Time Series Analysis: Forecasting and Control

709 Pages·2015·13.5 MB·English

by  Gwilym M. Jenkins

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TIME SERIES ANALYSIS
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TIME SERIES ANALYSIS
Forecasting and Control
Fifth Edition
GEORGEE.P.BOX
GWILYMM.JENKINS
GREGORYC.REINSEL
GRETAM.LJUNG
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LibraryofCongressCataloging-in-PublicationData:
Box,GeorgeE.P.
Timeseriesanalysis:forecastingandcontrol.--Fifthedition/GeorgeE.P.Box,GwilymM.Jenkins,
GregoryC.Reinsel,GretaM.Ljung.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-67502-1(cloth:alk.paper) 1. Time-seriesanalysis. 2. Predictiontheory. 3. Transfer
functions. 4. Feedbackcontrolsystems--Mathematicalmodels.I.Jenkins,GwilymM.II.Reinsel,GregoryC.
III.Ljung,GretaM.,1941-IV.Title.
QA280.B672016
519.5’5--dc23
2015015492
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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Tothememoryof
GeorgeE.P.Box GwilymM.Jenkins GregoryC.Reinsel
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CONTENTS
PREFACETOTHEFIFTHEDITION xix
PREFACETOTHEFOURTHEDITION xxiii
PREFACETOTHETHIRDEDITION xxv
1 Introduction 1
1.1 FiveImportantPracticalProblems, 2
1.1.1 ForecastingTimeSeries, 2
1.1.2 EstimationofTransferFunctions, 3
1.1.3 AnalysisofEffectsofUnusualInterventionEventstoaSystem, 4
1.1.4 AnalysisofMultivariateTimeSeries, 4
1.1.5 DiscreteControlSystems, 5
1.2 StochasticandDeterministicDynamicMathematicalModels, 6
1.2.1 Stationary and Nonstationary Stochastic Models for Forecasting
andControl, 7
1.2.2 TransferFunctionModels, 11
1.2.3 ModelsforDiscreteControlSystems, 13
1.3 BasicIdeasinModelBuilding, 14
1.3.1 Parsimony, 14
1.3.2 IterativeStagesintheSelectionofaModel, 15
AppendixA1.1 UseoftheRSoftware, 17
Exercises, 18
vii
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viii CONTENTS
PARTONE STOCHASTICMODELSANDTHEIRFORECASTING 19
2 AutocorrelationFunctionandSpectrumofStationaryProcesses 21
2.1 AutocorrelationPropertiesofStationaryModels, 21
2.1.1 TimeSeriesandStochasticProcesses, 21
2.1.2 StationaryStochasticProcesses, 24
2.1.3 PositiveDefinitenessandtheAutocovarianceMatrix, 26
2.1.4 AutocovarianceandAutocorrelationFunctions, 29
2.1.5 EstimationofAutocovarianceandAutocorrelationFunctions, 30
2.1.6 StandardErrorsofAutocorrelationEstimates, 31
2.2 SpectralPropertiesofStationaryModels, 34
2.2.1 PeriodogramofaTimeSeries, 34
2.2.2 AnalysisofVariance, 35
2.2.3 SpectrumandSpectralDensityFunction, 36
2.2.4 SimpleExamplesofAutocorrelationandSpectralDensity
Functions, 40
2.2.5 AdvantagesandDisadvantagesoftheAutocorrelationandSpectral
DensityFunctions, 43
Appendix A2.1 Link Between the Sample Spectrum and Autocovariance
FunctionEstimate, 43
Exercises, 44
3 LinearStationaryModels 47
3.1 GeneralLinearProcess, 47
3.1.1 TwoEquivalentFormsfortheLinearProcess, 47
3.1.2 AutocovarianceGeneratingFunctionofaLinearProcess, 50
3.1.3 StationarityandInvertibilityConditionsforaLinearProcess, 51
3.1.4 AutoregressiveandMovingAverageProcesses, 52
3.2 AutoregressiveProcesses, 54
3.2.1 StationarityConditionsforAutoregressiveProcesses, 54
3.2.2 AutocorrelationFunctionandSpectrumofAutoregressive
Processes, 56
3.2.3 TheFirst-OrderAutoregressiveProcess, 58
3.2.4 Second-OrderAutoregressiveProcess, 59
3.2.5 PartialAutocorrelationFunction, 64
3.2.6 EstimationofthePartialAutocorrelationFunction, 66
3.2.7 StandardErrorsofPartialAutocorrelationEstimates, 66
3.2.8 CalculationsinR, 67
3.3 MovingAverageProcesses, 68
3.3.1 InvertibilityConditionsforMovingAverageProcesses, 68
3.3.2 AutocorrelationFunctionandSpectrumofMovingAverage
Processes, 69
3.3.3 First-OrderMovingAverageProcess, 70
3.3.4 Second-OrderMovingAverageProcess, 71
3.3.5 DualityBetweenAutoregressiveandMovingAverageProcesses, 75
3.4 MixedAutoregressive--MovingAverageProcesses, 75