Introduction to Modern Time Series Analysis

Cover......Page 1
Introduction to Modern Time Series Analysis\r......Page 4
Preface to the Second Edition......Page 6
Preface to the First Edition......Page 8
Contents......Page 10
1 Introduction and Basics......Page 14
1.1 The Historical Development of Time Series Analysis......Page 15
1.2 Graphical Representations of Economic Time Series......Page 18
1.3 The Lag Operator......Page 23
1.4 Ergodicity and Stationarity......Page 25
Example 1.2......Page 27
Example 1.3......Page 32
1.5 The Wold Decomposition......Page 34
References......Page 35
Derivation of Wold’s Representation......Page 39
The Lag Operator......Page 41
Calculation of Moments......Page 42
An Alternative Method for the Calculation of Moments......Page 43
Example 2.1......Page 45
Example 2.2......Page 49
Example 2.3......Page 51
2.1.2 Second Order Autoregressive Processes......Page 52
Example 2.4......Page 55
Example 2.6......Page 59
2.1.3 Higher Order Autoregressive Processes......Page 61
Example 2.7......Page 63
2.1.4 The Partial Autocorrelation Function......Page 64
Example 2.8......Page 66
2.1.5 Estimating Autoregressive Processes......Page 68
Example 2.9......Page 69
2.2.1 First Order Moving Average Processes......Page 70
Example 2.10......Page 72
2.2.2 MA(1) and Temporal Aggregation......Page 74
Example 2.11......Page 76
2.2.3 Higher Order Moving Average Processes......Page 77
Example 2.13......Page 79
2.3 Mixed Processes......Page 80
2.3.1 ARMA(1,1) Processes......Page 81
2.3.2 ARMA(p,q) Processes......Page 87
2.4.1 Forecasts with Minimal Mean Squared Errors......Page 90
2.4.2 Forecasts of ARMA(p,q) Processes......Page 93
Forecasts with a Stationary AR(1) Process......Page 94
Forecasts with an Invertible MA(1) Process......Page 95
2.4.3 Evaluation of Forecasts......Page 97
Example 2.16......Page 100
2.5 The Relation between Econometric Models and ARMA Processes......Page 101
References......Page 102
3 Granger Causality......Page 106
3.1 The Definition of Granger Causality......Page 108
3.2.1 Characterisation of Causal Relations Using the Autoregressive and Moving Average Representations......Page 110
3.2.2 Characterisation of Causal Relations Using the Residuals of the Univariate Processes......Page 112
3.3.1 The Direct Granger Procedure......Page 115
Example 3.1......Page 116
Example 3.2......Page 119
3.3.3 The Hsiao Procedure......Page 123
Example 3.3......Page 124
3.4.1 The Direct Granger Procedure with More Than Two Variables......Page 127
Example 3.4......Page 128
Example 3.5......Page 129
3.4.2 Interpreting the Results of Bivariate Tests in Systems With More Than Two Variables......Page 130
3.5 Concluding Remarks......Page 131
References......Page 133
4 Vector Autoregressive Processes......Page 137
4.1 Representation of the System......Page 139
Example 4.1......Page 140
Example 4.2......Page 142
Example 4.3......Page 144
Example 4.4......Page 146
4.2 Granger Causality......Page 148
4.3 Impulse Response Analysis......Page 150
Example 4.6......Page 151
Example 4.7......Page 155
4.4 Variance Decomposition......Page 156
Example 4.9......Page 158
4.5 Concluding Remarks......Page 161
References......Page 162
5.1 Forms of Nonstationarity......Page 165
5.2 Trend Elimination......Page 171
5.3 Unit Root Tests......Page 175
5.3.1 The Dickey-Fuller Test......Page 177
Example 5.1......Page 178
5.3.2 The Augmented Dickey-Fuller Test......Page 180
Example 5.2......Page 182
5.3.3 The Phillips-Perron Test......Page 183
5.3.4 Unit Root Tests and Structural Breaks......Page 188
5.3.5 A Test with the Null Hypothesis of Stationarity......Page 190
Example 5.4......Page 191
5.4 Decomposition of Time Series......Page 193
Example 5.5......Page 196
Example 5.6......Page 197
Example 5.7......Page 199
5.5 Further Developments......Page 200
5.5.1 Fractional Integration......Page 201
Example 5.8......Page 202
5.5.2 Seasonal Integration......Page 203
5.6 Deterministic versus Stochastic Trends in Economic Time Series......Page 206
References......Page 208
Example 6.1......Page 214
Example 6.2......Page 216
6.1 Definition and Properties of Cointegrated Processes......Page 218
6.2.1 Bivariate Cointegration......Page 220
Example 6.3......Page 222
6.2.2 Cointegration with More Than Two Variables......Page 223
6.2.3 Testing Cointegration in Static Models......Page 224
Example 6.4......Page 227
Example 6.5......Page 228
6.2.4 Testing Cointegration in Dynamic Models......Page 230
Example 6.6......Page 233
6.3.1 The Vector Error Correction Representation......Page 234
Example 6.7......Page 235
6.3.2 The Johansen Approach......Page 237
Example 6.8......Page 241
Stochastic Trend Representation......Page 246
Conditional Error Correction Representation......Page 247
Example 6.10......Page 249
Forecasting......Page 250
6.4 Cointegration and Economic Theory......Page 251
References......Page 253
7 Nonstationary Panel Data......Page 259
7.1.1 Omitted Variable Bias......Page 260
7.1.2 Estimation and Testing......Page 261
Example 7.1......Page 263
7.2.1 First Generation Tests......Page 266
7.2.2 Second Generation Tests......Page 267
Example 7.2......Page 269
7.2.3 The Null Hypothesis of Stationarity......Page 270
7.3.1 The Inverse Normal Method......Page 271
7.3.2 Bonferroni-Type Tests......Page 273
Example 7.3......Page 274
7.4.1 Single Equation Approaches......Page 275
Example 7.4......Page 276
Example 7.5......Page 279
Example 7.6......Page 280
7.4.2 System Approaches......Page 281
7.5 Concluding Remarks......Page 282
References......Page 283
Example 8.1......Page 288
8.1.1 Definition and Representation......Page 292
Example 8.2......Page 294
8.1.2 Unconditional Moments......Page 295
8.1.3 Temporal Aggregation......Page 296
Example 8.4......Page 298
8.2.1 GARCH Models......Page 299
8.2.2 The GARCH(1,1) Process......Page 301
Example 8.6......Page 303
8.2.3 Nonlinear Extensions......Page 304
Example 8.7......Page 305
8.3 Estimation and Testing......Page 306
8.4 Multivariate Models......Page 308
8.4.1 VAR-Type Models......Page 309
8.4.2 Correlation Models......Page 311
8.5 ARCH/GARCH Models as Instruments of Financial Market Analysis......Page 312
References......Page 314
Index of Names and Authors......Page 318
Subject Index......Page 322