Climate time series analysis: classical statistical and bootstrap methods
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2014
|
| Edition: | 2. ed. |
| Series: | Atmospheric and oceanographic sciences library
51 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXXII, 454 S. graph. Darst. |
| ISBN: | 9783319044491 9783319374482 |
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MARC
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| 264 | 1 | |a Cham [u.a.] |b Springer |c 2014 | |
| 300 | |a XXXII, 454 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804152102634651648 |
|---|---|
| adam_text | Contents
Part I Fundamental Concepts
1
Introduction
.................................................................. 3
1.
1 Climate Archives, Variables and Dating
............................... 5
1.2
Noise and Statistical Distribution
...................................... 5
1.3
Persistence
............................................................... 8
1.4
Spacing
.................................................................. 10
1.5
Aim and Structure of this Book
........................................ 14
1.6
Background Material
.................................................... 19
2
Persistence Models
........................................................... 31
2.1
First-Order
Autoregressive
Model
..................................... 31
2.1.1
Even Spacing
.................................................... 32
2.1.2
Uneven Spacing
................................................. 34
2.2
Second-Order
Autoregressive
Model
.................................. 36
2.3
Mixed
Autoregressive
Moving Average Model
....................... 38
2.4
Other Models
............................................................ 39
2.4.1
Long-Memory Processes
....................................... 39
2.4.2
Nonlinear and Non-Gaussian Models
.......................... 40
2.5
Climate Theory
.......................................................... 42
2.5.1
Stochastic Climate Models
..................................... 42
2.5.2
Long Memory of Temperature Fluctuations?
................. 44
2.5.3
Long Memory of River Runoff
................................. 48
2.6
Background Material
.................................................... 50
2.7
Technical Issues
......................................................... 58
3
Bootstrap Confidence Intervals
............................................ 61
3.1
Error Bars and Confidence Intervals
................................... 62
3.1.1
Theoretical Example: Mean Estimation of
Gaussian White Noise
.......................................... 64
XVII
xviii
Contents
3.1.2
Theoretical Example: Standard Deviation
Estimation of Gaussian White Noise
.......................... 66
3.1.3
Real World
...................................................... 67
3.2
Bootstrap Principle
...................................................... 71
3.3
Bootstrap Resampling
.................................................. 72
3.3.1
Nonparametric: Moving Block Bootstrap
..................... 73
3.3.2
Parametric:
Autoregressive
Bootstrap
......................... 77
3.33
Parametric: Surrogate Data
..................................... 78
3.4
Bootstrap Confidence Intervals
......................................... 78
3.4.1
Normal Confidence Interval
.................................... 82
3.4.2
Student s
t
Confidence Interval
................................ 82
3.4.3
Percentile Confidence Interval
................................. 82
3.4.4
BCa Confidence Interval
....................................... 83
3.5
Examples
................................................................ 84
3.6
Bootstrap Hypothesis Tests
............................................. 85
3.7
Notation
................................................................. 88
3.8
Background Material
.................................................... 88
3.9
Technical Issues
......................................................... 100
Part
Π
Univariate Time Series
4
Regression 1
................................................................... 107
4.1
Linear Regression
....................................................... 108
4.1.1
Weighted Least-Squares and Ordinary
Least-Squares Estimation
...................................... 108
4Л.2
Generalized Least-Squares Estimation
........................ 110
4.1.3
Other Estimation Types
......................................... 112
4.1.4
Classical Confidence Intervals
................................. 113
4Λ
.5
Bootstrap Confidence Intervals
................................ 117
4.1.6
Monte Carlo Experiments: Ordinary
Least-Squares Estimation
...................................... 117
4.1.7
Timescale Errors
................................................ 122
4.2
Nonlinear Regression
................................................... 132
4.2Л
