Nonlinear Time Series Analysis

510 Pages·2018·10.33 MB·English

by  Ruey S. Tsay

NONLINEAR TIME SERIES
ANALYSIS
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NONLINEAR TIME
SERIES ANALYSIS
Ruey S.Tsay
UniversityofChicago,Chicago,Illinois,UnitedStates
Rong Chen
Rutgers,TheStateUniversityofNewJersey,
NewJersey,UnitedStates
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LibraryofCongressCataloging-in-PublicationData
Names:Tsay,RueyS.,1951-author.|Chen,Rong,1963-author.
Title:Nonlineartimeseriesanalysis/byRueyS.TsayandRongChen.
Description:Hoboken,NJ:JohnWiley&Sons,2019.|Series:Wileyseriesin
probabilityandstatistics|Includesindex.|
Identifiers:LCCN2018009385(print)|LCCN2018031564(ebook)|
ISBN9781119264064(pdf)|ISBN9781119264071(epub)|ISBN9781119264057(cloth)
Subjects:LCSH:Time-seriesanalysis.|Nonlineartheories.
Classification:LCCQA280(ebook)|LCCQA280.T7332019(print)|DDC519.5/5–dc23
LCrecordavailableathttps://lccn.loc.gov/2018009385
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CONTENTS
Preface xiii
1 WhyShouldWeCareAboutNonlinearity? 1
1.1 SomeBasicConcepts 2
1.2 LinearTimeSeries 3
1.3 ExamplesofNonlinearTimeSeries 3
1.4 NonlinearityTests 20
1.4.1 NonparametricTests 21
1.4.2 ParametricTests 31
1.5 Exercises 38
References 39
2 UnivariateParametricNonlinearModels 41
2.1 AGeneralFormulation 41
2.1.1 ProbabilityStructure 42
vii
viii CONTENTS
2.2 ThresholdAutoregressiveModels 43
2.2.1 ATwo-regimeTARModel 44
2.2.2 PropertiesofTwo-regimeTAR(1)Models 45
2.2.3 Multiple-regimeTARModels 48
2.2.4 EstimationofTARModels 50
2.2.5 TARModeling 52
2.2.6 Examples 55
2.2.7 PredictionsofTARModels 62
2.3 MarkovSwitchingModels 63
2.3.1 PropertiesofMarkovSwitchingModels 66
2.3.2 StatisticalInferenceoftheStateVariable 66
2.3.3 EstimationofMarkovSwitchingModels 69
2.3.4 SelectingtheNumberofStates 75
2.3.5 PredictionofMarkovSwitchingModels 75
2.3.6 Examples 76
2.4 SmoothTransitionAutoregressiveModels 92
2.5 Time-varyingCoefficientModels 99
2.5.1 FunctionalCoefficientARModels 99
2.5.2 Time-varyingCoefficientARModels 104
2.6 Appendix:MarkovChains 111
2.7 Exercises 114
References 116
3 UnivariateNonparametricModels 119
3.1 KernelSmoothing 119
3.2 LocalConditionalMean 125
3.3 LocalPolynomialFitting 129
3.4 Splines 134
3.4.1 CubicandB-Splines 138
3.4.2 SmoothingSplines 141
3.5 WaveletSmoothing 145
3.5.1 Wavelets 145
3.5.2 TheWaveletTransform 147
3.5.3 ThresholdingandSmoothing 150
3.6 NonlinearAdditiveModels 158
CONTENTS ix
3.7 IndexModelandSlicedInverseRegression 164
3.8 Exercises 169
References 170
4 NeuralNetworks,DeepLearning,andTree-based
Methods 173
4.1 NeuralNetworks 173
4.1.1 EstimationorTrainingofNeuralNetworks 176
4.1.2 AnExample 179
4.2 DeepLearning 181
4.2.1 DeepBeliefNets 182
4.2.2 Demonstration 184
4.3 Tree-basedMethods 195
4.3.1 DecisionTrees 195
4.3.2 RandomForests 212
4.4 Exercises 214
References 215
5 AnalysisofNon-GaussianTimeSeries 217
5.1 GeneralizedLinearTimeSeriesModels 218
5.1.1 CountDataandGLARMAModels 220
5.2 AutoregressiveConditionalMeanModels 229
5.3 MartingalizedGARMAModels 232
5.4 VolatilityModels 234
5.5 FunctionalTimeSeries 245
5.5.1 ConvolutionFARmodels 248
5.5.2 EstimationofCFARModels 251
5.5.3 FittedValuesandApproximateResiduals 253
5.5.4 Prediction 253
5.5.5 AsymptoticProperties 254
5.5.6 Application 254
Appendix:DiscreteDistributionsforCountData 260
5.6 Exercises 261
References 263
x CONTENTS
6 StateSpaceModels 265
6.1 AGeneralModelandStatisticalInference 266
6.2 SelectedExamples 269
6.2.1 LinearTimeSeriesModels 269
6.2.2 TimeSeriesWithObservationalNoises 271
6.2.3 Time-varyingCoefficientModels 272
6.2.4 TargetTracking 273
6.2.5 SignalProcessinginCommunications 279
6.2.6 DynamicFactorModels 283
6.2.7 FunctionalandDistributionalTimeSeries 284
6.2.8 MarkovRegimeSwitchingModels 289
6.2.9 StochasticVolatilityModels 290
6.2.10 Non-GaussianTimeSeries 291
6.2.11 MixedFrequencyModels 291
6.2.12 OtherApplications 292
6.3 LinearGaussianStateSpaceModels 293
6.3.1 FilteringandtheKalmanFilter 293
6.3.2 Evaluatingthelikelihoodfunction 295
6.3.3 Smoothing 297
6.3.4 PredictionandMissingData 299
6.3.5 SequentialProcessing 300
6.3.6 ExamplesandRDemonstrations 300
6.4 Exercises 325
References 327
7 NonlinearStateSpaceModels 335
7.1 LinearandGaussianApproximations 335
7.1.1 KalmanFilterforLinearNon-Gaussian
Systems 336
7.1.2 ExtendedKalmanFiltersforNonlinear
Systems 336
7.1.3 GaussianSumFilters 338
7.1.4 TheUnscentedKalmanFilter 339
7.1.5 EnsembleKalmanFilters 341
7.1.6 ExamplesandRimplementations 342