Time Series Analysis: Methods and Applications - Department of

777 Pages·2012·10.89 MB·English

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HANDBOOKOFSTATISTICS
VOLUME30
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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
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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
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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
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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
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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
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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
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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