Forecasting with exponential smoothing: the state space approach
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 359 S. graph. Darst. |
| ISBN: | 3540719164 9783540719168 |
Internformat
MARC
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| 245 | 1 | 0 | |a Forecasting with exponential smoothing |b the state space approach |c Rob J. Hyndman ... |
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| 300 | |a XIII, 359 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804137565832347648 |
|---|---|
| adam_text | Contents
Part I Introduction
1 Basic Concepts................................................ 3
1.1 Time Series Patterns....................................... 3
1.2 Forecasting Methods and Models.......................... 4
1.3 History of Exponential Smoothing......................... 5
1.4 State Space Models ....................................... 6
2 Getting Started ............................................... 9
2.1 Time Series Decomposition................................ 9
2.2 Classification of Exponential Smoothing Methods........... 11
2.3 Point Forecasts for the Best-Known Methods................ 12
2.4 Point Forecasts for All Methods............................ 17
2.5 State Space Models ....................................... 17
2.6 Initialization and Estimation............................... 23
2.7 Assessing Forecast Accuracy............................... 25
2.8 Model Selection .......................................... 27
2.9 Exercises................................................. 28
Part II Essentials
3 Linear Innovations State Space Models......................... 33
3.1 The General Linear Innovations State Space Model.......... 33
3.2 Innovations and One-Step-Ahead Forecasts................. 35
3.3 Model Properties......................................... 36
3.4 Basic Special Cases........................................ 38
3.5 Variations on the Common Models......................... 47
3.6 Exercises................................................. 51
X Contents
4 Nonlinear and Heteroscedastic Innovations State
Space Models.................................................
4.1 Innovations Form of the General State Space Model......... 53
4.2 Basic Special Cases........................................ 56
4.3 Nonlinear Seasonal Models................................ 61
4.4 Variations on the Common Models......................... 64
4.5 Exercises................................................. 66
5 Estimation of Innovations State Space Models.................. 67
5.1 Maximum Likelihood Estimation .......................... 67
5.2 A Heuristic Approach to Estimation........................ 71
5.3 Exercises................................................. 73
6 Prediction Distributions and Intervals ......................... 75
6.1 Simulated Prediction Distributions and Intervals............ 77
6.2 Class 1: Linear Homoscedastic State Space Models .......... 80
6.3 Class 2: Linear Heteroscedastic State Space Models.......... 83
6.4 Class 3: Some Nonlinear Seasonal State Space Models ....... 83
6.5 Prediction Intervals....................................... 88
6.6 Lead-Time Demand Forecasts for Linear Homoscedastic
Models................................................... 90
6.7 Exercises................................................. 94
Appendix: Derivations.................................... 95
7 Selection of Models........................................... 105
7.1 Information Criteria for Model Selection.................... 105
7.2 Choosing a Model Selection Procedure..................... 1°8
7.3 Implications for Model Selection Procedures................ 116
7.4 Exercises................................................. H 7
Appendix: Model Selection Algorithms..................... H
Part III Further Topics
8 Normalizing Seasonal Components............................ 1^
8.1 Normalizing Additive Seasonal Components ............... 124
8.2 Normalizing Multiplicative Seasonal Components........... 128
8.3 Application: Canadian Gas Production..................... 131
8.4 Exercises................................................. 1J*
Appendix: Derivations for Additive Seasonality............. 135
9 Models with Regressor Variables.............................. 137
9.1 The Linear Innovations Model with Regressors.............. 138
9.2 Some Examples........................................... 139
9.3 Diagnostics for Regression Models......................... 143
9.4 Exercises................................................. 147
