Signal extraction: efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
2005
|
| Series: | Lecture notes in economics and mathematical systems
547 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 279 S. graph. Darst. |
| ISBN: | 3540229353 |
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Record in the Search Index
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| adam_text | MARCWILDI
SIGNAL EXTRACTION
EFFICIENT ESTIMATION, UNIT ROOT-TESTS
AND EARLY DETECTION OF TURNING POINTS
WITH 80 FIGURES AND 15 TABLES
4Y SPRINGER
CONTENTS
PAR
T I THEOR
Y
1 INTRODUCTIO
N
3
1.1 OVERVIEW 3
1.2 A GENERAL MODEL-BASED-APPROACH 7
1.3 AN IDENTIFICATION PROBLEM 10
1.4 THE DIRECT FILTER APPROACH 12
1.5 SUMMARY 14
2 MODEL-BASE
D APPROACHES
17
2.1 INTRODUCTION 17
2.2 THE BEVERIDGE-NELSON DECOMPOSITION 18
2.3 THE CANONICAL DECOMPOSITION 19
2.3.1 AN ILLUSTRATIVE EXAMPLE
.- 20
2.3.2 THE AIRLINE-MODEL 24
2.3.3 AN EXAMPLE 29
2.3.4 THE REVISION ERROR VARIANCE 33
2.3.5 CONCLUDING REMARKS 35
2.4 STRUCTURAL COMPONENTS MODEL 36
2.5 CENSUS X-12-ARIMA 39
3 QMP-ZP
C FILTER
S
45
3.1 FILTERS : DEFINITIONS AND CONCEPTS 45
3.2 A RESTRICTED ARMA FILTER CLASS : QMP-FILTERS 51
3.3 ZPC-FILTERS 54
4 TH
E PERIODOGRAM
65
4.1 SPECTRAL DECOMPOSITION 65
4.2 CONVOLUTION THEOREM 69
4.3 THE PERIODOGRAM FOR INTEGRATED PROCESSES 76
4.3.1 INTEGRATED PROCESSES OF ORDER ONE 76
X CONTENTS
4.3.2 THE PERIODOGRAM FOR 7(2)-PROCESSES 79
5 DIRECT FILTER APPROACH (DFA)
91
5.1 OVERVIEW 92
5.2 CONSISTENCY (STATIONARY MA-PROCESSES) 94
5.3 CONSISTENCY (INTEGRATED PROCESSES) 102
5.4 CONDITIONAL OPTIMIZATION 112
5.5 EFFICIENCY 115
5.6 INFERENCE UNDER CONDITIONAL STATIONARITY 120
5.6.1 THE ASYMPTOTIC DISTRIBUTION OF THE PARAMETERS OF THE
LINEARIZED DFA 121
5.6.2 SPURIOUS DECREASE OF THE OPTIMIZATION CRITERION 127
5.6.3 TESTING FOR PARAMETER CONSTRAINTS 129
5.7 INFERENCE : UNIT-ROOTS 129
5.7.1 I(L)-PROCESS 130
5.7.2 I(2)-PROCESS 143
5.8 LINKS BETWEEN THE DFA AND THE MBA 145
6 FINIT
E SAMPLE PROBLEM
S AND REGULARITY
147
6.1 REGULARITY AND OVERFITTING 148
6.2 FILTER SELECTION CRITERION 151
6.2.1 OVERVIEW 151
6.2.2 THE MC-CRITERION 152
6.3 CROSS-VALIDATION 154
6.4 A SINGULARITY-PENALTY 155
6.5 VARIABLE FREQUENCY SAMPLING 159
PART I
I EMPIRICAL RESULT
S
7 EMPIRICAL COMPARISONS : MEAN SQUARE PERFORMANCE
167
7.1 GENERAL FRAMEWORK 167
7.2 A SIMULATION STUDY 169
7.2.1 AIRLINE-MODEL 170
7.2.2 QUASI -AIRLINE MODEL 176
7.2.3 STATIONARY INPUT SIGNALS 179
7.2.4 CONCLUSIONS 182
7.3 REAL-WORLD TIME SERIES 186
7.3.1 MEAN-SQUARE APPROXIMATION OF THE IDEAL TREND 189
7.3.2 MEAN-SQUARE APPROXIMATION OF THE CANONICAL TREND .
. 202
7.3.3 MEAN SQUARE APPROXIMATION OF THE CANONICAL
SEASONAL ADJUSTMENT FILTER 206
CONTENTS XI
8 EMPIRICAL COMPARISONS : TURNING POINT DETECTIO
N
213
8.1 TURNING POINT DETECTION FOR TH
E IDEAL TREND 214
8.1.1 SERIES LINEARIZED BY TRAMO 215
8.1.2 SERIES LINEARIZED BY X-12-ARIMA 219
8.2 TURNING POINT DETECTION FOR THE CANONICAL TREND 222
9 CONCLUSION
225
A DECOMPOSITION
S OF STOCHASTI
C PROCESSE
S
229
A.I WEAKLY STATIONARY PROCESSES OF FINITE VARIANCE 229
A. 1.1 SPECTRAL DECOMPOSITION AND CONVOLUTION THEOREM 229
A.1.2 THE WOLD DECOMPOSITION 231
A.2 NON-STATIONARY PROCESSES 233
B STOCHASTI
C PROPERTIE
S OF TH
E PERIODOGRAM
235
B.I PERIODOGRAM FOR FINITE VARIANCE STATIONARY PROCESSES 235
