Forecasting aggregated vector ARMA processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1987
|
| Schriftenreihe: | Lecture notes in economics and mathematical systems
284 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 323 S. |
| ISBN: | 3540172084 0387172084 |
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| 245 | 1 | 0 | |a Forecasting aggregated vector ARMA processes |c Helmut Lütkepohl |
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Datensatz im Suchindex
| _version_ | 1804115117217939456 |
|---|---|
| adam_text | CONTENTS
CHAPTER 1 . PROLOGUE 1
1.1 OBJECTIVE OF THE STUDY 1
1 .2 SURVEY OF THE STUDY 3
CHAPTER 2. VECTOR STOCHASTIC PROCESSES 6
2.1 DISCRETE-TIME, STATIONARY VECTOR STOCHASTIC PROCESSES 6
2.1.1 GENERAL ASSUMPTIONS 6
2.1.2 THE WOLD OR MOVING AVERAGE REPRESENTATION 8
2.1.3 AUTOREGRESSIVE REPRESENTATION 10
2.1.4 SPECTRAL REPRESENTATION 12
2.2 NONSTATIONARY PROCESSES 14
2.3 VECTOR AUTOREGRESSIVE MOVING AVERAGE PROCESSES 16
2.3.1 STATIONARY PROCESSES 16
2.3.2 NONSTATIONARY PROCESSES 20
2.4 ESTIMATION 21
2.4.1 MAXIMUM LIKELIHOOD ESTIMATION OF STATIONARY
GAUSSIAN VECTOR ARMA PROCESSES OF KNOWN ORDER.. 21
2.4.2 ESTIMATION OF VECTOR AUTOREGRESSIVE PROCESSES
OF KNOWN ORDER 23
2.4.3 MULTIVARIATE LEAST SQUARES ESTIMATION OF AR
PROCESSES WITH UNKNOWN ORDER 32
2.4.4 NONSTATIONARY PROCESSES 36
2.5 MODEL SPECIFICATION 36
2.5.1 AR ORDER DETERMINATION 36
2.5.2 SUBSET AUTOREGRESSIONS 41
2.5.3 THE BOX-JENKINS APPROACH 47
2.6 SUMMARY 47
CHAPTER 3. FORECASTING VECTOR STOCHASTIC PROCESSES 49
3.1 FORECASTING KNOWN PROCESSES 50
3.1.1 PREDICTORS BASED ON THE MOVING AVERAGE
REPRESENTATION 50
3.1.2 PREDICTORS BASED ON THE AUTOREGRESSIVE
REPRESENTATION 54
3.1.3 FORECASTING KNOWN VECTOR ARMA PROCESSES 57
3.2 FORECASTING VECTOR ARMA PROCESSES WITH ESTIMATED
COEFFICIENTS 58
3.2.1 THE GENERAL CASE 58
3.2.2 FINITE ORDER AR PROCESSES 65
3.3 FORECASTING AUTOREGRESSIVE PROCESSES OF UNKNOWN ORDER 73
3.3.1 THE ASYMPTOTIC MSE MATRIX 74
3.3.2 PROOF OF PROPOSITION 3.2 77
3.4 FORECASTING NONSTATIONARY PROCESSES 85
3.4.1 KNOWN PROCESSES - 86
3.4.2 ESTIMATED COEFFICIENTS 92
3.4.3 UNKNOWN ORDER 94
3.5 COMPARING FORECASTS 94
3.6 SUMMARY 95
CHAPTER 4. FORECASTING CONTEMPORANEOUSLY AGGREGATED KNOWN
PROCESSES 97
4.1 LINEAR TRANSFORMATIONS OF VECTOR STOCHASTIC PROCESSES 98
4.2 FORECASTING LINEARLY TRANSFORMED STATIONARY VECTOR
STOCHASTIC PROCESSES 100
4.2.1 THE PREDICTORS 100
4.2.2 COMPARISON OF THE PREDICTORS 104
4.2.3 EQUALITY OF THE PREDICTORS , 105
4.2.4 GRANGER-CAUSALITY 108
4.3 FORECASTING LINEARLY TRANSFORMED NONSTATIONARY
PROCESSES 110
4.4 LINEARLY TRANSFORMED VECTOR ARMA PROCESSES 113
4.4.1 FINITE ORDER MA PROCESSES 113
4.4.2 ARMA PROCESSES 114
4 .5 SUMMARY AND COMMENTS 117
CHAPTER 5. FORECASTING CONTEMPORANEOUSLY AGGREGATED ESTIMATED
PROCESSES 119
5.1 SUMMARY OF ASSUMPTIONS AND PREDICTORS 120
5.2 ESTIMATED COEFFICIENTS 121
5.2.1 COMPARISON OF Y(H) ANDY
FC
(H) 123
5.2.2 COMPARISON OF Y(H) ANDY^(H) 127
5.3 UNKNOWN ORDERS AND ESTIMATED COEFFICIENTS 129
5.4 NONSTATIONARY PROCESSES , 132
5.5 SMALL SAMPLE RESULTS 133
5.5.1 DESIGN OF THE MONTE CARLO EXPERIMENT 133
5.5.2 SIMULATION RESULTS FOR AR PROCESS I 134
5.5.3 SIMULATION RESULTS FOR AR PROCESS II 139
5.5.4 SIMULATION RESULTS FOR MA PROCESS I 142
5.5.5 SIMULATION RESULTS FOR MA PROCESS II 145
5.5.6 SIMULATION RESULTS FOR MA PROCESS III 147
5.6 AN EMPIRICAL EXAMPLE 149
5 . 7 CONCLUSIONS 1 58
CHAPTER 6. FORECASTING TEMPORALLY AND CONTEMPORANEOUSLY
AGGREGATED KNOWN PROCESSES ,, 161
