matlab计量经济学工具箱Word下载.docx
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matlab计量经济学工具箱Word下载.docx
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Amodelobjectholdsalltheinformationnecessarytoestimate,simulate,andforecasteconometricmodels.
Parametricformofthemodel
Numberofmodelparameters(e.g.,thedegreeofthemodel)
Innovationdistribution(GaussianorStudent'
st)
Amountofpresampledataneededtoinitializethemodel
Example1:
AR
(2)
wheretheinnovationsareindependentandidenticallydistributednormalrandomvariableswithmean0andvariance0.2.Thisisaconditionalmeanmodel,sousearima.
>
model=arima('
AR'
{0.8,-0.2},'
Variance'
0.2,'
Constant'
0)
Example2:
GARCH(1,1)model
model=garch('
GARCH'
NaN,'
ARCH'
NaN)
或者
model=garch(1,1)
ParameterswithNaNvaluesneedtobeestimatedorotherwisespecifiedbeforeyoucanforecastorsimulatethemodel.
TodisplaythevalueofthepropertyARforthecreatedvariableobject,
model.AR
model.Distribution=struct('
Name'
'
t'
DoF'
8)
Methodsarefunctionsthatacceptmodelobjectsasinputs.InEconometricsToolbox,
estimate
infer
forecast
simulate
Example3:
FitanARMA(2,1)modeltosimulateddata
1)Simulate500datapointsfromtheARMA(2,1)model
simModel=arima('
{0.5,-0.3},'
MA'
0,'
0.1);
rng(5);
Y=simulate(simModel,500);
2)SpecifyanARMA(2,1)modelwithnoconstantandunknowncoefficientsandvariance.
model=arima(2,0,1);
model.Constant=0
3)FittheARMA(2,1)modeltoY.
fit=estimate(model,Y)
Example4:
loadData_EquityIdx
nasdaq=Dataset.NASDAQ;
r=price2ret(nasdaq);
r0=r(1:
2);
rn=r(3:
end);
FitaGARCH(1,1)modeltothereturns,andinfertheloglikelihoodobjectivefunctionvalue.
model1=garch(1,1);
fit1=estimate(model1,rn,'
E0'
r0);
[~,LogL1]=infer(fit1,rn,'
Wold'
stheorem:
youcanwriteallweaklystationarystochasticprocessesinthegenerallinearform
Thus,byWold'
stheorem,youcanmodel(orcloselyapproximate)everystationarystochasticprocessas
Theconditionalmeanandvariancemodels
StationaritytestsIfyourdataisnotstationary,considertransformingyourdata.Stationarityisthefoundationofmanytimeseriesmodels.
Youcandifferenceaserieswithaunitrootuntilitisstationary,Or,considerusinganonstationaryARIMAmodelifthereisevidenceofaunitrootinyourdata.
SeasonalARIMAmodelsuseseasonaldifferencingtoremoveseasonaleffects.Youcanalsoincludeseasonallagstomodelseasonalautocorrelation.
ConductaLjung-BoxQ-testtotestautocorrelationsatseverallagsjointly.Ifautocorrelationispresent,considerusingaconditionalmeanmodel.
Lookingforautocorrelationinthesquaredresidualseriesisonewaytodetectconditional
Heteroscedasticity.Tomodelconditionalheteroscedasticity,considerusingaconditionalvariancemodel.
YoucanuseaStudent’stdistributiontomodelfattertailsthanaGaussiandistribution(excess
kurtosis).
Youcancomparenestedmodelsusingmisspecificationtests,suchasthelikelihoodratiotest,Wald’stest,orLagrangemultipliertest.
TheJohansenandEngle-Grangercointegrationtestsassessevidenceofcointegration.ConsiderusingtheVECmodelformodelingmultivariate,cointegratedseries.Itcanintroducespuriousregressioneffects.
Theexample“SpecifyingStaticTimeSeriesModels”explorescointegrationinstaticregression
models.Type>
showdemoDemo_StaticModels.
WhyTransform?
Isolatetemporalcomponentsofinterest.
Removetheeffectofnuisancecomponents(likeseasonality).
Makeaseriesstationary.
Reducespuriousregressioneffects.
Stabilizevariabilitythatgrowswiththeleveloftheseries.
Maketwoormoretimeseriesmoredirectlycomparable.
P207
Anexampleofastaticconditionalmeanmodelistheordinarylinearregressionmodel.
Adynamicconditionalmeanmodelspecifiestheevolutionoftheconditionalmean,
Examples:
ByWold’sdecomposition,youcanwritetheconditionalmeanofanystationaryprocessytas
And
istheconstantunconditionalmeanofthestationaryprocess.
arima(p,D,q):
nonseasonalARterms(p),theorderofnonseasonalintegration(D),andthenumberofnonseasonalMAterms(q).
Whensimulatingtimeseriesmodels,onedraw(or,real
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