Forecasting with Univariate Box - Jenkins Models: Concepts and Cases (Wiley Series in Probability and Statistics)

Forecasting With Univariate Box- Jenkins Models CONCEPTS AND CASES......Page 1
CONTENTS......Page 11
PART I. BASIC CONCEPTS......Page 21
1.1 Planning and forecasting......Page 23
1.2 What this book is about......Page 24
1.3 Time-series data......Page 26
1.4 Single-series (univariate) analysis......Page 28
1.5 When may UBJ models be used?......Page 29
1.6 The Box-Jenkins modeling procedure......Page 36
1.7 UBJ models compared with other models......Page 39
Summary......Page 40
Questions and problems......Page 41
2.1 Differencing......Page 44
2.3 Two analytical tools: the estimated autocorrelation function (acf) and estimated partial autocorrelation function (pacf)......Page 49
Summary......Page 63
Questions and problems......Page 64
3.1 Process, realization, and model......Page 65
3.2 Two common processes......Page 67
3.3 Statistical inference at the identification stage......Page 87
Summary......Page 94
Appendix 3 A: Expected value rules and definitions......Page 96
Questions and problems......Page 97
4.1 What is a good model?......Page 100
4.2 Two examples of UBJ-ARIMA modeling......Page 103
Summary......Page 111
Questions and problems......Page 112
5 Notation and the interpretation of ARIMA models......Page 114
5.1 Three processes and ARIMA (p,d,q) notation......Page 115
5.2 Backshift notation......Page 116
5.3 Interpreting ARIMA models I: optimal extrapolation of past values of a single series......Page 123
5.4 Interpreting ARIMA models II: rationalizing them from their context......Page 125
5.5 Interpreting ARIMA models III: ARIMA(O,d,q) models as exponentially weighted moving averages......Page 129
Summary......Page 135
Questions and problems......Page 137
6 Identification: stationary models......Page 139
6.1 Theoretical acfs and pacf's for five common processes......Page 141
6.2 Stationarity......Page 150
6.3 Invertibility......Page 153
6.4 Deriving theoretical acf's for the MA(1) process......Page 156
6.5 Deriving theoretical acf's for the AR(1) process......Page 162
Summary......Page 168
Appendix 6A: The formal conditions for stationarity and invertibility......Page 170
Questions and problems......Page 172
7.1 Nonstationary mean......Page 175
7.2 Nonstationary variance......Page 195
7.3 Differencing and deterministic trends......Page 206
Summary......Page 209
Appendix 7A: Integration......Page 210
8.1 Principles of estimation......Page 212
8.2 Nonlinear least-squares estimation......Page 217
8.3 Estimation-stage results: have we found a good model?......Page 220
Summary......Page 228
Appendix 8A: Marquardt’s compromise......Page 229
8A.1 Overview......Page 230
8A.2 Application to an MA(1)......Page 232
8B.1 Conditional least squares......Page 240
8B.2 Unconditional least squares......Page 241
9.1 Are the random shocks independent?......Page 244
9.2 Other diagnostic checks......Page 250
9.3 Reformulating a model......Page 253
Summary......Page 257
Questions and problems......Page 258
10 Forecasting......Page 260
10.1 The algebra of ARIMA forecasts......Page 261
10.2 The dispersion of ARIMA forecasts......Page 272
10.3 Forecasting from data in logarithmic form......Page 276
10.4 The optimality of ARIMA forecasts......Page 278
Summary......Page 279
Appendix 10A:The complementarity of ARIMA models and econometric models......Page 281
Questions and problems......Page 283
11 Seasonal and other periodic models......Page 285
11.1 Periodic data......Page 288
11.2 Theoretical acf s and pacf s for seasonal processes......Page 290
11.3 Seasonal differencing......Page 294
11.4 Seasonal-nonseasonal multiplicative models......Page 300
11.5 An example of a seasonal-nonseasonal multiplicative model......Page 302
11.6 Nonmultiplicative models......Page 308
Summary......Page 312
Questions and problems......Page 313
PART II. THE ART OF ARIMA MODELING......Page 315
12 Practical Rules......Page 317
Case Studies: Introduction......Page 331
GROUP A STATIONARY, NONSEASONAL MODELS......Page 333
Case 1 Change in business inventories......Page 335
Case 2 Saving rate......Page 348
Case3 Coal production......Page 367
Case 4 Housing permits......Page 389
GROUP B NONSTATIONARY, NONSEASONAL MODELS......Page 409
Case 5 Rail freight......Page 411
Case 6 AT&T stock price......Page 422
Case 7 Real-estate loans......Page 431
Case 8 Parts availability......Page 445
GROUP C NONSTATIONARY, SEASONAL MODELS......Page 459
Case 9 Air-carrier freight......Page 461
Case 10 Profit margin......Page 483
Case 11 Boston armed robberies......Page 492
Case 12 Machine-tool shipments......Page 512
Case 13 Cigarconsumption......Page 526
Case 14 College enrollment......Page 543
Case15 Exports......Page 554
t-distribution table......Page 570
Chi-squared distribution table......Page 572
References......Page 573
Index......Page 577