Singular spectrum analysis for time series:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2013
|
| Series: | Springer briefs in statistics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | VII, 119 S. graph. Darst. |
| ISBN: | 3642349129 9783642349126 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 PRELIMINARIES 1
1.2 SSA METHODOLOGY AND THE STRUCTURE O F THE BOOK 3
1.3 SSA TOPICS OUTSIDE THE SCOPE O F THIS B O O K 6
1.4 C O M M O N SYMBOLS AND ACRONYMS 8
REFERENCES 9
2 BASIC SSA 11
2.1 THE MAIN ALGORITHM 11
2.1.1 DESCRIPTION O F THE ALGORITHM 11
2.1.2 ANALYSIS O F THE F O U R STEPS IN BASIC SSA 13
2.2 POTENTIAL O F BASIC S S A 19
2.2.1 EXTRACTION O F TRENDS AND SMOOTHING 19
2.2.2 EXTRACTION O F PERIODIC COMPONENTS 21
2.2.3 COMPLEX TRENDS AND PERIODICITIES WITH VARYING AMPLITUDES 2 2
2.2.4 FINDING STRUCTURE IN SHORT T I M E SERIES 2 3
2.2.5 ENVELOPES O F OSCILLATING SIGNALS AND ESTIMATION O F VOLATILITY 2
4
2.3 MODELS O F T I M E SERIES AND S S A OBJECTIVES 2 5
2.3.1 SSA AND MODELS O F T I M E SERIES 2 5
2.3.2 CLASSIFICATION O F THE MAIN S S A TASKS 35
2.3.3 SEPARABILITY O F COMPONENTS O F T I M E SERIES 37
2.4 CHOICE O F PARAMETERS IN BASIC S S A 3 9
2.4.1 GENERAL ISSUES 3 9
2.4.2 GROUPING FOR GIVEN W I N D O W LENGTH 4 3
2.4.3 W I N D O W LENGTH 4 7
2.4.4 SIGNAL EXTRACTION 5 3
2.4.5 AUTOMATIC IDENTIFICATION O F SSA COMPONENTS 5 4
HTTP://D-NB.INFO/1027026826
IMAGE 2
VI C O N T E N T S
2.5 SOME VARIATIONS O F BASIC SSA 5 8
2.5.1 PREPROCESSING 5 8
2.5.2 CENTERING IN SSA 5 9
2.5.3 STATIONARY SERIES AND TOEPLITZ SSA 6 0
2.5.4 ROTATIONS FOR SEPARABILITY. S S A - I C A 61
2.5.5 SEQUENTIAL SSA 6 5
2.5.6 COMPUTER IMPLEMENTATION O F S S A 67
2.5.7 REPLACING THE S V D WITH OTHER PROCEDURES 6 8
REFERENCES 6 9
3 SSA FOR FORECASTING, INTERPOLATION, FILTRATION AND ESTIMATION . . . .
71 3.1 S S A FORECASTING ALGORITHMS 71
3.1.1 MAIN IDEAS AND NOTATION 71
3.1.2 FORMAL DESCRIPTION O F THE ALGORITHMS 7 3
3.1.3 SSA FORECASTING ALGORITHMS: SIMILARITIES AND DISSIMILARITIES 7 5
3.1.4 APPENDIX: VECTORS IN A SUBSPACE 77
3.2 L R R AND ASSOCIATED CHARACTERISTIC POLYNOMIALS 7 8
3.2.1 BASIC FACTS 7 8
3.2.2 ROOTS O F THE CHARACTERISTIC POLYNOMIALS 7 9
3.2.3 MIN-NORM L R R 8 0
3.3 RECURRENT FORECASTING AS APPROXIMATE CONTINUATION 83
3.3.1 APPROXIMATE SEPARABILITY AND FORECASTING ERRORS 83
3.3.2 APPROXIMATE CONTINUATION AND THE CHARACTERISTIC POLYNOMIALS 8 4
3.4 CONFIDENCE BOUNDS FOR THE FORECAST 86
3.4.1 MONTE CARLO AND BOOTSTRAP CONFIDENCE INTERVALS 87
3.4.2 CONFIDENCE INTERVALS: COMPARISON O F FORECASTING METHODS 89
3.5 SUMMARY AND RECOMMENDATIONS ON FORECASTING PARAMETERS. . . . 9 0
3.6 CASE STUDY: 'FORTIFIED WINE' 9 4
'3.6.1 LINEAR RECURRENCE RELATION GOVERNING THE T I M E SERIES 9 4
3.6.2 CHOICE O F FORECASTING METHODS AND PARAMETERS 9 6
3.7 MISSING VALUE IMPUTATION 9 8
3.7.1 S S A FOR T I M E SERIES WITH MISSING DATA: ALGORITHM . . . . 9 9
3.7.2 DISCUSSION 102
3.7.3 EXAMPLE 102
3.8 SUBSPACE-BASED METHODS AND ESTIMATION O F SIGNAL PARAMETERS 104
3.8.1 BASIC FACTS 105