Climate Transition Model: Ramp
.............................. 133
4.2.2
Trend-Change Model: Break
................................... 139
4.3
Nonparametric Regression or Smoothing
.............................. 144
4.3.1
Kernel Estimation
............................................... 144
4.3.2
Bootstrap Confidence Intervals and Bands
.................... 146
4.3.3
Extremes or Outlier Detection
................................. 147
4.4
Background Material
.................................................... 151
4.5
Technical Issues
......................................................... 164
5
Spectral Analysis
............................................................. 169
5.1
Spectrum
................................................................. 170
5.1.1
Example: AR(1) Process, Discrete Time
...................... 172
Contents xix
5.1.2
Example: AR(2) Process, Discrete Time
...................... 172
5.1.3
Physical Meaning
............................................... 172
5.2
Spectral Estimation
..................................................... 173
5.2.1
Periodogram
..................................................... 174
5.2.2
Welch s Overlapped Segment Averaging
...................... 178
5.2.3
Multitaper Estimation
.......................................... 179
5.2.4
Lomb-Scargle Estimation
...................................... 187
5.2.5
Peak Detection: Red-Noise Hypothesis
........................ 192
5.2.6
Example: Peaks in Monsoon Spectrum
........................ 194
5.2.7
Aliasing
......................................................... 196
5.2.8
Timescale Errors
................................................ 197
5.2.9
Example: Peaks in Monsoon Spectrum (Continued)
.......... 198
5.3
Background Material
.................................................... 203
5.4
Technical Issues
......................................................... 213
6
Extreme Value Time Series
................................................. 217
6.1
Data Types
............................................................... 218
6.1.1
Event Times
..................................................... 218
6.1.2
Peaks Over Threshol
d
.......................................... 218
6.1.3
Block Extremes
................................................. 219
6.1.4
Remarks on Data Selection
..................................... 220
6.2
Stationary Models
....................................................... 220
6.2.1
Generalized Extreme Value Distribution
...................... 220
6.2.2
Generalized Pareto Distribution
................................ 223
6.2.3
Bootstrap Confidence Intervals
................................ 228
6.2.4
Example: Elbe Summer Floods,
1852-2002.................. 228
6.2.5
Persistence
...................................................... 230
6.2.6
Remark: Tail Estimation
........................................ 232
6.2.7
Remark: Optimal Estimation
................................... 233
6.3
Nonstationary Models
.................................................. 233
6.3.1
Time-Dependent Generalized Extreme Value Distribution
... 234
6.3.2
Inhomogeneous
Poisson
Process
............................... 235
6.3.3
Hybrid: Poisson-Extreme Value Distribution
................. 247
6.4
Sampling and Time Spacing
............................................ 250
6.5
Background Material
.................................................... 255
6.6
Technical Issues
......................................................... 264
Part
Ш
Divariate
Tíme
Series
7
Correlation
.................................................................... 271
7.1
Pearson s Correlation Coefficient
...................................... 272
7.1.1
Remark: Alternative Correlation Measures
.................... 273
7.1.2
Classical Confidence intervals,
Nonpersistent
Processes
..... 273
7.1.3
Divariate
Time Series Models
.................................. 275
xx Contents
7.1.4
Classical Confidence Intervals, Persistent Processes
.......... 277
7.1.5
Bootstrap Confidence Intervals
................................ 277
7.2
Spearman s Rank Correlation Coefficient
............................. 283
7.2.1
Classical Confidence Intervals,
Nonpersistent
Processes
..... 284
7.2.2
Classical Confidence Intervals, Persistent Processes
.......... 285
7.2.3
Bootstrap Confidence Intervals
................................ 285
7.3
Monte Carlo Experiments
.............................................. 287
7.4
Example: Elbe Runoff Variations
...................................... 292
7.5
Unequal Timescales
..................................................... 294
7.5.1
Binned Correlation
.............................................. 295
7.5.2
Synchrony Correlation
.......................................... 298
7.5.3
Monte Carlo Experiments
...................................... 299
7.5.4
Example: Vostok Ice Core Records
............................ 305
