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8/7/2019 Brief Introduction to Stata 10 Time Analysis
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8/7/2019 Brief Introduction to Stata 10 Time Analysis
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IntheTimeunitanddisplayformatforthetimevariable sectionselecttheformatofthedata,whichinourcasewouldbeYearly.ThenclickeitherSubmitorOKbuttontocompletethecommand.
Thiswholeprocesscanalsobeperformedusingthecommandinterface.Writetssetyear,yearlyinthe
commandwindowforthepresentcase.Ifforexample,indatathetimevariableisdefinedastimeand
the format is monthly, then all one need to write in the command window is tsset time, monthly
Similarlyhaditbeaquarterlydatarequiredtowritetssettime,quarterly.Thefollowingoutputwillbe
displayed:
.tssetyear,yearly
timevariable:year,1981to2004
delta:1year
Timeseriesplotofvariables
Thefirstthingoneshoulddointimeseriesanalysisisgetaviewofthetimeseriesplotofallthevariables
intheanalysis.ToseeaplotofavariablegotoGraphics>>Time-seriesgraphs>>Lineplots.Forthetime
beingconcentrateonlyonthePlotstabonthepopped-upcommandwindow.ClickontheCreatebutton
toseeanotherpopped-upcommandwindow.IntheMaintabselecttheTime-seriesplotintheChoosea
plotcategoryandtypesectionandintheSelecttypedrop-downmenuselectLine.IntheYvariabledrop-
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downmenuselectthevariabletoplotagainsttime.Forexampleselecttheconvariableinourdata
andthenselectthe Submitbutton.Itmaytakefewsecondstoviewtheplotofthevariable.Theplotof
theconvariableinourcaselookslikethefollowing:
Figure:Lineplot
Thisgraph can alsobegenerated usingthe command interface bywriting twoway(tsline con)inthe
command window. One can either select Scatter in the Select type drop-down menu or use the
command interface and write twoway (tsline con, recast(scatter)). The command for line connected
scatterplotistwoway(tslinecon,recast(connected)).
Figure:Scatterplot Figure:Lineconnectedscatterplot
Similargraphsofothervariablescanalsobegeneratedusingthesamecommand.Forexample,forthe
variablergdppcusethecommandof twoway(tsline rgdppc)forlineplotor twoway(tsline rgdppc,
recast(connected))forlineconnectedscatterplot.SavethegraphsusingtheSavegraphbuttononthegraphwindowinthedesiredfolder.
Unit-roottestingforsinglevariable
Mostofthetimeseriesvariablesarenon-stationary.Tocheckfortheunit-rootinthevariablesthereare
manyalternatives.However,themostrecommendedmethodsaretheAugmentedDickey-Fuller(ADF
testandthePhillips-Perron(P-P)test.ToperformtheADFtestgotoStatistics>>Timeseries>>Tests>>
AugmentedDickey-Fullerunit-roottest.IntheMaintabofthepopped-upwindowselectthevariableto
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testfromthedrop-downmenuof Variable.InthesectionofOptionscheckthedesiredboxestohavein
the test.For example, ina single variableunit-root testing the box ofSuppress constant term in the
regressionshouldnotbechecked.Ontheotherhand,theinclusionoftrendand/ordriftterminthe
regressiondependsonthenatureoftheplotofthevariable.Selectthenumberoflagstoincludethe
testfromtheLaggeddifferencestab.Therearenocertainrulestoselectthenumberoflags.OnecanuseAkaike'sinformationcriterion(AIC)orSchwarzBayesianinformationcriteriontodeterminethenumber
oflags.ThereisaruleofthumbthatmanyEconometriciansuseindetermininglags,whichstatesthatif
thedataisyearlythenuseonlyonelag;ifthedataisquarterly,thenuseatleast4lags,andsimilarlyi
thedataismonthly,useupto12lags.Inthisguidetestforunit-rootinthevariableofcon,onelaghas
beenused.Theoutputintheresultwindowlookslikethefollowing:
Wecanaccomplishthesametaskusingthecommandwindow byusing the commandofdfuller con
regresslags(1),whichismucheasiertouse.
