Time-Series Forecasting

TIME-SERIES FORECASTING......Page 2
Contents......Page 5
Preface......Page 7
Abbreviations and Notation......Page 9
CHAPTER 1: Introduction......Page 10
Table of Contents......Page 0
1.1 Types of forecasting method......Page 12
1.2 Some preliminary questions......Page 14
1.3 The dangers of extrapolation......Page 16
1.4 Are forecasts genuinely out-of-sample?......Page 17
1.5 Brief overview of relevant literature......Page 18
2.1 Different types of time series......Page 20
2.2 Objectives of time-series analysis......Page 21
2.3 Simple descriptive techniques......Page 22
2.3.1 The time plot......Page 23
2.3.3 Transformations......Page 25
2.3.4 Cleaning the data......Page 26
2.3.5 Trend......Page 27
2.3.6 Seasonal variation......Page 30
2.4 Stationary stochastic processes......Page 33
2.5 Some classes of univariate time-series model......Page 36
2.5.1 The purely random process......Page 37
2.5.4 Moving average processes......Page 38
2.6 The correlogram......Page 39
3.1.1 Autoregressive (AR) processes......Page 43
3.1.2 Moving average (MA) processes......Page 45
3.1.3 ARMA processes......Page 47
3.1.4 Some theoretical remarks on ARMA processes......Page 48
3.1.5 ARIMA processes......Page 50
3.1.6 SARIMA processes......Page 51
3.1.7 Periodic AR models......Page 52
3.1.8 Fractional integrated ARMA (ARFIMA) and long-memory models......Page 53
3.1.9 Testing for unit roots......Page 54
3.2 State space models......Page 57
3.3 Growth curve models......Page 61
3.4 Non-linear models......Page 62
3.4.1 Non-linear autoregressive processes......Page 66
3.4.2 Some other non-linear models......Page 68
3.4.3 Models for changing variance......Page 70
3.4.4 Neural networks......Page 73
3.4.5 Chaos......Page 77
3.5 Time-series model building......Page 80
3.5.1 Model formulation......Page 81
3.5.2 Model selection......Page 83
3.5.3 Model checking......Page 86
3.5.4 Further comments on modelling......Page 88
4.1 The prediction problem......Page 92
4.2 Model-based forecasting......Page 95
4.2.1 Forecasting with general linear processes......Page 96
4.2.2 The Box-Jenkins forecasting procedure......Page 98
4.2.3 Forecasting with state-space models –the Kalman filter......Page 99
4.2.4 Forecasting with non-linear models......Page 101
4.3 Ad hoc forecasting methods......Page 102
4.3.1 Simple exponential smoothing......Page 103
4.3.2 Holt’s linear trend method......Page 105
4.3.3 The Holt-Winters forecasting procedure......Page 106
4.3.4 Other methods......Page 107
4.3.5 Combining forecasts......Page 110
4.4 Some interrelationships and combinations......Page 111
5.1 Introduction......Page 116
5.1.1 Is feedback present?......Page 118
5.1.2 Are forecasts out-of-sample?......Page 119
5.1.3 Cross-correlations for stationary multivariate processes......Page 120
5.1.4 Initial data analysis......Page 121
5.2.1 Regression models......Page 124
5.2.2 Transfer function models......Page 130
5.3 Vector AR and ARMA models......Page 137
5.3.2 Vector ARMA models......Page 138
5.3.3 VAR models......Page 139
5.3.4 VMA,VARIMA and VARMAX models......Page 141
5.3.5 Fitting VAR and VARMA models......Page 142
5.3.6 Forecasting with VAR, VARMA and VARIMA models......Page 143
5.4 Cointegration......Page 145
5.5 Econometric models......Page 149
5.6 Other approaches......Page 151
5.7 Some relationships between models......Page 155
6.1 Introduction......Page 157
6.3 Measuring forecast accuracy......Page 158
6.4 Forecasting competitions and case studies......Page 163
6.4.1 General remarks......Page 164
6.4.2 Review of empirical evidence......Page 167
Results for multivariate models......Page 170
Results for periodic and long-memory models......Page 171
Results for neural nets......Page 172
6.5 Choosing an appropriate forecasting method......Page 174
6.5.1 A general strategy for making non-automatic univariate forecasts......Page 179
6.5.2 Implementation in practice......Page 181
6.6 Summary......Page 184
7.1 Introduction......Page 186
7.1.2 Some reasons for neglect......Page 187
7.1.3 Computing a simultaneous prediction region......Page 188
7.1.4 Density fore asts and fan charts......Page 189
7.2 Notation......Page 190
7.3 The need for different approaches......Page 191
7.4 Expected mean square prediction error......Page 192
7.5.1 Introduction......Page 195
7.5.2 P.I.s derived from a fitted probability model......Page 196
7.5.3 P.I.s derived by assuming that a method is optimal......Page 198
7.5.4P.I.s based on ‘approximate’ formulae......Page 200
7.5.5 Empirically based P.I.s......Page 201
7.5.6 Simulation and resampling methods......Page 202
7.5.7 The Bayesian approach......Page 206
7.5.8 P.I.s for transformed variables......Page 208
7.5.9 Judgemental P.I.s.......Page 209
7.6 A comparative assessment......Page 210
7.7 Why are P.I.s too narrow?......Page 211
7.8 An example......Page 216
7.9 Summary and recommendations......Page 218
8.1 Introduction to model uncertainty......Page 220
8.2 Modelbuilding and data dredging......Page 222
8.2.1 Data dredging......Page 223
8.3 Examples......Page 225
8.4 Inference after model selection: Some findings......Page 233
8.4.1 Prediction intervals are too narrow......Page 234
8.4.2 The results of computational studies......Page 236
8.4.3 Model checking......Page 237
8.5.1 Choosing a single model......Page 238
8.5.2 Using more than one model......Page 240
8.5.3 Bayesian model averaging......Page 242
8.5.4 Check out-of-sample forecast accuracy with data splitting......Page 243
8.5.5 Handling structural breaks......Page 244
8.6 Summary and discussion......Page 246
References......Page 249