7.6
Background Material
.................................................... 306
7.7
Technical Issues
......................................................... 319
8
Regression II
.................................................................. 321
8.1
Linear Regression
....................................................... 322
8.1.1
Ordinary Least-Squares Estimation
............................ 322
8.1.2
Weighted Least-Squares for Both Variables Estimation
...... 325
8.1.3
Wald-Bartlett Procedure
....................................... 327
8.2
Bootstrap Confidence Intervals
......................................... 328
8.2.1
Simulating Incomplete Prior Knowledge
...................... 331
8.3
Monte Carlo Experiments
.............................................. 331
8.3.1
Easy Setting
..................................................... 332
8.3.2
Realistic Setting: Incomplete Prior Knowledge
............... 335
8.3.3
Dependence on Accuracy of Prior Knowledge
................ 335
8.3.4
Mis-Specified Prior Knowledge
................................ 339
8.4
Example: Climate Sensitivity
........................................... 340
8.5
Prediction
................................................................ 341
8.5.1
Example: Calibration of a Proxy Variable
..................... 345
8.6
Lagged Regression
...................................................... 346
8.6.1
Example: CO2 and Temperature Variations in the
Pleistocene
...................................................... 348
8.7
Background Material
.................................................... 352
8.8
Technical Issues
......................................................... 358
Part IV Outlook
9
Future
Directions
............................................................ 363
9.1
Timescale Modelling
..........................................-.......... 363
9.2
Novel
Estimadon
Problems
............................................. 364
9.3
Higher Dimensions
...................................................... 365
Contents xxi
9.4
Climate
Models......................................................... 366
9.4.1
Fitting Climate Models to Observations
....................... 367
9.4.2
Forecasting with Climate Models
.............................. 368
9.4.3
Design of the Cost Function
.................................... 369
9.4.4
Climate Model Bias
............................................ 370
9.5
Optimal Estimation
..................................................... 371
9.6
Background Material
.................................................... 374
References
......................................................................... 377
Author Index
...................................................................... 431
Subject Index
..................................................................... 441
Atmospheric and
Océanographie
Sciences Library
5Ί
Manfred Mudelsee
Climate Time Series Analysis
Classical Statistical and Bootstrap Methods, Second Edition
Climate is a paradigm of a complex system. Analysing climate data is an exciting
challenge which is increased by non-normal distributional shape, serial dependence,
uneven spacing and
t
і
mescale
uncertainties.
Ulis
book presents bootstrap resampling
asa
computing-intensive method able to meet the challenge. It shows the bootstrap to
perform reliably in
lhe
most important statistical estimation techniques: regression,
spectral
analysis, extreme values and correlation.
This
bo» -k
is written tor climatoiogi-ls
лпа
applied statisticians. It explains step by step
the bootstrap algorithms (including novel adaptions) and methods for confidence
interval construction. It tests the accuracy or the algorithms by means of Monte Carlo
experiments.
H
analyses a large array of climate time series, giving a detailed account
on the data
млс
tiie associated
climatológica)
questions.
Manfred Mudelsee received his diploma in Physics from the University of Heidelberg
and his doctoral degree in Geology from the University of Kiel. He was then a postdoc¬
toral researcher
m
Statistics at the
University
*.->(
Kent at Canterbury, research scientist
in Meteorology at the University
oť
Leipzig and visiting scholar in Earth Sciences at
Boston University; currently he dues climate research at the Alfred VVegener Institute
for
Pola*
.-.nei
Marine Research.
Bremerhaven.
I Hs science focuses on climate extremes,
tir.ie series anah sis ¿n< mathematical simulation methods. He lias authored over
60
peer-reviewed articles. In his
ιοολ
Nature paper, Mudelsee introduced the bootstrap
method to tlood risk anaK sis. In
2005,
he founded the company Climate Risk
Λ
nah
sis.
4
ice
2011,
he gives practical courses on basis of this bonk.
..-
comprehensive mathematical and statistical summary afthne-series analysis techniques
i i< climate applications
...
accessible to readers with knowledge o!
