时间序列分析课件

时间序列分析WhatIsTime-SeriesAQuantitativeForecastingMethodtoPredictFutureValuesNumericalDataObtainedatRegularTimeIntervalsProjectionsBasedonPastandPresentObservationsExample:

Year: 1994 1995 1996 1997 1998Sales: 75.3 74.2 78.5 79.7 80.2Time-SeriesComponents

时间序列的组成Time-SeriesCyclicalRandomTrendSeasonalTrendComponent

趋势项OverallUpwardorDownwardMovementDataTakenOveraPeriodofYearsSalesTimeUpwardtrendCyclicalComponent

周期项UpwardorDownwardSwingsMayVaryinLengthUsuallyLasts2-10YearsSalesTimeCycleSeasonalComponent

季节项UpwardorDownwardSwingsRegularPatternsObservedWithin1YearSalesTime(MonthlyorQuarterly)WinterRandomorIrregularComponent

随机项Erratic,Nonsystematic,Random,慠esidual?FluctuationsDuetoRandomVariationsofNatureAccidentsShortDurationandNon-repeating

Multiplicative Time-SeriesModel

相乘时间序列模型UsedPrimarilyforForecastingObservedValueinTimeSeriesistheproduct ofComponentsForAnnualData:ForQuarterlyorMonthlyData:Ti

=TrendCi

=CyclicalIi

=IrregularSi

=SeasonalMovingAverages

移动平均UsedforSmoothingSeriesofArithmeticMeansOverTimeResultDependentUponChoiceofL,LengthofPeriodforComputingMeansForAnnualTime-Series,LShouldbeOddExample:3-yearMovingAverageFirstAverage:SecondAverage:MovingAverageExampleYear Units Moving Ave1994 2NA1995 5

3

1996 2

31997 2

3.671998 75

1999 6NAJohnisabuildingcontractorwitharecordofatotalof24singlefamilyhomesconstructedovera6yearperiod.ProvideJohnwithaMovingAverageGraph.MovingAverageExampleSolutionYear ResponseMoving Ave1994 2

NA1995 5

3

1996 2

31997 2

3.671998 7

5

1999 6

NA94959697989986420SalesExponentialSmoothing

指数平滑WeightedMovingAverageWeightsDeclineExponentiallyMostRecentObservationWeightedMostUsedforSmoothingandShortTermForecastingWeightsAre:SubjectivelyChosenRangesfrom0to1Closeto0forSmoothingCloseto1forForecastingExponentialWeight:ExampleYear ResponseSmoothingValue

Forecast

(W=.2)

1994 2

2

NA1995 5

(.2)(5)+(.8)(2)=2.6

2

1996 2

(.2)(2)+(.8)(2.6)=2.482.61997 2

(.2)(2)+(.8)(2.48)=2.3842.481998 7

(.2)(7)+(.8)(2.384)=3.3072.384 1999 6

(.2)(6)+(.8)(3.307)=3.846

3.307ExponentialWeight:ExampleGraph94959697989986420SalesYearDataSmoothedTheLinearTrendModelYearCodedSales94 0295 1596 2297 3298 4799 56Projectedtoyear2000ExcelOutputTheQuadraticTrendModel

二次趋势模型ExcelOutputYearCodedSales94 0295 1596 2297 3298 4799 56TheExponentialTrendModel

指数趋势模型orExcelOutputofValuesinlogsYearCodedSales94 0295 1596 2297 3298 4799 56AutogregressiveModeling

自回归建模UsedforForecastingTakesAdvantageofAutocorrelation1storder-correlationbetweenconsecutive values2ndorder-correlationbetweenvalues2 periodsapartAutoregressiveModelfor

pthorder:RandomErrorAutoregressiveModel:ExampleTheOfficeConceptCorp.hasacquiredanumberofofficeunits(inthousandsofsquarefeet)overthelast8years.Developthe2ndorderAutoregressivemodels.YearUnits

924 93 3 942 95396 297 298 4

996AutoregressiveModel:

ExampleSolutionYear

Yi

Yi-1

Yi-2

92 4 ---

---

93 3 4

---942 3

4953 2

39623

297 22

398 42

299 64

2ExcelOutputDevelopthe2ndorder tableUseExceltoruna regressionmodelAutoregressiveModelExample:ForecastingUsethe2ndordermodeltoforecastnumberofunitsfor2000:AutoregressiveModelingSteps

自回归建模步骤1.Choosep:Notethatdf=n-2p-12.Formaseriesof搇agpredictor?variables

Yi-1,Yi-2

,?Yi-p3.UseExceltorunregressionmodelusingallpvariables4.Testsignificanceof

ApIfnullhypothesisrejected,thismodelisselectedIfnullhypothesisnotrejected,decreasepby1andrepeatSelectingAForecastingModel

筛选预测模型PerformAResidualAnalysisLookforpatternordirectionMeasureSumSquareErrors-SSE(residualerrors)MeasureResidualErrorsUsingMADUseSimplestModelPrincipleofParsimonyResidualAnalysis

残差分析RandomerrorsTrendnotaccountedforCyclicaleffectsnotaccountedforSeasonaleffectsnotaccountedforTTTTeeee0000MeasuringErrorsSumSquareError(SSE)MeanAbsoluteDeviation(MAD)PrincipalofParsimonySuppose2ormoremodelsprovidegoodfitfordataSelecttheSimplestModelSimplestmodeltypes:least-squareslinearleast-squarequadratic1storderautoregressiveMorecomplextypes:2ndand3rdorderautoreg