Introductory Time Series with R (Use R!)

by Andrew V. Metcalfe (Contributor), Paul S.P. Cowpertwait (Author)

• New

  Illustrated
  2009

  $57.73

  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 ...16 1. 5 Decompositionofseries ...19 1. 5. 1 Notation...19 1. 5. 2 Models...1 9 1. 5. 3 Estimatingtrendsandseasonale?ects ...20 1. 5. 4 Smoothing ...21 1. 5. 5 DecompositioninR...22 1. 6 Summaryofcommandsusedinexamples...24 1. 7 Exercises...24 2 Correlation...27 2. 1 Purpose...27 2. 2 Expectationandtheensemble...