Introductory time series with R:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Series: | Use R!
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 254 S. zahlr. graph. Darst. |
| ISBN: | 9780387886978 |
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MARC
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| 100 | 1 | |a Cowpertwait, Paul S. P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory time series with R |c Paul S. P. Cowpertwait ; Andrew V. Metcalfe |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XV, 254 S. |b zahlr. graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804138844819292160 |
|---|---|
| adam_text | Contents
Preface
........................................................
vii
1
Time Series Data
.......................................... 1
1.1
Purpose
................................................ 1
1.2
Time series
............................................. 2
1.3
R
language
.............................................. 3
1.4
Plots, trends, and seasonal variation
....................... 4
1.4.1
A flying start: Air passenger bookings
................ 4
1.4.2
Unemployment: Maine
............................. 7
1.4.3
Multiple time series: Electricity, beer and chocolate data
10
1.4.4
Quarterly exchange rate: GBP to NZ dollar
........... 14
1.4.5
Global temperature series
.......................... 16
1.5
Decomposition of series
.................................. 19
1.5.1
Notation
......................................... 19
1.5.2
Models
........................................... 19
1.5.3
Estimating trends and seasonal effects
............... 20
1.5.4
Smoothing
....................................... 21
1.5.5
Decomposition in
R
................................ 22
1.6
Summary of commands used in examples
................... 24
1.7
Exercises
............................................... 24
2
Correlation
................................................ 27
2.1
Purpose
................................................ 27
2.2
Expectation and the ensemble
............................. 27
2.2.1
Expected value
.................................... 27
2.2.2
The ensemble and stationarity
...................... 30
2.2.3
Ergodic series*
.................................... 31
2.2.4
Variance function
................................. 32
2.2.5
Autocorrelation
................................... 33
Contents
2.3
The correlogram
......................................... 35
2.3.1 General
discussion.................................
35
2.3.2
Example based on air passenger series
............... 37
2.3.3
Example based on the Font Reservoir series
........... 40
2.4
Covariance of sums of random variables
.................... 41
2.5
Summary of commands used in examples
................... 42
2.6
Exercises
............................................... 42
Forecasting Strategies
..................................... 45
3.1
Purpose
................................................ 45
3.2
Leading variables and associated variables
.................. 45
3.2.1
Marine coatings
................................... 45
3.2.2
Building approvals publication
...................... 46
3.2.3
Gas supply
....................................... 49
3.3
Bass model
............................................. 51
3.3.1
Background
...................................... 51
3.3.2
Model definition
................................... 51
3.3.3
Interpretation of the Bass model*
................... 51
3.3.4
Example
......................................... 52
3.4
Exponential smoothing and the Holt-Winters method
........ 55
3.4.1
Exponential smoothing
............................. 55
3.4.2
Holt-Winters method
.............................. 59
3.4.3
Four-year-ahead forecasts for the air passenger data
... 62
3.5
Summary of commands used in examples
................... 64
3.6
Exercises
............................................... 64
Basic Stochastic Models
................................... 67
4.1
Purpose
................................................ 67
4.2
White noise
............................................. 68
4.2.1
Introduction
...................................... 68
4.2.2
Definition
........................................ 68
4.2.3
Simulation in
R
................................... 68
4.2.4
Second-order properties and the correlogram
.......... 69
4.2.5
Fitting a white noise model
......................... 70
4.3
Random walks
.......................................... 71
4.3.1
Introduction
...................................... 71
4.3.2
Definition
........................................ 71
4.3.3
The backward shift operator
........................ 71
4.3.4
Random walk: Second-order properties
............... 72
4.3.5
Derivation of second-order properties*
............... 72
4.3.6
The difference operator
............................ 72
4.3.7
Simulation
....................................... 73
4.4
Fitted models and diagnostic plots
......................... 74
4.4.1
Simulated random walk series
....................... 74
4.4.2
Exchange rate series
............................... 75
Contents xi
4.4.3
Random walk with drift
............................ 77
4.5
Autoregressive
models
................................... 79
4.5.1
Definition
........................................ 79
4.5.2
Stationary and non-stationary
AR
processes
.......... 79
4.5.3