3.8.2 E S P R I T 106
3.8.3 OVERVIEW O F OTHER SUBSPACE-BASED METHODS 108
3.8.4 C A D Z O W ITERATIONS 110
IMAGE 3
C O N T E N T S VII
3.9 SSA AND FILTERS I L L
3.9.1 LINEAR FILTERS AND T H E I R CHARACTERISTICS I L L
3.9.2 SSA RECONSTRUCTION AS A LINEAR FILTER 112
3.9.3 MIDDLE POINT FILTER 113
3.9.4 LAST POINT FILTER AND FORECASTING 115
3.9.5 CAUSAL SSA (LAST-POINT SSA) 116
REFERENCES 118 |
| any_adam_object | 1 |
| author | Goljandina, Nina E. Žigljavskij, Anatolij Aleksandrovič 1953- |
| author_GND | (DE-588)132720949 (DE-588)124189199 |
| author_facet | Goljandina, Nina E. Žigljavskij, Anatolij Aleksandrovič 1953- |
| author_role | aut aut |
| author_sort | Goljandina, Nina E. |
| author_variant | n e g ne neg a a ž aa aaž |
| building | Verbundindex |
| bvnumber | BV040795266 |
| classification_rvk | SK 845 |
| ctrlnum | (OCoLC)830878500 (DE-599)DNB1027026826 |
| dewey-full | 519.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.55 |
| dewey-search | 519.55 |
| dewey-sort | 3519.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| language | English |
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| physical | VII, 119 S. graph. Darst. |
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| spelling | Goljandina, Nina E. Verfasser (DE-588)132720949 aut Singular spectrum analysis for time series Anatoly Zhigljavsky ; Nina Golyandina Berlin Springer 2013 VII, 119 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer briefs in statistics Zeitreihe (DE-588)4127298-5 gnd rswk-swf Spektralanalyse Stochastik (DE-588)4056125-2 gnd rswk-swf Zeitreihe (DE-588)4127298-5 s Spektralanalyse Stochastik (DE-588)4056125-2 s DE-604 Žigljavskij, Anatolij Aleksandrovič 1953- Verfasser (DE-588)124189199 aut Erscheint auch als Online-Ausgabe 978-3-642-34913-3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4164545&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025775482&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goljandina, Nina E. Žigljavskij, Anatolij Aleksandrovič 1953- Singular spectrum analysis for time series Zeitreihe (DE-588)4127298-5 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd |
| subject_GND | (DE-588)4127298-5 (DE-588)4056125-2 |
| title | Singular spectrum analysis for time series |
| title_auth | Singular spectrum analysis for time series |
| title_exact_search | Singular spectrum analysis for time series |
| title_full | Singular spectrum analysis for time series Anatoly Zhigljavsky ; Nina Golyandina |
| title_fullStr | Singular spectrum analysis for time series Anatoly Zhigljavsky ; Nina Golyandina |
| title_full_unstemmed | Singular spectrum analysis for time series Anatoly Zhigljavsky ; Nina Golyandina |
| title_short | Singular spectrum analysis for time series |
| title_sort | singular spectrum analysis for time series |
| topic | Zeitreihe (DE-588)4127298-5 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd |
| topic_facet | Zeitreihe Spektralanalyse Stochastik |
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