Time Series Analysis: Methods and Applications - Department of PDF
Preview Time Series Analysis: Methods and Applications - Department of
DULOV 06-ch02-009-018-9780123877796 2011/5/27 10:40 Page 19 #11 Thispageintentionallyleftblank Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 01-fm-i-iv-9780444538581 2012/4/24 0:34 Page 1 #1 HANDBOOKOFSTATISTICS VOLUME30 Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 01-fm-i-iv-9780444538581 2012/4/24 0:34 Page 2 #2 Handbook of Statistics VOLUME 30 GeneralEditor C.R. Rao C.R.RaoAIMSCS,UniversityofHyderabadCampus,Hyderabad,India Amsterdam•Boston•Heidelberg•London•NewYork•Oxford Paris•SanDiego•SanFrancisco•Singapore•Sydney•Tokyo Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 01-fm-i-iv-9780444538581 2012/4/24 0:34 Page 3 #3 Volume 30 Time Series Analysis: Methods and Applications Editedby Tata Subba Rao UniversityofManchester,UK Suhasini Subba Rao TexasA&MUniversity,CollegeStation,Texas,USA C.R. Rao C.R.RaoAIMSCS,UniversityofHyderabadCampus,Hyderabad,India Amsterdam•Boston•Heidelberg•London•NewYork•Oxford Paris•SanDiego•SanFrancisco•Singapore•Sydney•Tokyo North-HollandisanimprintofElsevier Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 01-fm-i-iv-9780444538581 2012/4/24 0:34 Page 4 #4 North-HollandisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,Oxford,OX51GB,UK Radarweg29,POBox211,1000AEAmsterdam,TheNetherlands Firstedition2012 Copyright(cid:13)c 2012ElsevierB.V.Allrightsreserved. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeanselectronic,mechanical,photocopying, recordingorotherwisewithoutthepriorwrittenpermissionofthepublisher. PermissionsmaybesoughtdirectlyfromElsevier’sScience&TechnologyRights DepartmentinOxford,UK:phone(+44)(0)1865843830;fax(+44)(0)1865853333; email:permissions@elsevier.com.Alternativelyyoucansubmityourrequestonlineby visitingtheElsevierwebsiteathttp://elsevier.com/locate/permissions,andselecting ObtainingpermissiontouseElseviermaterial. Notice Noresponsibilityisassumedbythepublisherforanyinjuryand/ordamagetopersons orpropertyasamatterofproductsliability,negligenceorotherwise,orfromanyuse oroperationofanymethods,products,instructionsorideascontainedinthematerial herein.Becauseofrapidadvancesinthemedicalsciences,inparticular,independent verificationofdiagnosesanddrugdosagesshouldbemade. BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress. ISBN:978-0-444-53858-1 ISSN:0169-7161 ForinformationonallNorth-Hollandpublications visitourwebsiteatstore.elsevier.com Typesetby:diacriTech,India PrintedandboundinGreatBritain 12 13 14 15 10 9 8 7 6 5 4 3 2 1 Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 02-toc-v-xii-9780444538581 2012/4/24 0:35 Page v #1 Table of Contents Volume30 TimeSeries PrefacetoHandbook–30 xiii Contributors:Vol.30 xvii Part I. BootstrapandTestsforLinearityofaTimeSeries 1 Ch.1. BootstrapMethodsforTimeSeries 3 Jens-PeterKreissandSoumendraNathLahiri 1. Introduction 3 2. Residualbootstrapforparametricandnonparametricmodels 6 3. Autoregressive-sievebootstrap 9 4. BootstrapforMarkovchains 11 5. Blockbootstrapmethods 13 6. Frequencydomainbootstrapmethods 16 7. Mixtureoftwobootstrapmethods 17 8. Bootstrapunderlong-rangedependence 21 Acknowledgment 23 References 23 Ch.2. TestingTimeSeriesLinearity:TraditionalandBootstrap Methods 27 ArthurBerg,TimothyMcMurryandDimitrisN.Politis 1. Introduction 27 2. AbriefsurveyoflinearityandGaussianitytests 28 3. Linearandnonlineartimeseries 30 4. AR-sievebootstraptestsoflinearity 33 5. Subsamplingtestsoflinearity 35 References 40 v Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 02-toc-v-xii-9780444538581 2012/4/24 0:35 Page vi #2 vi TableofContents Ch.3. TheQuestforNonlinearityinTimeSeries 43 SimoneGiannerini 1. Introduction 43 2. Definingalinearprocess 45 3. Testingfornonlinearity 48 4. Conclusions 59 Acknowledgments 60 References 60 Part II. NonlinearTimeSeries 65 Ch.4. ModellingNonlinearandNonstationaryTimeSeries 67 DagTjøstheim 1. Introduction 67 2. Nonlinearstationarymodels 68 3. Linearnonstationarity 75 4. Nonlinearandnonstationaryprocesses 79 5. Time-varyingparametersandstate-spacemodels 90 References 93 Ch.5. MarkovSwitchingTimeSeriesModels 99 Ju¨rgenFranke 1. Introduction 99 2. Markovswitchingautoregressions 101 3. OtherMarkovswitchingtimeseriesmodels 117 4. Markovswitchingincontinuoustime 118 Acknowledgments 119 References 120 Ch.6. AReviewofRobustEstimationunderConditional Heteroscedasticity 123 KanchanMukherjee 1. Introduction 123 2. GARCH(p,q)andGJR(1,1)models 