Introduction to Time Series Analysis and Forecasting

671 Pages·2015·6.19 MB·English

by  Douglas C. Montgomery

Wiley Series in Probability and Statistics
Introduction to
TiMe SerieS
AnALySiS AnD
ForeCASTing
Second edition
Douglas C. Montgomery
Cheryl L. Jennings
Murat Kulahci

INTRODUCTION TO
TIME SERIES ANALYSIS
AND FORECASTING
WILEYSERIESINPROBABILITYANDSTATISTICS
EstablishedbyWALTERA.SHEWHARTandSAMUELS.WILKS
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Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume.
INTRODUCTION TO
TIME SERIES ANALYSIS
AND FORECASTING
Second Edition
DOUGLAS C. MONTGOMERY
ArizonaStateUniversity
Tempe,Arizona,USA
CHERYL L. JENNINGS
ArizonaStateUniversity
Tempe,Arizona,USA
MURAT KULAHCI
TechnicalUniversityofDenmark
Lyngby,Denmark
and
Lulea˚ UniversityofTechnology
Lulea˚,Sweden
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10 9 8 7 6 5 4 3 2 1
CONTENTS
PREFACE xi
1 INTRODUCTION TO FORECASTING 1
1.1 TheNatureandUsesofForecasts / 1
1.2 SomeExamplesofTimeSeries / 6
1.3 TheForecastingProcess / 13
1.4 DataforForecasting / 16
1.4.1 TheDataWarehouse / 16
1.4.2 DataCleaning / 18
1.4.3 Imputation / 18
1.5 ResourcesforForecasting / 19
Exercises / 20
2 STATISTICS BACKGROUND FOR FORECASTING 25
2.1 Introduction / 25
2.2 GraphicalDisplays / 26
2.2.1 TimeSeriesPlots / 26
2.2.2 PlottingSmoothedData / 30
2.3 NumericalDescriptionofTimeSeriesData / 33
2.3.1 StationaryTimeSeries / 33
v
vi CONTENTS
2.3.2 AutocovarianceandAutocorrelationFunctions / 36
2.3.3 TheVariogram / 42
2.4 UseofDataTransformationsandAdjustments / 46
2.4.1 Transformations / 46
2.4.2 TrendandSeasonalAdjustments / 48
2.5 GeneralApproachtoTimeSeriesModelingand
Forecasting / 61
2.6 EvaluatingandMonitoringForecastingModel
Performance / 64
2.6.1 ForecastingModelEvaluation / 64
2.6.2 ChoosingBetweenCompetingModels / 74
2.6.3 MonitoringaForecastingModel / 77
2.7 RCommandsforChapter2 / 84
Exercises / 96
3 REGRESSION ANALYSIS AND FORECASTING 107
3.1 Introduction / 107
3.2 LeastSquaresEstimationinLinearRegressionModels / 110
3.3 StatisticalInferenceinLinearRegression / 119
3.3.1 TestforSignificanceofRegression / 120
3.3.2 TestsonIndividualRegressionCoefficientsand
GroupsofCoefficients / 123
3.3.3 ConfidenceIntervalsonIndividualRegression
Coefficients / 130
3.3.4 ConfidenceIntervalsontheMeanResponse / 131
3.4 PredictionofNewObservations / 134
3.5 ModelAdequacyChecking / 136
3.5.1 ResidualPlots / 136
3.5.2 ScaledResidualsandPRESS / 139
3.5.3 MeasuresofLeverageandInfluence / 144
3.6 VariableSelectionMethodsinRegression / 146
3.7 GeneralizedandWeightedLeastSquares / 152
3.7.1 GeneralizedLeastSquares / 153
3.7.2 WeightedLeastSquares / 156
3.7.3 DiscountedLeastSquares / 161
3.8 RegressionModelsforGeneralTimeSeriesData / 177
CONTENTS vii
3.8.1 DetectingAutocorrelation:TheDurbin–Watson
Test / 178
3.8.2 EstimatingtheParametersinTimeSeries
RegressionModels / 184
3.9 EconometricModels / 205
3.10 RCommandsforChapter3 / 209
Exercises / 219
4 EXPONENTIAL SMOOTHING METHODS 233
4.1 Introduction / 233
4.2 First-OrderExponentialSmoothing / 239
4.2.1 TheInitialValue,ỹ / 241
0
4.2.2 TheValueof𝜆 / 241
4.3 ModelingTimeSeriesData / 245
4.4 Second-OrderExponentialSmoothing / 247
4.5 Higher-OrderExponentialSmoothing / 257
4.6 Forecasting / 259
4.6.1 ConstantProcess / 259
4.6.2 LinearTrendProcess / 264
4.6.3 Estimationof𝜎2 / 273
e
4.6.4 AdaptiveUpdatingoftheDiscountFactor / 274
4.6.5 ModelAssessment / 276
4.7 ExponentialSmoothingforSeasonalData / 277
4.7.1 AdditiveSeasonalModel / 277
4.7.2 MultiplicativeSeasonalModel / 280
4.8 ExponentialSmoothingofBiosurveillanceData / 286
4.9 ExponentialSmoothersandArimaModels / 299
4.10 RCommandsforChapter4 / 300
Exercises / 311
5 AUTOREGRESSIVE INTEGRATED MOVING
AVERAGE (ARIMA) MODELS 327
5.1 Introduction / 327
5.2 LinearModelsforStationaryTimeSeries / 328
5.2.1 Stationarity / 329
5.2.2 StationaryTimeSeries / 329
viii CONTENTS
5.3 FiniteOrderMovingAverageProcesses / 333
5.3.1 TheFirst-OrderMovingAverageProcess,
MA(1) / 334
5.3.2 TheSecond-OrderMovingAverageProcess,
MA(2) / 336
5.4 FiniteOrderAutoregressiveProcesses / 337
5.4.1 First-OrderAutoregressiveProcess,AR(1) / 338
5.4.2 Second-OrderAutoregressiveProcess,AR(2) / 341
5.4.3 GeneralAutoregressiveProcess,AR(p) / 346
5.4.4 PartialAutocorrelationFunction,PACF / 348
5.5 MixedAutoregressive–MovingAverageProcesses / 354
5.5.1 StationarityofARMA(p,q)Process / 355
5.5.2 InvertibilityofARMA(p,q)Process / 355
5.5.3 ACFandPACFofARMA(p,q)Process / 356
5.6 NonstationaryProcesses / 363
5.6.1 SomeExamplesofARIMA(p,d,q)Processes / 363
5.7 TimeSeriesModelBuilding / 367
5.7.1 ModelIdentification / 367
5.7.2 ParameterEstimation / 368
5.7.3 DiagnosticChecking / 368
5.7.4 ExamplesofBuildingARIMAModels / 369
5.8 ForecastingArimaProcesses / 378
5.9 SeasonalProcesses / 383
5.10 ArimaModelingofBiosurveillanceData / 393
5.11 FinalComments / 399
5.12 RCommandsforChapter5 / 401
Exercises / 412
6 TRANSFER FUNCTIONS AND INTERVENTION
MODELS 427
6.1 Introduction / 427
6.2 TransferFunctionModels / 428
6.3 TransferFunction–NoiseModels / 436
6.4 Cross-CorrelationFunction / 436
6.5 ModelSpecification / 438
6.6 ForecastingwithTransferFunction–NoiseModels / 456