Contents XI
10 Some Properties of Linear Models............................. 149
10.1 Minimal Dimensionality for Linear Models................. 149
10.2 Stability and the Parameter Space.......................... 152
10.3 Conclusions.............................................. 161
10.4 Exercises................................................. 161
11 Reduced Forms and Relationships with ARIMA Models........ 163
11.1 ARIMA Models........................................... 164
11.2 Reduced Forms for Two Simple Cases...................... 168
11.3 Reduced Form for the General Linear Innovations Model .... 170
11.4 Stationarity and Invertibility............................... 171
11.5 ARIMA Models in Innovations State Space Form............ 173
11.6 Cyclical Models........................................... 176
11.7 Exercises................................................. 176
12 Linear Innovations State Space Models with Random
Seed States................................................... 179
12.1 Innovations State Space Models with a Random
Seed Vector............................................... 180
12.2 Estimation ............................................... 182
12.3 Information Filter......................................... 185
12.4 Prediction................................................ 193
12.5 Model Selection .......................................... 194
12.6 Smoothing Time Series.................................... 195
12.7 Kalman Filter............................................. 197
12.8 Exercises................................................. 200
Appendix: Triangularization of Stochastic Equations......... 203
13 Conventional State Space Models.............................. 209
13.1 State Space Models ....................................... 210
13.2 Estimation ............................................... 212
13.3 Reduced Forms........................................... 215
13.4 Comparison of State Space Models......................... 219
13.5 Smoothing and Filtering................................... 223
13.6 Exercises................................................. 226
Appendix: Maximizing the Size of the Parameter Space...... 227
14 Time Series with Multiple Seasonal Patterns................... 229
14.1 Exponential Smoothing for Seasonal Data................... 231
14.2 Multiple Seasonal Processes............................... 234
14.3 An Application to Utility Data............................. 240
14.4 Analysis of Traffic Data.................................... 246
14.5 Exercises................................................. 250
Appendix: Alternative Forms.............................. 251
XII Contents
15 Nonlinear Models for Positive Data............................ 255
15.1 Problems with the Gaussian Model......................... 256
15.2 Multiplicative Error Models............................... 260
15.3 Distributional Results..................................... 263
15.4 Implications for Statistical Inference........................ 266
15.5 Empirical Comparisons ................................... 270
15.6 An Appraisal............................................. 274
15.7 Exercises................................................. 275
16 Models for Count Data........................................ 277
16.1 Models for Nonstationary Count Time Series................ 278
16.2 Croston s Method......................................... 281
16.3 Empirical Study: Car Parts................................. 283
16.4 Exercises................................................. 286
17 Vector Exponential Smoothing................................. 287
17.1 The Vector Exponential Smoothing Framework ............. 288
17.2 Local Trend Models....................................... 290
17.3 Estimation ............................................... 290
17.4 Other Multivariate Models ................................ 293
17.5 Application: Exchange Rates............................... 296
17.6 Forecasting Experiment................................... 299
17.7 Exercises................................................. 299
Part IV Applications
18 Inventory Control Applications................................ 303
18.1 Forecasting Demand Using Sales Data...................... 304
18.2 Inventory Systems........................................ 308
18.3 Exercises................................................. 315
19 Conditional Heteroscedasticity and Applications in Finance..... 317