125 3. DataanalysisfortheGARCHandGJRmodels 131 4. ValueatriskandM-tests 134 5. DataanalysisbasedonVaR 137 6. NonlinearAR–ARCHmodel 142 7. DataanalysisfortheAR–ARCHmodel 150 8. Conclusions 153 Acknowledgments 153 References 153 Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 02-toc-v-xii-9780444538581 2012/4/24 0:35 Page vii #3 TableofContents vii Part III. HighDimensionalTimeSeries 155 Ch.7. FunctionalTimeSeries 157 SiegfriedHo¨rmannandPiotrKokoszka 1. Introduction 157 2. TheHilbertspacemodelforfunctionaldata 160 3. Functionalautoregressivemodel 166 4. Weaklydependentfunctionaltimeseries 175 5. Furtherreading 184 Acknowledgments 184 References 185 Ch.8. CovarianceMatrixEstimationinTimeSeries 187 WeiBiaoWuandHanXiao 1. Introduction 187 2. Asymptoticsofsamplecovariances 189 3. Low-dimensionalcovariancematrixestimation 193 4. High-dimensionalcovariancematrixestimation 200 Acknowledgments 206 References 206 Part IV. TimeSeriesandQuantileRegression 211 Ch.9. TimeSeriesQuantileRegressions 213 ZhijieXiao 1. Anintroductiontoquantileregression 213 2. Quantileregressionforautoregressivetimeseries 215 3. QuantileregressionforARCHandGARCHmodels 224 4. Quantileregressionswithdependenterrors 229 5. NonparametricandsemiparametricQRmodels 231 6. Otherdynamicquantilemodels 237 7. Extremalquantileregressions 240 8. Quantileregressionfornonstationarytimeseries 242 9. Timeseriesquantileregressionapplications 247 10.Conclusion 255 Acknowledgment 255 References 255 Part V. BiostatisticalApplications 259 Ch.10.FrequencyDomainTechniquesintheAnalysis ofDNASequences 261 DavidS.Stoffer 1. Introduction 261 2. Thespectralenvelope 267 Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 02-toc-v-xii-9780444538581 2012/4/24 0:35 Page viii #4 viii TableofContents 3. Localspectralenvelope 274 4. Detectionofgenomicdifferences 283 Appendix:Principalcomponentandcanonicalcorrelationanalysis fortimeseries 289 Acknowledgment 293 References 293 Ch.11.SpatialTimeSeriesModelingforfMRIDataAnalysis inNeurosciences 297 TohruOzaki 1. Introduction 297 2. Atraditionalapproach:Spatialandtemporalcovariancefunctions 298 3. SPMandtheimplieddeterminism 299 4. InnovationapproachandtheNN-ARXmodel 302 5. Likelihoodandthesignificanceoftheassumptions 304 6. Applicationstoconnectivitystudyandbrainmapping 310 7. Concludingremarks 311 Acknowledgement 312 References 312 Ch.12.CountTimeSeriesModels 315 KonstantinosFokianos 1. Introduction 315 2. Poissonregressionmodeling 317 3. Poissonregressionmodelsforcounttimeseries 319 4. Otherregressionmodelsforcounttimeseries 334 5. Integerautoregressivemodels 337 6. Conclusions 343 Appendix 343 Acknowledgments 344 References 344 Part VI. NonstationaryTimeSeries 349 Ch.13.LocallyStationaryProcesses 351 RainerDahlhaus 1. Introduction 351 2. Timevaryingautoregressiveprocesses–Adeepexample 353 3. Locallikelihoods,derivativeprocesses,andnonlinearmodelswithtime varyingparameters 367 4. Ageneraldefinition,linearprocessesandtimevaryingspectraldensities 379 Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusiness useonlybytheauthor(s),editor(s),reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonline orinprint.Thisproofcopyisthecopyrightpropertyofthepublisherandisconfidentialuntilformalpublication. RAO 02-toc-v-xii-9780444538581 2012/4/24 0:35 Page ix #5 TableofContents ix 5. Gaussianlikelihoodtheoryforlocallystationaryprocesses 387 6. Empiricalspectralprocesses 393 7. Additionaltopicsandfurtherreferences 402 Acknowledgment 408 References 408 Ch.14.AnalysisofMultivariateNonstationaryTimeSeriesUsing theLocalizedFourierLibrary 415 HernandoOmbao 1. Introduction 415 2. OverviewofSLEXanalysis 419 3. SelectingthebestSLEXsignalrepresentation 424 4. Classificationanddiscriminationoftimeseries 432 5. Summary 442 Acknowledgments 442 References 442 Ch.15.AnAlternativePerspectiveonStochasticCoefficientRegression Models 445 SuhasiniSubbaRao 1. Introduction 446 2. Thestochasticcoefficientregressionmodel 447 3. Theestimators 450 4. TestingforrandomnessofthecoefficientsintheSCRmodel 453 5. Asymptoticpropertiesoftheestimators 456 6. Realdataanalysis 465 Acknowledgments 473 References 473 Part VII. Spatio-TemporalTimeSeries 475 Ch.16.HierarchicalBayesianModelsforSpace–TimeAirPollution Data 477 SujitK.Sahu 1. Introduction 477 2. Hierarchicalmodels 479 3. Predictiondetails 484 4. Anexample 485 5. Furtherdiscussion 492 Acknowledgment 492 Appendix:ConditionaldistributionsforGibbssampling 492 References 494
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