-
college-level
liiłciUus
and statistics ™ (Computers and Geosciences)
A key part of the book thai separates
n
troni
other time series works is the explicit dis-
c ussioti of time uncertainty*., a very useful text for those wishing to understand how to
arutľvse
clinuitc time series. (Journal of
1
inie
series Analysis)
utstemding: one of the
besu
books on advanced practical time series analysis I have
1
i id I. Hand. Past-President
Кочаї
Statistical Societv)
Earth Sciences
ISSN
1383-8601
џ-
springer com
|
| any_adam_object | 1 |
| author | Mudelsee, Manfred |
| author_facet | Mudelsee, Manfred |
| author_role | aut |
| author_sort | Mudelsee, Manfred |
| author_variant | m m mm |
| building | Verbundindex |
| bvnumber | BV041787503 |
| classification_rvk | QT 800 RB 10103 RB 10429 UT 6200 |
| ctrlnum | (OCoLC)884984158 (DE-599)BVBBV041787503 |
| discipline | Physik Geologie / Paläontologie Wirtschaftswissenschaften Geographie |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV041787503 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:05:23Z |
| institution | BVB |
| isbn | 9783319044491 9783319374482 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027233212 |
| oclc_num | 884984158 |
| open_access_boolean | |
| owner | DE-29 DE-703 DE-521 |
| owner_facet | DE-29 DE-703 DE-521 |
| physical | XXXII, 454 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series | Atmospheric and oceanographic sciences library |
| series2 | Atmospheric and oceanographic sciences library |
| spelling | Mudelsee, Manfred Verfasser aut Climate time series analysis classical statistical and bootstrap methods Manfred Mudelsee 2. ed. Cham [u.a.] Springer 2014 XXXII, 454 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Atmospheric and oceanographic sciences library 51 Hier auch später erschienene, unveränderte Nachdrucke Klimaanalyse (DE-588)4466593-3 gnd rswk-swf Klimatologie (DE-588)4031178-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Bootstrap-Statistik (DE-588)4139168-8 gnd rswk-swf Klimatologie (DE-588)4031178-8 s Datenanalyse (DE-588)4123037-1 s DE-604 Klimaanalyse (DE-588)4466593-3 s Zeitreihenanalyse (DE-588)4067486-1 s Bootstrap-Statistik (DE-588)4139168-8 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-3-319-04450-7 Atmospheric and oceanographic sciences library 51 (DE-604)BV010783916 51 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027233212&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027233212&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mudelsee, Manfred Climate time series analysis classical statistical and bootstrap methods Atmospheric and oceanographic sciences library Klimaanalyse (DE-588)4466593-3 gnd Klimatologie (DE-588)4031178-8 gnd Datenanalyse (DE-588)4123037-1 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Bootstrap-Statistik (DE-588)4139168-8 gnd |
| subject_GND | (DE-588)4466593-3 (DE-588)4031178-8 (DE-588)4123037-1 (DE-588)4067486-1 (DE-588)4139168-8 |
| title | Climate time series analysis classical statistical and bootstrap methods |
| title_auth | Climate time series analysis classical statistical and bootstrap methods |
| title_exact_search | Climate time series analysis classical statistical and bootstrap methods |
| title_full | Climate time series analysis classical statistical and bootstrap methods Manfred Mudelsee |
| title_fullStr | Climate time series analysis classical statistical and bootstrap methods Manfred Mudelsee |
| title_full_unstemmed | Climate time series analysis classical statistical and bootstrap methods Manfred Mudelsee |
| title_short | Climate time series analysis |
| title_sort | climate time series analysis classical statistical and bootstrap methods |
| title_sub | classical statistical and bootstrap methods |
| topic | Klimaanalyse (DE-588)4466593-3 gnd Klimatologie (DE-588)4031178-8 gnd Datenanalyse (DE-588)4123037-1 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Bootstrap-Statistik (DE-588)4139168-8 gnd |
| topic_facet | Klimaanalyse Klimatologie Datenanalyse Zeitreihenanalyse Bootstrap-Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027233212&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027233212&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010783916 |
| work_keys_str_mv | AT mudelseemanfred climatetimeseriesanalysisclassicalstatisticalandbootstrapmethods |