19.1 The Black-Scholes Model.................................. 318
19.2 Autoregressive Conditional Heteroscedastic Models......... 319
19.3 Forecasting............................................... 322
19.4 Exercises................................................. 324
20 Economic Applications: The Beveridge-Nelson
Decomposition ............................................... 325
20.1 The Beveridge—Nelson Decomposition ..................... 328
20.2 State Space Form and Applications......................... 330
20.3 Extensions of the Beveridge-Nelson Decomposition
to Nonlinear Processes.................................... 334
20.4 Conclusion............................................... 336
20.5 Exercises................................................. 336
Contents XIII
References........................................................ 339
Author Index ..................................................... 349
Data Index........................................................ 353
Subject Index..................................................... 355
|
| adam_txt |
Contents
Part I Introduction
1 Basic Concepts. 3
1.1 Time Series Patterns. 3
1.2 Forecasting Methods and Models. 4
1.3 History of Exponential Smoothing. 5
1.4 State Space Models . 6
2 Getting Started . 9
2.1 Time Series Decomposition. 9
2.2 Classification of Exponential Smoothing Methods. 11
2.3 Point Forecasts for the Best-Known Methods. 12
2.4 Point Forecasts for All Methods. 17
2.5 State Space Models . 17
2.6 Initialization and Estimation. 23
2.7 Assessing Forecast Accuracy. 25
2.8 Model Selection . 27
2.9 Exercises. 28
Part II Essentials
3 Linear Innovations State Space Models. 33
3.1 The General Linear Innovations State Space Model. 33
3.2 Innovations and One-Step-Ahead Forecasts. 35
3.3 Model Properties. 36
3.4 Basic Special Cases. 38
3.5 Variations on the Common Models. 47
3.6 Exercises. 51
X Contents
4 Nonlinear and Heteroscedastic Innovations State
Space Models. "
4.1 Innovations Form of the General State Space Model. 53
4.2 Basic Special Cases. 56
4.3 Nonlinear Seasonal Models. 61
4.4 Variations on the Common Models. 64
4.5 Exercises. 66
5 Estimation of Innovations State Space Models. 67
5.1 Maximum Likelihood Estimation . 67
5.2 A Heuristic Approach to Estimation. 71
5.3 Exercises. 73
6 Prediction Distributions and Intervals . 75
6.1 Simulated Prediction Distributions and Intervals. 77
6.2 Class 1: Linear Homoscedastic State Space Models . 80
6.3 Class 2: Linear Heteroscedastic State Space Models. 83
6.4 Class 3: Some Nonlinear Seasonal State Space Models . 83
6.5 Prediction Intervals. 88
6.6 Lead-Time Demand Forecasts for Linear Homoscedastic
Models. 90
6.7 Exercises. 94
Appendix: Derivations. 95
7 Selection of Models. 105
7.1 Information Criteria for Model Selection. 105
7.2 Choosing a Model Selection Procedure. 1°8
7.3 Implications for Model Selection Procedures. 116
7.4 Exercises. H'7
Appendix: Model Selection Algorithms. H"
Part III Further Topics
8 Normalizing Seasonal Components. 1^
8.1 Normalizing Additive Seasonal Components . 124
8.2 Normalizing Multiplicative Seasonal Components. 128
8.3 Application: Canadian Gas Production. 131
8.4 Exercises. 1J*
Appendix: Derivations for Additive Seasonality. 135
9 Models with Regressor Variables. 137
9.1 The Linear Innovations Model with Regressors. 138
9.2 Some Examples. 139
9.3 Diagnostics for Regression Models. 143
9.4 Exercises. 147
Contents XI
10 Some Properties of Linear Models. 149
10.1 Minimal Dimensionality for Linear Models. 149
10.2 Stability and the Parameter Space. 152
10.3 Conclusions. 161
10.4 Exercises. 161
11 Reduced Forms and Relationships with ARIMA Models. 163
11.1 ARIMA Models. 164
11.2 Reduced Forms for Two Simple Cases. 168
11.3 Reduced Form for the General Linear Innovations Model . 170
11.4 Stationarity and Invertibility. 171
11.5 ARIMA Models in Innovations State Space Form. 173
11.6 Cyclical Models. 176
11.7 Exercises. 176
12 Linear Innovations State Space Models with Random
Seed States. 179
12.1 Innovations State Space Models with a Random
Seed Vector. 180
12.2 Estimation . 182
12.3 Information Filter. 185
12.4 Prediction. 193
12.5 Model Selection . 194
12.6 Smoothing Time Series. 195
12.7 Kalman Filter. 197
12.8 Exercises. 200
Appendix: Triangularization of Stochastic Equations. 203
13 Conventional State Space Models. 209
13.1 State Space Models . 210
13.2 Estimation . 212
13.3 Reduced Forms. 215
13.4 Comparison of State Space Models. 219
13.5 Smoothing and Filtering. 223
13.6 Exercises. 226
Appendix: Maximizing the Size of the Parameter Space. 227