TodothePhillips-Perron(P-P)testgotoStatistics>>Timeseries>>Tests>>Phillips-Perronunitroots
test.IntheMaintabselectconintheVariable:drop-downmenuandselectthe defaultlagsoption
andthenpressthesubmitbutton.Insteadofthisusethecommandofpperroncontodothesamething
Theresultwouldlooklikethefollowing:
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Usingthestepsdescribedonecandotheunit-roottestforallthevariablesinthemodelofanalysis.One
pointshouldbenotedisthattheplotofavariablegivesacluewhethertoincludeatrendintotheunit-
roottest.Forexample,theplotofrealGDPpercapitaisgivenbelow.
Theplotclearlyshowsthatthevariablehasabuilt-intrend.So,oneshouldincludethetrendintothe
test.Inourdataforthevariablergdppc,theoptimaltestresultcomesupwithatrendandwith4lags
intotheADFtest.Thecommandforthetestisdfullerrgdppc,trendregresslags(4).FortheP-Ptestthe
commandispperronrgdppc,trend.
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TheresultsshowthatthefirstdifferenceofconisstationaryastheADFteststatistic(-3.093)isgreate
thanthe5%criticalvalue(-3.000)inabsolutetermsand/ortheMackinnonp-valueoftheP-Pstatisticis
approximatelyzero.Similarly,usethesamemethodtoshowthatalltheothervariablesarestationaryin
thefirstdifferencedform.So,thevariablesareintegratedoforderone {I(1)}.Remembertoincludea
trendtermintotheunit-roottestofthedrgdppcvariable.
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Testingforcointegrationin{I(1)}variables:ErrorCorrectionModel(ECM)
Using the data one can estimate a linear demand function of cigarettes. In estimating the demand
functionwithtimeseriesdata,theestimationmethodologyisverycrucial(seeforinstanceHarris,1995)
Themajorconcernwiththetimeseriesisthatifnon-stationarityofdataseriespersiststhenitmayleadtospuriousrelationship.Toavoidthisproblem,itisnecessarytousethecointegrationmethodology.The
regressionequationcanbeestimatedfortheperiodof1981to2004usingtheEngel-Granger(E-G)two-
step procedure (Engel and Granger, 1987). The first step is to estimate a long-run equation using
ordinaryleastsquares(OLS)withvariables,whichareintegratedoforderone, I(1),intheirlevels.In
ordertoavoidspuriousregression,residualbasedcointegrationtestcanbeused,wherethestationarity
oftheresidualimpliesaconintegratingrelationshipamongthevariablesinthelongrunequation.The
secondstepoftheE-Gprocedureistoestimatethecorrespondingerror-correctionmodel(ECM),based
onthelongruncointegratingrelationshiptoobservetheshortrundynamics(EngelandGranger,1987).
OnecanestimateanECMusingtheresidualfromthelong-runequation.TheECMisbasedonstationary
data(asalltheI(1)regressorsareinfirstdifferenceform)andincludesthelaggedresidualsofthelongrunequation,whichisalsoI(0)whenthevariableshavecointegratingrelationship.Onethingyoushould
know is that the dummy variables are not continuous. As a result, you need not worry about the
stationarityofthedummyvariables.Thetwodummyvariablesfortheyearof1993and1995arehereto
controlfortheunusualtroughandspikesrespectivelyintheconsumptiondata.
ThefirststepoftheE-GistorunanOLSregressiononthevariablesintheirlevels.Thecommandforthe
regressionisregconrelprcrgdppcdum93dum95.
Togettheresidualfromthisregressionwecanusethecommandof predictresid,r,whereresidisthe
variablenameofthepredictedresidual.Theunit-rootoftheresidualcanbetestedbyADFand/orP-P
test.However,onemustrememberthatinthiscaseyouhavetocheckforthenoconstantterminthe
regressionoptionandthecriticalvaluesshouldbecalculatedusingtheMacKinnonsresponsesurface
analysistable(Mackinnon,1991).ThecommandfortheADFtestforresidualis dfullerresid,noconstant
regresslags(3)andfortheP-Ptestispperronresid,noconstantregress.