6 .1 MACRO PROCESSES 163
6.2 SIX PREDICTORS 166
6 .3 COMPARISON OF PREDICTORS 173
6.4 NONSTATIONARY PROCESSES 179
6.4.1 DIFFERENCING TO OBTAIN STATIONARITY 179
6.4.2 FORECASTING AGGREGATED NONSTATIONARY PROCESSES 181
6.5 TEMPORALLY AND CONTEMPORANEOUSLY AGGREGATED VECTOR
ARMA PROCESSES 182
6 .6 CONCLUSIONS AND COMMENTS 186
CHAPTER 7. TEMPORAL AGGREGATION OF STOCK VARIABLES -
SYSTEMATICALLY MISSING OBSERVATIONS 187
7.1 FORECASTING KNOWN PROCESSES WITH SYSTEMATICALLY
MISSING OBSERVATIONS 189
7.2 PROCESSES WITH ESTIMATED COEFFICIENTS 192
7.3 PROCESSES WITH UNKNOWN ORDERS AND ESTIMATED
COEFFICIENTS 198
7.4 NONSTATIONARY TIME SERIES WITH SYSTEMATICALLY MISSING
OBSERVATIONS 200
7.5 MONTE CARLO RESULTS 203
7.5.1 UNIVARIATE AR PROCESSES 203
7.5.2 BIVARIATE AR PROCESS 206
7.5.3 MA(M) PROCESSES 208
7.5.4 UNIVARIATE MA(1) PROCESS 211
7.5.5 SUMMARY OF SMALL SAMPLE RESULTS 215
7.6 EMPIRICAL EXAMPLES 215
7.6.1 CONSUMPTION EXPENDITURES 216
7.6.2 INVESTMENT 219
7.7 CONCLUDING REMARKS 220
7.A APPENDIX: PROOF OF RELATION (7.2.18) 222
CHAPTER 8. TEMPORAL AGGREGATION OF FLOW VARIABLES 224
8.1 FORECASTING WITH KNOWN PROCESSES 225
8.2 FORECASTS BASED ON PROCESSES WITH ESTIMATED
COEFFICIENTS 230
8.3 FORECASTING WITH AUTOREGRESSIVE PROCESSES OF
UNKNOWN ORDER 236
8.4 TEMPORALLY AGGREGATED NONSTATIONARY PROCESSES 238
8 .5 SMALL SAMPLE COMPARISON 240
8.5.1 A UNIVARIATE AR PROCESS 240
8.5.2 A UNIVARIATE MA(2) PROCESS 242
8.5.3 A UNIVARIATE MA(3) PROCESS 244
8.5.4 A BIVARIATE MA PROCESS 246
8.5.5 A SYSTEM WITH A STOCK AND A FLOW VARIABLE 248
8.6 EXAMPLES 250
8.6.1 CONSUMPTION 250
8.6.2 INVESTMENT 253
8 . 7 SUMMARY AND CONCLUSIONS 255
8.A APPENDIX: PROOF OF RELATION (8.2.23) 256
CHAPTER 9. JOINT TEMPORAL AND CONTEMPORANEOUS AGGREGATION 258
9.1 SUMMARY OF PROCESSES AND PREDICTORS 259
9.2 PREDICTION BASED ON PROCESSES WITH ESTIMATED
COEFFICIENTS 263
9.2.1 GENERAL RESULTS 263
9 . 2 . 2 AN EXAMPLE 26 7
9.2.3 CONCLUSIONS FOR PROCESSES WITH ESTIMATED
COEFFICIENTS 274
9.3 PREDICTION BASED ON ESTIMATED PROCESSES WITH
UNKNOWN ORDERS 275
9.3.1 GENERAL COMMENTS 2 75
9.3.2 COMPARISON OF MSES 278
9.3.3 SUMMARY AND DISCUSSION OF RESULTS FOR PROCESSES
WITH UNKNOWN ORDERS 280
9.4 MONTE CARLO COMPARISON OF PREDICTORS 281
9.4.1 SIMULATION RESULTS FOR AR PROCESS 282
9.4.2 SIMULATION RESULTS FOR MA PROCESS 289
9.4.3 DISCUSSION OF SMALL SAMPLE RESULTS 296
9.5 FORECASTS OF U.S. GROSS PRIVATE DOMESTIC INVESTMENT .. 299
9.5.1 FIRST DIFFERENCES OF INVESTMENT DATA 299
9.5.2 AGGREGATION OF ORIGINAL INVESTMENT DATA 303
9 .6 SUMMARY AND CONCLUSIONS 304
CHAPTER 10. EPILOGUE 309
10.1 SUMMARY AND CONCLUSIONS 309
10.2 SOME REMAINING PROBLEMS 311
APPENDIX. DATA USED FOR EXAMPLES 313
BIBLIOGRAPHY 316
|
| any_adam_object | 1 |
| author | Lütkepohl, Helmut 1951- |
| author_GND | (DE-588)10979544X |
| author_facet | Lütkepohl, Helmut 1951- |
| author_role | aut |
| author_sort | Lütkepohl, Helmut 1951- |
| author_variant | h l hl |
| building | Verbundindex |
| bvnumber | BV000668951 |
| callnumber-first | H - Social Science |
| callnumber-label | HA30 |
| callnumber-raw | HA30.3.L87 1987 |
| callnumber-search | HA30.3.L87 1987 |
| callnumber-sort | HA 230.3 L87 41987 |
| callnumber-subject | HA - Statistics |
| classification_rvk | QH 170 SI 853 |
| classification_tum | MAT 634f MAT 605f |
| ctrlnum | (OCoLC)15018901 (DE-599)BVBBV000668951 |
| dewey-full | 519.5/519 519.5/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 19 519.5/5 |
| dewey-search | 519.5/5 19 519.5/5 |
