Terence Mills' best-selling graduate textbook provides detailed coverage of the latest research techniques and findings relating to the empirical analysis of financial markets. In its previous editions it has become required reading for many graduate courses on the econometrics of financial modelling. The third edition, co-authored with Raphael Markellos, contains a wealth of new material reflecting the developments of the last decade. Particular attention is paid to the wide range of nonlinear models that are used to analyse financial data observed at high frequencies and to the long memory characteristics found in financial time series. The central material on unit root processes and the modelling of trends and structural breaks has been substantially expanded into a chapter of its own. There is also an extended discussion of the treatment of volatility, accompanied by a new chapter on nonlinearity and its testing.
Author(s): Terence C. Mills, Raphael N. Markellos
Edition: 3
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 472
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Figures......Page 10
Tables......Page 13
Preface to the third edition......Page 15
1 Introduction......Page 17
2.1.1 Stochastic processes, realisations and ergodicity......Page 25
2.1.2 Stationarity......Page 26
2.2 Stochastic difference equations......Page 28
2.3.1 Autoregressive processes......Page 30
2.3.2 Moving average processes......Page 33
2.3.3 General AR and MA processes......Page 34
2.3.4 Autoregressive moving average models......Page 42
2.5.1 Sample autocorrelation and partial autocorrelation functions......Page 44
2.5.2 Model-building procedures......Page 45
2.6 Non-stationary processes and ARIMA models......Page 53
2.6.1 Non-stationarity in variance......Page 54
2.6.2 Non-stationarity in mean......Page 55
2.7 ARIMA modelling......Page 64
2.8 Seasonal ARIMA modelling......Page 69
2.9 Forecasting using ARIMA models......Page 73
3 Univariate linear stochastic models: testing for unit roots and alternative trend specifications......Page 81
3.1 Determining the order of integration of a time series......Page 83
3.2.1 An introduction to unit root tests......Page 85
3.2.2 Extensions to the Dickey–Fuller test......Page 93
3.2.3 Non-parametric tests for a unit root......Page 96
3.3 Trend stationarity versus difference stationarity......Page 101
3.4 Other approaches to testing for unit roots......Page 105
3.5 Testing for more than one unit root......Page 112
3.6 Segmented trends, structural breaks and smooth transitions......Page 114
3.7 Stochastic unit root processes......Page 121
4.1.1 Unobserved component models......Page 127
4.1.2 Signal extraction......Page 133
4.2.1 Alternative measures of persistence......Page 140
4.2.2 Testing for trend reversion......Page 143
4.2.3 Mean reverting models in continuous time......Page 146
4.3.1 A broader definition of stationarity......Page 150
4.3.2 ARFIMA models......Page 152
4.3.2 Testing for fractional differencing......Page 157
4.3.3 Estimation of ARFIMA models......Page 161
5.1 Martingales, random walks and non-linearity......Page 167
5.2 Testing the random walk hypothesis......Page 169
5.2.1 Autocorrelation tests......Page 170
5.2.2 Calendar effects......Page 172
5.3 Measures of volatility......Page 173
5.4.1 Stochastic volatility models......Page 182
5.4.2 Estimation of stochastic volatility models......Page 187
5.5.1 Development of generalised ARCH processes......Page 190
5.5.2 Modifications of GARCH processes......Page 195
5.5.3 Non-linear GARCH processes......Page 198
5.5.4 Long-memory volatility processes: the FIGARCH model......Page 200
5.5.5 Estimation of ARMA models with ARCH errors......Page 202
5.5.6 Testing for the presence of ARCH errors......Page 205
5.5.7 ARCH and theories of asset pricing......Page 207
5.6.1 Simple and exponential moving averages......Page 215
5.6.2 Autoregressive conditional duration models......Page 216
5.6.3 Modelling higher moments of the conditional distribution......Page 218
5.7 The forecasting performance of alternative volatility models......Page 220
6 Univariate non-linear stochastic models: further models and testing procedures......Page 222
6.1.1 The bilinear process......Page 223
6.1.2 A comparison of ARCH and bilinearity......Page 225
6.1.3 State-dependent and related models......Page 231
6.2 Regime-switching models: Markov chains and smooth transition autoregressions......Page 232
6.3.1 Non-parametric modelling......Page 239
6.3.2 Kernel regression......Page 240
6.3.3 Neural networks......Page 242
6.4 Non-linear dynamics and chaos......Page 248
6.5 Testing for non-linearity......Page 251
7 Modelling return distributions......Page 263
7.1 Descriptive analysis of returns series......Page 264
7.2 Two models for returns distributions......Page 265
7.3 Determining the tail shape of a returns distribution......Page 270
7.4 Empirical evidence on tail indices......Page 273
7.5 Testing for covariance stationarity......Page 277
7.6 Modelling the central part of returns distributions......Page 280
7.7 Data-analytic modelling of skewness and kurtosis......Page 282
7.8 Distributional properties of absolute returns......Page 284
7.9 Summary and further extensions......Page 287
8.1.1 Regression with non-integrated time series......Page 290
8.1.2 Hypothesis testing......Page 295
8.1.3 Instrumental variable estimation......Page 298
8.1.4 Generalised methods of moments estimation......Page 299
8.2.1 The GARCH-M model......Page 303
8.2.2 GARCH option pricing models......Page 307
8.3.1 Choosing the maximum lag, m......Page 309
8.3.2 Testing for normality, linearity and homoskedasticity......Page 311
8.3.3 Parameter stability......Page 313
8.4 Robust estimation......Page 320
8.5 The multivariate linear regression model......Page 323
8.6.1 Concepts of exogeneity and causality......Page 325
8.6.2 Tests of Granger causality......Page 328
8.6.3 Determining the order of a VAR......Page 331
8.7 Variance decompositions, innovation accounting and structural VARs......Page 332
8.8 Vector ARMA models......Page 335
8.9 Multivariate GARCH models......Page 339
9 Regression techniques for integrated financial time series......Page 345
9.1 Spurious regression......Page 346
9.2 Cointegrated processes......Page 354
9.3 Testing for cointegration in regression......Page 362
9.4 Estimating cointegrating regressions......Page 368
9.5.1 VARs with I(1) variables......Page 372
9.5.2 VARs with cointegrated variables......Page 374
9.5.3 Estimation of VECMs and tests of the cointegrating rank......Page 378
9.5.4 Identification of VECMs......Page 382
9.5.5 Exogeneity in VECMs......Page 384
9.5.6 Structural VECMs......Page 387
9.6 Causality testing in VECMs......Page 389
9.7 Impulse response asymptotics in non-stationary VARs......Page 391
9.8 Testing for a single long-run relationship......Page 393
9.9 Common trends and cycles......Page 399
10.1.1 Present value models and the ‘simple’ efficient markets hypothesis......Page 404
10.1.2 Rational bubbles......Page 409
10.1.3 The ‘dividend ratio model’: a log-linear approximation to the present value model......Page 414
10.2.1. Non-linear generalisations......Page 417
10.2.2 Testing for cointegration with infinite variance errors and structural breaks......Page 425
Data appendix......Page 427
References......Page 428
Index......Page 462