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The MacKinnon critical values for the cointegrating equation of 3 variables without trend using 24
observations at1%,5%and 10% levelofsignificance are -4.954, -4.114, and -3.717 respectively. The
Dickey-Fuller critical values for this regression at 1%, 5%, and 10% level are -2.66, -1.95, and -1.60
respectively.So,onecanclearlyseethattheMacKinnoncriticalvaluesaremuchhigherthantheDickey-
Fullercriticalvalues.AsaresultusingtheD-Fcriticalvaluescanleadtoerrorinstatisticalanalysis.
OnecanseethattheADFteststatistic(-2.947)islowerthantheMacKinnoncriticalvalueevenat10%level.So,usingADFtestonecannotsaythattheresidualfromtheregressionisstationary.However,the
P-Pteststatistic(-4.406)ishigherthantheMacKinnoncriticalvalueat5%level.So,itshowsthatthe
residual is stationary.Considering the fact that asDittmann(2002) argued,Phillips-Perrontest when
appliedtoresidualbasedconintegrationdeterminationaremorepowerfulthantheADFtest,onecan
arguethatthereexistsacointegratingrelationshipinthelong-rundemandequationofcigarettes.
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Onecanrunashortrunerrorcorrectionmodel(ECM).IntheECM,theoneperiodlaggedresidualfor
annualdataactsastheerrorcorrectionterm.Toget theoneperiod lagged residualonecanuse the
commandasgenlagresid=resid[_n-1].
ThecommandfortheECMinthiscaseisregdcondrelprcdrgdppcddum93ddum95lagresid.
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References:
IngolfDittmann(2002):Residual-BasedTestsforFractionalCointegration:AMonteCarloStudy,Journal
ofTimeSeriesAnalysis,Volume21Issue6,Pages615647.
JamesMacKinnon(1991):CriticalValuesforCointegrstionTests,inR.EngelandC.Granger,Long-run
EconomicRelationships,OxfordUniversityPress.Richard I. D. Harris (1995): Using Cointegration analysis in Econometric Modelling, FT Prentice Hal
Publication.
RobertAngelandCliveGranger(1987):Cointegrationanderrorcorrection:Representation,estimatio
andtesting,Econometrica,55:251-276.
Appendix:Thedatasetusedforthistutorial:
year con relprc rgdppc dum93 dum95 trend
1981 754.15 12.54 10273.60 0 0 1
1982 788.90 13.59 10322.57 0 0 2
1983 701.55 13.24 10518.93 0 0 3
1984 735.55 14.83 10832.18 0 0 4
1985 719.65 15.30 10951.98 0 0 5
1986 718.25 15.91 11199.04 0 0 6
1987 738.10 16.47 11376.67 0 0 7
1988 701.55 17.27 11408.75 0 0 8
1989 704.40 16.20 11473.76 0 0 9
1990 614.45 19.83 11797.61 0 0 10
1991 680.20 17.89 11938.95 0 0 11
1992 625.80 16.76 12286.00 0 0 12
1993 575.80 17.34 12724.48 1 0 13
1994 632.75 17.20 12994.34 0 0 14
1995 868.95 16.10 13381.83 0 1 15
1996 811.10 15.36 13768.54 0 0 16
1997 930.05 14.69 14297.28 0 0 17
1998 994.45 15.49 14815.08 0 0 18
1999 977.90 16.66 15315.05 0 0 19
2000 986.60 15.74 15997.47 0 0 20
2001 1006.00 15.59 16607.80 0 0 21
2002 1019.20 15.08 17117.09 0 0 22
2003 1124.95 14.70 17773.69 0 0 23
2004 1151.25 14.06 18504.51 0 0 24
Note:
Thetheoreticalpremiseandmethodologyusedinthistutorialisforillustrativepurposesonly.
AdditionalResources
QuestionspertainingtoStata-10forTimeSeriesAnalysiscanbesubmittedtoNYUsDataServiceStudio