B.2 PERIODOGRAM FOR INFINITE VARIANCE STATIONARY PROCESSES 243
B.2.1 MOVING AVERAGE PROCESSES OF INFINITE VARIANCE 243
B.2.2 AUTOCORRELATION FUNCTION, NORMALIZED SPECTRAL
DENSITY AND (SELF) NORMALIZED PERIODOGRAM 244
B.3 THE PERIODOGRAM FOR INTEGRATED PROCESSES 246
C A LEAST-SQUARES ESTIMAT
E
255
C.I ASYMPTOTIC DISTRIBUTION OF THE PARAMETERS 255
C.2 A GENERALIZED INFORMATION CRITERION 266
D MISCELLANEOUS
269
D.I INITIALIZATION OF ARMA-FILTERS 269
E NON-LINEAR PROCESSE
S
271
REFERENCES
275
|
| any_adam_object | 1 |
| author | Wildi, Marc 1963- |
| author_GND | (DE-588)115383468 |
| author_facet | Wildi, Marc 1963- |
| author_role | aut |
| author_sort | Wildi, Marc 1963- |
| author_variant | m w mw |
| building | Verbundindex |
| bvnumber | BV019574508 |
| classification_rvk | QH 237 QH 254 |
| ctrlnum | (OCoLC)249237768 (DE-599)BVBBV019574508 |
| dewey-full | 330.0112 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.0112 |
| dewey-search | 330.0112 |
| dewey-sort | 3330.0112 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV019574508 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:40Z |
| institution | BVB |
| isbn | 3540229353 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012914085 |
| oclc_num | 249237768 |
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| owner | DE-384 DE-83 |
| owner_facet | DE-384 DE-83 |
| physical | XI, 279 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Wildi, Marc 1963- Verfasser (DE-588)115383468 aut Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables Marc Wildi Berlin u.a. Springer 2005 XI, 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 547 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Schätzung (DE-588)4193791-0 s DE-604 Lecture notes in economics and mathematical systems 547 (DE-604)BV000000036 547 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012914085&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wildi, Marc 1963- Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables Lecture notes in economics and mathematical systems Zeitreihenanalyse (DE-588)4067486-1 gnd Schätzung (DE-588)4193791-0 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4193791-0 |
| title | Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables |
| title_auth | Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables |
| title_exact_search | Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables |
| title_full | Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables Marc Wildi |
| title_fullStr | Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables Marc Wildi |
| title_full_unstemmed | Signal extraction efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables Marc Wildi |
| title_short | Signal extraction |
| title_sort | signal extraction efficient estimation unit root tests and early detection of turning points with 15 tables |
| title_sub | efficient estimation, "unit root"-tests and early detection of turning points ; with 15 tables |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Schätzung (DE-588)4193791-0 gnd |
| topic_facet | Zeitreihenanalyse Schätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012914085&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT wildimarc signalextractionefficientestimationunitroottestsandearlydetectionofturningpointswith15tables |