14 Time Series with Multiple Seasonal Patterns. 229
14.1 Exponential Smoothing for Seasonal Data. 231
14.2 Multiple Seasonal Processes. 234
14.3 An Application to Utility Data. 240
14.4 Analysis of Traffic Data. 246
14.5 Exercises. 250
Appendix: Alternative Forms. 251
XII Contents
15 Nonlinear Models for Positive Data. 255
15.1 Problems with the Gaussian Model. 256
15.2 Multiplicative Error Models. 260
15.3 Distributional Results. 263
15.4 Implications for Statistical Inference. 266
15.5 Empirical Comparisons . 270
15.6 An Appraisal. 274
15.7 Exercises. 275
16 Models for Count Data. 277
16.1 Models for Nonstationary Count Time Series. 278
16.2 Croston's Method. 281
16.3 Empirical Study: Car Parts. 283
16.4 Exercises. 286
17 Vector Exponential Smoothing. 287
17.1 The Vector Exponential Smoothing Framework . 288
17.2 Local Trend Models. 290
17.3 Estimation . 290
17.4 Other Multivariate Models . 293
17.5 Application: Exchange Rates. 296
17.6 Forecasting Experiment. 299
17.7 Exercises. 299
Part IV Applications
18 Inventory Control Applications. 303
18.1 Forecasting Demand Using Sales Data. 304
18.2 Inventory Systems. 308
18.3 Exercises. 315
19 Conditional Heteroscedasticity and Applications in Finance. 317
19.1 The Black-Scholes Model. 318
19.2 Autoregressive Conditional Heteroscedastic Models. 319
19.3 Forecasting. 322
19.4 Exercises. 324
20 Economic Applications: The Beveridge-Nelson
Decomposition . 325
20.1 The Beveridge—Nelson Decomposition . 328
20.2 State Space Form and Applications. 330
20.3 Extensions of the Beveridge-Nelson Decomposition
to Nonlinear Processes. 334
20.4 Conclusion. 336
20.5 Exercises. 336
Contents XIII
References. 339
Author Index . 349
Data Index. 353
Subject Index. 355 |
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| id | DE-604.BV023258462 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:30:51Z |
| indexdate | 2024-07-09T21:14:19Z |
| institution | BVB |
| isbn | 3540719164 9783540719168 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016443701 |
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| physical | XIII, 359 S. graph. Darst. |
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| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Forecasting with exponential smoothing the state space approach Rob J. Hyndman ... Berlin [u.a.] Springer 2008 XIII, 359 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Business forecasting Smoothing (Statistics) Zustandsraum (DE-588)4132647-7 gnd rswk-swf Exponential smoothing (DE-588)4153384-7 gnd rswk-swf Prognosemodell (DE-588)4125215-9 gnd rswk-swf Prognosemodell (DE-588)4125215-9 s Exponential smoothing (DE-588)4153384-7 s Zustandsraum (DE-588)4132647-7 s DE-604 Hyndman, Rob J. Sonstige (DE-588)135530091 oth Erscheint auch als Online-Ausgabe 978-3-540-71918-2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016443701&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Forecasting with exponential smoothing the state space approach Business forecasting Smoothing (Statistics) Zustandsraum (DE-588)4132647-7 gnd Exponential smoothing (DE-588)4153384-7 gnd Prognosemodell (DE-588)4125215-9 gnd |
| subject_GND | (DE-588)4132647-7 (DE-588)4153384-7 (DE-588)4125215-9 |
| title | Forecasting with exponential smoothing the state space approach |
| title_auth | Forecasting with exponential smoothing the state space approach |
| title_exact_search | Forecasting with exponential smoothing the state space approach |
| title_exact_search_txtP | Forecasting with exponential smoothing the state space approach |
| title_full | Forecasting with exponential smoothing the state space approach Rob J. Hyndman ... |
| title_fullStr | Forecasting with exponential smoothing the state space approach Rob J. Hyndman ... |
| title_full_unstemmed | Forecasting with exponential smoothing the state space approach Rob J. Hyndman ... |
| title_short | Forecasting with exponential smoothing |
| title_sort | forecasting with exponential smoothing the state space approach |
| title_sub | the state space approach |
| topic | Business forecasting Smoothing (Statistics) Zustandsraum (DE-588)4132647-7 gnd Exponential smoothing (DE-588)4153384-7 gnd Prognosemodell (DE-588)4125215-9 gnd |
| topic_facet | Business forecasting Smoothing (Statistics) Zustandsraum Exponential smoothing Prognosemodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016443701&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hyndmanrobj forecastingwithexponentialsmoothingthestatespaceapproach |