Introductory Time Series with R

✍ Scribed by Cowpertwait, Paul S P;Metcalfe, Andrew V

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 262
• Series: Use R
• Category: Library

✦ Synopsis

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. . . . . . . . . . . . . . . . . . . . . . . . .

✦ Table of Contents

Preface......Page 6
Contents......Page 8
Purpose......Page 15
Time series......Page 16
R language......Page 17
A flying start: Air passenger bookings......Page 18
Unemployment: Maine......Page 21
Multiple time series: Electricity, beer and chocolate data......Page 24
Quarterly exchange rate: GBP to NZ dollar......Page 28
Global temperature series......Page 30
Models......Page 33
Estimating trends and seasonal effects......Page 34
Smoothing......Page 35
Decomposition in R......Page 36
Exercises......Page 38
Expected value......Page 40
The ensemble and stationarity......Page 43
Ergodic series......Page 44
Variance function......Page 45
Autocorrelation......Page 46
General discussion......Page 48
Example based on air passenger series......Page 50
Example based on the Font Reservoir series......Page 53
Covariance of sums of random variables......Page 54
Exercises......Page 55
Marine coatings......Page 57
Building approvals publication......Page 58
Gas supply......Page 61
Interpretation of the Bass model......Page 63
Example......Page 64
Exponential smoothing......Page 67
Holt-Winters method......Page 71
Four-year-ahead forecasts for the air passenger data......Page 74
Exercises......Page 76
Purpose......Page 79
Simulation in R......Page 80
Second-order properties and the correlogram......Page 81
Fitting a white noise model......Page 82
The backward shift operator......Page 83
The difference operator......Page 84
Simulation......Page 85
Simulated random walk series......Page 86
Exchange rate series......Page 87
Random walk with drift......Page 89
Stationary and non-stationary AR processes......Page 91
Derivation of second-order properties for an AR(1) process......Page 92
Simulation......Page 93
Model fitted to simulated series......Page 94
Exchange rate series: Fitted AR model......Page 96
Global temperature series: Fitted AR model......Page 97
Exercises......Page 99
Purpose......Page 102
Definition......Page 103
Simulation......Page 104
Model fitted to simulated data......Page 105
Model fitted to the temperature series (1970--2005)......Page 106
Autocorrelation and the estimation of sample statistics......Page 107
GLS fit to simulated series......Page 109
Additive seasonal indicator variables......Page 110
Example: Seasonal model for the temperature series......Page 111
Harmonic seasonal models......Page 112
Simulation......Page 113
Fit to simulated series......Page 114
Harmonic model fitted to temperature series (1970--2005)......Page 116
Example using the air passenger series......Page 120
Example of a simulated and fitted non-linear series......Page 124
Log-normal residual errors......Page 126
Example using the air passenger data......Page 128
Exercises......Page 129
Strictly stationary series......Page 132
MA(q) process: Definition and properties......Page 133
R examples: Correlogram and simulation......Page 134
Model fitted to simulated series......Page 135
Exchange rate series: Fitted MA model......Page 137
Definition......Page 138
Derivation of second-order properties......Page 139
Exchange rate series......Page 140
Electricity production series......Page 141
Wave tank data......Page 144
Exercises......Page 146
Differencing and the electricity series......Page 148
Integrated model......Page 149
Definition and examples......Page 150
Simulation and fitting......Page 151
IMA(1, 1) model fitted to the beer production series......Page 152
Definition......Page 153
Fitting procedure......Page 154
S&P500 series......Page 156
Modelling volatility: Definition of the ARCH model......Page 158
Extensions and GARCH models......Page 159
Simulation and fitted GARCH model......Page 160
Fit to S&P500 series......Page 161
Volatility in climate series......Page 163
Exercises......Page 166
Fractional differencing......Page 169
Fitting to simulated data......Page 171
Nile minima......Page 174
Bellcore Ethernet data......Page 175
Bank loan rate......Page 176
Simulation......Page 177
Exercises......Page 178
Sine waves......Page 181
Unit of measurement of frequency......Page 182
Fitting sine waves......Page 183
White noise......Page 185
AR(1): Positive coefficient......Page 187
AR(2)......Page 188
Sampling interval and record length......Page 189
Record length......Page 191
Fault detection on electric motors......Page 193
Measurement of vibration dose......Page 194
Climatic indices......Page 197
Bank loan rate......Page 199
Discrete Fourier transform (DFT)......Page 200
The spectrum of a random process......Page 202
Derivation of spectrum......Page 203
Leakage......Page 204
Confidence intervals......Page 205
Padding......Page 206
Summary of additional commands used......Page 207
Exercises......Page 208
Linear system......Page 210
Estimator of the gain function......Page 211
Simulated single mode of vibration system......Page 212
Ocean-going tugboat......Page 214
Non-linearity......Page 216
Exercises......Page 217
Spurious regression......Page 219
Tests for unit roots......Page 222
Definition......Page 224
Exchange rate series......Page 226
Bivariate and multivariate white noise......Page 227
Vector autoregressive models......Page 228
VAR model fitted to US economic series......Page 230
Exercises......Page 235
Purpose......Page 237
Dynamic linear model......Page 238
Filtering......Page 239
Prediction......Page 240
Smoothing......Page 241
Random walk plus noise model......Page 242
Regression model with time-varying coefficients......Page 244
Fitting to univariate time series......Page 246
Bivariate time series -- river salinity......Page 247
Estimating the variance matrices......Page 250
Discussion......Page 251
Exercises......Page 252
References......Page 255
Index......Page 257

✦ Subjects

Computer Science;Programming;Science;Mathematics;Nonfiction;Reference