Second-order properties of an AR(1) model
........... 80
4.5.4
Derivation of second-order properties for an AR(1)
process*
.......................................... 80
4.5.5
Correlogram of an AR(1) process
.................... 81
4.5.6
Partial autocorrelation
............................. 81
4.5.7
Simulation
....................................... 81
4.6
Fitted models
........................................... 82
4.6.1
Model fitted to simulated series
..................... 82
4.6.2
Exchange rate series: Fitted
AR
model
............... 84
4.6.3
Global temperature series: Fitted
AR
model
.......... 85
4.7
Summary of
R
commands
................................. 87
4.8
Exercises
............................................... 87
Regression
................................................. 91
5.1
Purpose
................................................ 91
5.2
Linear models
........................................... 92
5.2.1
Definition
........................................ 92
5.2.2
Stationarity
...................................... 93
5.2.3
Simulation
....................................... 93
5.3
Fitted models
........................................... 94
5.3.1
Model fitted to simulated data
...................... 94
5.3.2
Model fitted to the temperature series
(1970-2005)___ 95
5.3.3
Autocorrelation and the estimation of sample statistics*
96
5.4
Generalised least squares
................................. 98
5.4.1
GLS fit to simulated series
.......................... 98
5.4.2
Confidence interval for the trend in the temperature
series
............................................ 99
5.5
Linear models with seasonal variables
...................... 99
5.5.1
Introduction
...................................... 99
5.5.2
Additive seasonal indicator variables
................. 99
5.5.3
Example: Seasonal model for the temperature series
.. . 100
5.6
Harmonic seasonal models
................................101
5.6.1
Simulation
.......................................102
5.6.2
Fit to simulated series
.............................103
5.6.3
Harmonic model fitted to temperature series
(1970-2005) 105
5.7
Logarithmic transformations
..............................109
5.7.1
Introduction
......................................109
5.7.2
Example using the air passenger series
...............109
5.8
Non-linear models
.......................................113
5.8.1
Introduction
......................................113
5.8.2
Example of a simulated and fitted non-linear series
. .. . 113
xii Contents
5.9
Forecasting from regression
...............................115
5.9.1
Introduction
......................................115
5.9.2
Prediction in
R
....................................115
5.10
Inverse transform and bias correction
......................115
5.10.1
Log-normal residual errors
..........................115
5.10.2
Empirical correction factor for forecasting means
......117
5.10.3
Example using the air passenger data
................117
5.11
Summary of
R
commands
.................................118
5.12
Exercises
...............................................118
6
Stationary Models
.........................................121
6.1
Purpose
................................................121
6.2
Strictly stationary series
..................................121
6.3
Moving average models
...................................122
6.3.1
MA(q) process: Definition and properties
.............122
6.3.2
R
examples: Correlogram and simulation
.............123
6.4
Fitted MA models
.......................................124
6.4.1
Model fitted to simulated series
.....................124
6.4.2
Exchange rate series: Fitted MA model
..............126
6.5
Mixed models: The
ARMA
process
........................127
6.5.1
Definition
........................................127
6.5.2
Derivation of second-order properties*
...............128
6.6
ARMA
models: Empirical analysis
.........................129
6.6.1
Simulation and fitting
..............................129
6.6.2
Exchange rate series
...............................129
6.6.3
Electricity production series
........................130
6.6.4
Wave tank data
...................................133
6.7
Summary of
R
commands
.................................135
6.8
Exercises
...............................................135
7
Non-stationary Models
....................................137
7.1
Purpose
................................................137
7.2
Non-seasonal ARIMA models
.............................137
7.2.1
Differencing and the electricity series
................137
7.2.2
Integrated model
..................................138
7.2.3
Definition and examples
............................139
7.2.4
Simulation and fitting
..............................140
7.2.5
IMA(1,
1)
model fitted to the beer production series
... 141
7.3
Seasonal ARIMA models
.................................142
7.3.1
Definition
........................................142
7.3.2
Fitting procedure
..................................143
7.4
ARCH models
..........................................145
7.4.1
S&P500 series
....................................145
7.4.2
Modelling volatility: Definition of the ARCH model
-----147
7.4.3
Extensions and GARCH models
.....................148
Contents xiii
7.4.4 Simulation and
fitted GARCH
model
................149
7.4.5
Fit to S&P500 series...............................
