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E-raamat: Introductory Time Series with R

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  • Sari: Use R!
  • Ilmumisaeg: 28-May-2009
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9780387886985
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Introductory Time Series with RSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Use R!
  • Ilmumisaeg: 28-May-2009
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9780387886985
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This book gives the reader a step-by-step introduction to analyzing time series using the open source software R. Each time series model is illustrated through practical applications addressing contemporary issues, and is defined in mathematical notation.



Rhasacommandlineinterfacethato ersconsiderableadvantagesovermenu systemsintermsofe ciencyandspeedoncethecommandsareknownandthe languageunderstood. However,thecommandlinesystemcanbedauntingfor the rst-timeuser,sothereisaneedforconcisetextstoenablethestudentor analysttomakeprogresswithRintheirareaofstudy. Thisbookaimstoful l thatneedintheareaoftimeseries toenablethenon-specialisttoprogress, atafairlyquickpace,toalevelwheretheycancon dentlyapplyarangeof timeseriesmethodstoavarietyofdatasets. Thebookassumesthereader hasaknowledgetypicalofa rst-yearuniversitystatisticscourseandisbased aroundlecturenotesfromarangeoftimeseriescoursesthatwehavetaught overthelasttwentyyears. Someofthismaterialhasbeendeliveredtopo- graduate nancestudentsduringaconcentratedsix-weekcourseandwaswell received,soaselectionofthematerialcouldbemasteredinaconcentrated course,althoughingeneralitwouldbemoresuitedtobeingspreadovera completesemester. Thebookisbasedaroundpracticalapplicationsandgenerallyfollowsa similar format for each time series model being studied. First, there is an introductory motivational section that describes practical reasons why the modelmaybeneeded. Second,themodelisdescribedandde nedinma- ematicalnotation. Themodelisthenusedtosimulatesyntheticdatausing Rcodethatcloselyre ectsthemodelde nitionandthen ttedtothes- theticdatatorecovertheunderlyingmodelparameters. Finally,themodel is ttedtoanexamplehistoricaldatasetandappropriatediagnosticplots given. By using R, the whole procedure can be reproduced by the reader, 1 anditisrecommendedthatstudentsworkthroughmostoftheexamples. Mathematical derivations are provided in separate frames and starred sec- 1 WeusedtheRpackageSweavetoensurethat,ingeneral,yourcodewillproduce thesameoutputasours. However,forstylisticreasonswesometimeseditedour code;e. g. ,fortheplotstherewillsometimesbeminordi erencesbetweenthose generatedbythecodeinthetextandthoseshownintheactual gures. vii viii Preface tionsandcanbeomittedbythosewantingtoprogressquicklytopractical applications. Attheendofeachchapter,aconcisesummaryoftheRc- mands that were used is given followed by exercises. All data sets used in thebook,andsolutionstotheoddnumberedexercises,areavailableonthe websitehttp://www. massey. ac. nz/?pscowper/ts. WethankJohnKimmelofSpringerandtheanonymousrefereesfortheir helpfulguidanceandsuggestions,BrianWebbyforcarefulreadingofthetext andvaluablecomments,andJohnXieforusefulcommentsonanearlierdraft. TheInstituteofInformationandMathematicalSciencesatMasseyUniv- sity and the School of Mathematical Sciences, University of Adelaide, are acknowledgedforsupportandfundingthatmadeourcollaborationpossible. Paul thanks his wife, Sarah, for her continual encouragement and support duringthewritingofthisbook,andourson,Daniel,anddaughters,Lydia andLouise,forthejoytheybringtoourlives. AndrewthanksNataliefor providinginspirationandherenthusiasmfortheproject. PaulCowpertwaitandAndrewMetcalfe MasseyUniversity,Auckland,NewZealand UniversityofAdelaide,Australia December2008 Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 TimeSeriesData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Timeseries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3 Rlanguage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 4 Plots,trends,andseasonalvariation . . . . . . . . . . . . . . . . . . . . . . . 4 1. 4. 1 A yingstart:Airpassengerbookings. . . . . . . . . . . . . . . . 4 1. 4. 2 Unemployment:Maine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1. 4. 3 Multipletimeseries:Electricity,beerandchocolatedata 10 1. 4. 4 Quarterlyexchangerate:GBPtoNZdollar. . . . . . . . . . . 14 1. 4. 5 Globaltemperatureseries . . . . . . . . .

Arvustused

From the reviews:

The bookgives a very broad and practical overview of the most common models for time series analysis in the time domain and in the frequency domain, with emphasis on how to implement them with base R and existing R packages such as Rnlme, MASS, tseries, fracdiff, mvtnorm, vars, and sspir. The authors explain the models by first giving a basic theoretical introduction followed by simulation of data from a particular model and fitting the latter to the simulated data to recover the parameters. After that, they fit the class of models to either environmental, finance, economics, or physics data. There are many applications to climate change and oceanography. The R programs for the simulations are given even if there are R functions that would do the simulation. All examples given can be reproduced by the reader using the code providedin all chapters. Exercises at the end of each chapter are interesting, involving simulation, estimation, description, graphical analysis, and some theory. Data sets used throughout the book are available in a web site or come with base R or the R packages used. The book is a great guide to those wishing to get a basic introduction to modern time series modeling in practice, and in a short amount of time. (Journal of Statistical Software, January 2010, Vol. 32, Book Review 4)

Later year undergraduates, beginning graduate students, and researchers and graduate students in any discipline needing to explore and analyse time series data. This very readable text covers a wide range of time series topics, always however within a theoretical framework that makes normality assumptions. The range of models that are discussed is unusually wide for an introductory text. The mathematical theory is remarkably complete . This text is recommended for its wide-ranging and insightful coverage of time series theory and practice. (John H. Maindonald, International Statistical Review, Vol. 78 (3), 2010)

The authors present a textbook for students and applied researchers for time series analysis and linear regression analysis using R as the programming and command language. The book is written for students with knowledge of a first-year university statistics course in New-Zealand and Australia, but it also might serve as a useful tools for applied researchers interested in empirical procedures and applications which are not menu driven as it is the case for most econometric software packages nowadays. (Herbert S. Buscher, Zentralblatt MATH, Vol. 1179, 2010)

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
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
3 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
4 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
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
5 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
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
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
8 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
9 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
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
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 Daniell 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
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
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 Bivariate 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
Paul Cowpertwait is an associate professor in mathematical sciences (analytics) at Auckland University of Technology with a substantial research record in both the theory and applications of time series and stochastic models. Andrew Metcalfe is an associate professor in the School of Mathematical Sciences at the University of Adelaide, and an author of six statistics text books and numerous research papers. Both authors have extensive experience of teaching time series to students at all levels.
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