 94
Questions and problems 96
References 97



6 Present value models and tests for rationality and
market efficiency 99
6.1 The basic present value model and its time
series characteristics 99
6.2 The VAR representation 101
6.3 The present value model in logarithms with
time-varying discount rates 104
6.4 The VAR representation for the present value model in the
log-linear form 106
6.5 Variance decomposition 107
6.6 Examples and cases 108
6.7 Empirical literature 114
Questions and problems 116
References 116


7 State space models and the Kalman filter 118
7.1 State space expression 118
7.2 Kalman filter algorithm 119
7.3 Time-varying coefficient models 120
7.4 State space models of commonly used time series processes 121
7.4.1 AR(p) process 121
7.4.2 ARMA(p,q) process 122
7.4.3 Stochastic volatility 123
7.4.4 Time-varying coefficients 124
7.5 Examples and cases 125
7.6 Empirical literature 130
Questions and problems 132
References 132


8 Frequency domain analysis of time series 134
8.1 The Fourier transform and spectra 134
8.2 Multivariate spectra, phases and coherence 138
8.3 Frequency domain representations of commonly used time series
processes 139
8.3.1 AR(p) process 139
8.3.2 MA(q) process 140
8.3.3 VAR (p) process 140
8.4 Test statistics for persistence and time series properties 140
8.4.1 Persistence spectra 140
8.4.2 Test statistics and associated patterns and behaviour 141
8.5 Examples and cases 145
8.6 Empirical literature 149
Questions and problems 152
References 153


9 Research tools and sources of information 155
9.1 Financial economics and econometrics literature
on the Internet 155
9.2 Econometrics packages for financial and economic
time series 157
9.3 Learned societies and professional associations 159
9.4 Organisations and institutions 162
9.4.1 International financial institutions and
other organisations 162
9.4.2 Major stock exchanges, option and futures
exchanges and regulators 164
9.4.3 Central banks 168