150
7.4.6
Volatility in climate series
..........................152
7.4.7
GARCH in forecasts and simulations
................155
7.5
Summary of
R
commands
.................................155
7.6
Exercises
...............................................155
Long-Memory Processes
...................................159
8.1
Purpose
................................................159
8.2
Fractional differencing
...................................159
8.3
Fitting to simulated data
.................................161
8.4
Assessing evidence of long-term dependence
.................164
8.4.1
Nile minima
......................................164
8.4.2
Bellcore Ethernet data
.............................165
8.4.3
Bank loan rate
....................................166
8.5
Simulation
..............................................167
8.6
Summary of additional commands used
....................168
8.7
Exercises
...............................................168
Spectral Analysis
..........................................171
9.1
Purpose
................................................171
9.2
Periodic signals
.........................................171
9.2.1
Sine waves
........................................171
9.2.2
Unit of measurement of frequency
...................172
9.3
Spectrum
...............................................173
9.3.1
Fitting sine waves
......
r
..........................173
9.3.2
Sample spectrum
..................................175
9.4
Spectra of simulated series
................................175
9.4.1
White noise
......................................175
9.4.2
AR(1): Positive coefficient
..........................177
9.4.3
AR(1): Negative coefficient
.........................178
9.4.4
AR(2)
...........................................178
9.5
Sampling interval and record length
........................179
9.5.1
Nyquist frequency
.................................181
9.5.2
Record length
.....................................181
9.6
Applications
............................................183
9.6.1
Wave tank data
...................................183
9.6.2
Fault detection on electric motors
...................183
9.6.3
Measurement of vibration dose
......................184
9.6.4
Climatic indices
...................................187
9.6.5
Bank loan rate
....................................189
9.7
Discrete Fourier transform (DFT)*
........................190
9.8
The spectrum of a random process*
........................192
9.8.1
Discrete white noise
...............................193
9.8.2 AR..............................................193
xiv Contents
9.8.3
Derivation of spectrum
.............................193
9.9
Autoregressive
spectrum estimation
........................194
9.10
Finer details
............................................194
9.10.1
Leakage
..........................................194
9.10.2
Confidence intervals
...............................195
9.10.3
Danieli
windows
...................................196
9.10.4
Padding
..........................................196
9.10.5
Tapering
.........................................197
9.10.6
Spectral analysis compared with wavelets
.............197
9.11
Summary of additional commands used
....................197
9.12
Exercises
...............................................198
10
System Identification
......................................201
10.1
Purpose
................................................201
10.2
Identifying the gain of a linear system
......................201
10.2.1
Linear system
.....................................201
10.2.2
Natural frequencies
................................202
10.2.3
Estimator of the gain function
......................202
10.3
Spectrum of an AR(p) process
............................203
10.4
Simulated single mode of vibration system
..................203
10.5
Ocean-going tugboat
.....................................205
10.6
Non-linearity
........
