Cover 1
Half-title 3
Title 5
Copyright 6
Contents 7
Figures 10
Tables 13
Preface to the third edition 15
1 Introduction 17
2 Univariate linear stochastic models: basic concepts 25
2.1 Stochastic processes, ergodicity and stationarity 25
2.1.1 Stochastic processes, realisations and ergodicity 25
2.1.2 Stationarity 26
2.2 Stochastic difference equations 28
2.3 ARMA processes 30
2.3.1 Autoregressive processes 30
2.3.2 Moving average processes 33
2.3.3 General AR and MA processes 34
2.3.4 Autoregressive moving average models 42
2.4 Linear stochastic processes 44
2.5 ARMA model building 44
2.5.1 Sample autocorrelation and partial autocorrelation functions 44
2.5.2 Model-building procedures 45
2.6 Non-stationary processes and ARIMA models 53
2.6.1 Non-stationarity in variance 54
2.6.2 Non-stationarity in mean 55
2.7 ARIMA modelling 64
2.8 Seasonal ARIMA modelling 69
2.9 Forecasting using ARIMA models 73
3 Univariate linear stochastic models: testing for unit roots and alternative trend specifications 81
3.1 Determining the order of integration of a time series 83
3.2 Testing for a unit root 85
3.2.1 An introduction to unit root tests 85
3.2.2 Extensions to the Dickey\u2013Fuller test 93
3.2.3 Non-parametric tests for a unit root 96
3.3 Trend stationarity versus difference stationarity 101
3.4 Other approaches to testing for unit roots 105
3.5 Testing for more than one unit root 112
3.6 Segmented trends, structural breaks and smooth transitions 114
3.7 Stochastic unit root processes 121
4 Univariate linear stochastic models: further topics 127
4.1 Decomposing time series: unobserved component models and signal extraction 127
4.1.1 Unobserved component models 127
4.1.2 Signal extraction 133
4.2 Measures of persistence and trend reversion 140
4.2.1 Alternative measures of persistence 140
4.2.2 Testing for trend reversion 143
4.2.3 Mean reverting models in continuous time 146
4.3 Fractional integration and long memory processes 150
4.3.1 A broader definition of stationarity 150
4.3.2 ARFIMA models 152
4.3.2 Testing for fractional differencing 157
4.3.3 Estimation of ARFIMA models 161
5 Univariate non-linear stochastic models: martingales, random walks and modelling volatility 167
5.1 Martingales, random walks and non-linearity 167
5.2 Testing the random walk hypothesis 169
5.2.1 Autocorrelation tests 170
5.2.2 Calendar effects 172
5.3 Measures of volatility 173
5.4 Stochastic volatility 182
5.4.1 Stochastic volatility models 182
5.4.2 Estimation of stochastic volatility models 187
5.5 ARCH processes 190
5.5.1 Development of generalised ARCH processes 190
5.5.2 Modifications of GARCH processes 195
5.5.3 Non-linear GARCH processes 198
5.5.4 Long-memory volatility processes: the FIGARCH model 200
5.5.5 Estimation of ARMA models with ARCH errors 202
5.5.6 Testing for the presence of ARCH errors 205
5.5.7 ARCH and theories of asset pricing 207
5.6 Some models related to ARCH 215
5.6.1 Simple and exponential moving averages 215
5.6.2 Autoregressive conditional duration models 216
5.6.3 Modelling higher moments of the conditional distribution 218
5.7 The forecasting performance of alternative volatility models 220
6 Univariate non-linear stochastic models: further models and testing procedures 222
6.1 Bilinear and related models 223
6.1.1 The bilinear process 223
6.1.2 A comparison of ARCH and bilinearity 225
6.1.3 State-dependent and related models 231
6.2 Regime-switching models: Markov chains and smooth transition autoregressions 232
6.3 Non-parametric and neural network models 239
6.3.1 Non-parametric modelling 239
6.3.2 Kernel regression 240
6.3.3 Neural networks 242
6.4 Non-linear dynamics and chaos 248
6.5 Testing for non-linearity 251
7 Modelling return distributions 263
7.1 Descriptive analysis of returns series 264
7.2 Two models for returns distributions 265
7.3 Determining the tail shape of a returns distribution 270
7.4 Empirical evidence on tail indices 273
7.5 Testing for covariance stationarity 277
7.6 Modelling the central part of returns distributions 280
7.7 Data-analytic modelling of skewness and kurtosis 282
7.8 Distributional properties of absolute returns 284
7.9 Summary and further extensions 287
8 Regression techniques for non-integrated financial time series 290
8.1 Regression models 290
8.1.1 Regression with non-integrated time series 290
8.1.2 Hypothesis testing 295
8.1.3 Instrumental variable estimation 298
8.1.4 Generalised methods of moments estimation 299
8.2 ARCH-in-mean regression models 303
8.2.1 The GARCH-M model 303
8.2.2 GARCH option pricing models 307
8.3 Misspecification testing 309
8.3.1 Choosing the maximum lag, m 309
8.3.2 Testing for normality, linearity and homoskedasticity 311
8.3.3 Parameter stability 313
8.4 Robust estimation 320
8.5 The multivariate linear regression model 323
8.6 Vector autoregressions 325
8.6.1 Concepts of exogeneity and causality 325
8.6.2 Tests of Granger causality 328
8.6.3 Determining the order of a VAR 331
8.7 Variance decompositions, innovation accounting and structural VARs 332
8.8 Vector ARMA models 335
8.9 Multivariate GARCH models 339
9 Regression techniques for integrated financial time series 345
9.1 Spurious regression 346
9.2 Cointegrated processes 354
9.3 Testing for cointegration in regression 362
9.4 Estimating cointegrating regressions 368
9.5 VARs with integrated variables 372
9.5.1 VARs with I(1) variables 372
9.5.2 VARs with cointegrated variables 374
9.5.3 Estimation of VECMs and tests of the cointegrating rank 378
9.5.4 Identification of VECMs 382
9.5.5 Exogeneity in VECMs 384
9.5.6 Structural VECMs 387
9.6 Causality testing in VECMs 389
9.7 Impulse response asymptotics in non-stationary VARs 391
9.8 Testing for a single long-run relationship 393
9.9 Common trends and cycles 399
10 Further topics in the analysis of integrated financial time series 404
10.1 Present value models, excess volatility and cointegration 404
10.1.1 Present value models and the \u2018simple\u2019 efficient markets hypothesis 404
10.1.2 Rational bubbles 409
10.1.3 The \u2018dividend ratio model\u2019: a log-linear approximation to the present value model 414
10.2 Generalisations and extensions of cointegration and error correction models 417
10.2.1. Non-linear generalisations 417
10.2.2 Testing for cointegration with infinite variance errors and structural breaks 425
Data appendix 427
References 428
Index 462