| dewey-sort | 3519.5 15 219 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV000668951 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:31Z |
| institution | BVB |
| isbn | 3540172084 0387172084 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000417445 |
| oclc_num | 15018901 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-355 DE-BY-UBR DE-20 DE-N2 DE-19 DE-BY-UBM DE-521 DE-634 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-355 DE-BY-UBR DE-20 DE-N2 DE-19 DE-BY-UBM DE-521 DE-634 DE-188 |
| physical | X, 323 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Lütkepohl, Helmut 1951- Verfasser (DE-588)10979544X aut Forecasting aggregated vector ARMA processes Helmut Lütkepohl Berlin [u.a.] Springer 1987 X, 323 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 284 Time-series analysis Econometrics Economic forecasting -- Statistical methods Vektor (DE-588)4202708-1 gnd rswk-swf Prognose (DE-588)4047390-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf ARMA-Modell (DE-588)4002933-5 gnd rswk-swf Prognoseverfahren (DE-588)4358095-6 gnd rswk-swf Aggregation (DE-588)4000728-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Prognose (DE-588)4047390-9 s ARMA-Modell (DE-588)4002933-5 s Aggregation (DE-588)4000728-5 s DE-604 Zeitreihenanalyse (DE-588)4067486-1 s 1\p DE-604 Vektor (DE-588)4202708-1 s 2\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 3\p DE-604 Prognoseverfahren (DE-588)4358095-6 s 4\p DE-604 Lecture notes in economics and mathematical systems 284 (DE-604)BV000000036 284 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000417445&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lütkepohl, Helmut 1951- Forecasting aggregated vector ARMA processes Lecture notes in economics and mathematical systems Time-series analysis Econometrics Economic forecasting -- Statistical methods Vektor (DE-588)4202708-1 gnd Prognose (DE-588)4047390-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd ARMA-Modell (DE-588)4002933-5 gnd Prognoseverfahren (DE-588)4358095-6 gnd Aggregation (DE-588)4000728-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4202708-1 (DE-588)4047390-9 (DE-588)4067486-1 (DE-588)4002933-5 (DE-588)4358095-6 (DE-588)4000728-5 (DE-588)4057630-9 |
| title | Forecasting aggregated vector ARMA processes |
| title_auth | Forecasting aggregated vector ARMA processes |
| title_exact_search | Forecasting aggregated vector ARMA processes |
| title_full | Forecasting aggregated vector ARMA processes Helmut Lütkepohl |
| title_fullStr | Forecasting aggregated vector ARMA processes Helmut Lütkepohl |
| title_full_unstemmed | Forecasting aggregated vector ARMA processes Helmut Lütkepohl |
| title_short | Forecasting aggregated vector ARMA processes |
| title_sort | forecasting aggregated vector arma processes |
| topic | Time-series analysis Econometrics Economic forecasting -- Statistical methods Vektor (DE-588)4202708-1 gnd Prognose (DE-588)4047390-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd ARMA-Modell (DE-588)4002933-5 gnd Prognoseverfahren (DE-588)4358095-6 gnd Aggregation (DE-588)4000728-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Time-series analysis Econometrics Economic forecasting -- Statistical methods Vektor Prognose Zeitreihenanalyse ARMA-Modell Prognoseverfahren Aggregation Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000417445&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT lutkepohlhelmut forecastingaggregatedvectorarmaprocesses |