f
..................................207
10.7
Exercises
...............................................208
11
Multivariate Models
.......................................211
11.1
Purpose
................................................211
11.2
Spurious regression
......................................211
11.3
Tests for unit roots
......................................214
11.4
Cointegration
...........................................216
11.4.1
Definition
........................................216
11.4.2
Exchange rate series
...............................218
11.5
Bivariate and multivariate white noise
.....................219
11.6
Vector
autoregressive
models
..............................220
11.6.1
VAR
model fitted to US economic series
..............222
11.7
Summary of
R
commands
.................................227
11.8
Exercises
...............................................227
12
State Space Models
........................................229
12.1
Purpose
................................................229
12.2
Linear state space models
................................230
12.2.1
Dynamic linear model
..............................230
12.2.2
Filtering*
........................................231
12.2.3
Prediction*
.......................................232
12.2.4
Smoothing*
......................................233
12.3
Fitting to simulated univariate time series
..................234
Contents xv
12.3.1
Random walk plus noise model
......................234
12.3.2
Regression model with time-varying coefficients
.......236
12.4
Fitting to univariate time series
...........................238
12.5
Divariate
time series
-
river salinity
........................239
12.6
Estimating the variance matrices
..........................242
12.7
Discussion
..............................................243
12.8
Summary of additional commands used
....................244
12.9
Exercises
...............................................244
References
.....................................................247
Index
..........................................................249
|
| any_adam_object | 1 |
| author | Cowpertwait, Paul S. P. Metcalfe, Andrew V. |
| author_GND | (DE-588)13874923X |
| author_facet | Cowpertwait, Paul S. P. Metcalfe, Andrew V. |
| author_role | aut aut |
| author_sort | Cowpertwait, Paul S. P. |
| author_variant | p s p c psp pspc a v m av avm |
| building | Verbundindex |
| bvnumber | BV035409039 |
| callnumber-first | Q - Science |
| callnumber-label | QA280 |
| callnumber-raw | QA280 |
| callnumber-search | QA280 |
| callnumber-sort | QA 3280 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | MR 2200 QH 237 SK 845 ST 250 ST 601 |
| classification_tum | DAT 307f MAT 634f |
| ctrlnum | (OCoLC)611049551 (DE-599)DNB992520924 |
| dewey-full | 519.5/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 |
| dewey-search | 519.5/5 |
| dewey-sort | 3519.5 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035409039 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:34:35Z |
| institution | BVB |
| isbn | 9780387886978 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017329574 |
| oclc_num | 611049551 |
| open_access_boolean | |
| owner | DE-20 DE-473 DE-BY-UBG DE-945 DE-N2 DE-703 DE-91G DE-BY-TUM DE-11 DE-91 DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-1049 DE-824 DE-M347 DE-19 DE-BY-UBM DE-188 DE-521 DE-83 |
| owner_facet | DE-20 DE-473 DE-BY-UBG DE-945 DE-N2 DE-703 DE-91G DE-BY-TUM DE-11 DE-91 DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-1049 DE-824 DE-M347 DE-19 DE-BY-UBM DE-188 DE-521 DE-83 |
| physical | XV, 254 S. zahlr. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Use R! |
| spelling | Cowpertwait, Paul S. P. Verfasser aut Introductory time series with R Paul S. P. Cowpertwait ; Andrew V. Metcalfe New York, NY Springer 2009 XV, 254 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Use R! R Programm (DE-588)4705956-4 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s R Programm (DE-588)4705956-4 s DE-604 Metcalfe, Andrew V. Verfasser (DE-588)13874923X aut Erscheint auch als Online-Ausgabe 978-0-387-88698-5 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017329574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cowpertwait, Paul S. P. Metcalfe, Andrew V. Introductory time series with R R Programm (DE-588)4705956-4 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4067486-1 |
| title | Introductory time series with R |
| title_auth | Introductory time series with R |
| title_exact_search | Introductory time series with R |
| title_full | Introductory time series with R Paul S. P. Cowpertwait ; Andrew V. Metcalfe |
| title_fullStr | Introductory time series with R Paul S. P. Cowpertwait ; Andrew V. Metcalfe |
| title_full_unstemmed | Introductory time series with R Paul S. P. Cowpertwait ; Andrew V. Metcalfe |
| title_short | Introductory time series with R |
| title_sort | introductory time series with r |
| topic | R Programm (DE-588)4705956-4 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | R Programm Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017329574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cowpertwaitpaulsp introductorytimeserieswithr AT metcalfeandrewv introductorytimeserieswithr |