Methods to Remove Autocorrelation - Econometric Modeling - Lecture Notes, Study notes for Econometrics. Agra University

Econometrics

Description: Econometric models are statistical models used in econometric. This modelling tool help economist develop future economy plan for the company. This lecture note discuss important points for understanding Econometric modelling, it includes Methods, Remove, Autocorrelation, Difference, Iterative, Regression, Sensex
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ui=ρui1+εt
Fortherunstest,inColumnVIoftheabovetable,thetotalnumberofpositivevalues(N1),andthetotal
numberofnegativevalues(N2)arecounted.WealsocountthatR=80timesuichangedsignsfrom
positivetonegativeandthenfromnegativetopositive.
So,fortheRunstest,wehaveN1=677,N2=720,N=N1+N2=1397,andR=80.
So,E(R)=+1= +1=698.84
Var(R)== =348.34
Then,for95%confidencelevel(orequivalently,5%significancelevel),ifobservedRfallsbetween
E(R)±1.96σR,thenthereisnoautocorrelation,butifitfallsoutside,itcanbesaidthatautocorrelation
exists.
Now,E(R) + 1.96σR=698.84+1.96*348.34=735.42
andE(R) - 1.96σR=698.84‐1.96*348.34=662.26
ButobservedRis80,anditliesoutsidetheinterval[662.26,735.42]
So,againweinferthatthereISautocorrelation.
Sonow,wecansaythatwecannotbelievethesignificancesoftheβisthatwegotfromOLS.Wefirst
havetoremovetheautocorrelationandthenfindthesignificancetomakecorrectconclusionsabout
whichfactorsaffectgoldprices.
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Thatis,ourdetectionofautocorrelationisover,andwecannowmovetothenextstep,thatis,removal
ofautocorrelation.
Thereare4methodstoremoveautocorrelation:
1. FirstdifferenceMethod(applicablehere,sinced<R2)
2. FindρfromDurbinWatsondstatistic,anduseGeneralisedLeastSquaresRegression
3. FindρfromEqn.2,anduseGeneralisedLeastSquaresRegression
4. UseiterativeMethodslikeCochraneOrcutt(needtousesoftwaresforthis)
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Method1:FirstDifferenceMethod:
Goldpricet=β1+β2*USDexchangeratet+β3*Sensext+β4*oilpricet
()Goldpricet1=β1+β2*USDexchangeratet1+β3*Sensext1+β4*oilpricet1
(Goldpricet‐Goldpricet1)=β2*(USDratet‐USDratet1)+β3*(Sensext‐Sensext1)+β4*(oilpricet‐oil
pricet)
t=β2*t+β3*t+β4*t
where t=(Goldpricet‐Goldpricet1), t=(USDratet‐USDratet1),t=(Sensext‐
Sensext1)andt=(oilpricet‐oilpricet)
TheresultsfromtheOLSareasfollows:
=25.293*+(0.182)*+0.165* 
StdError19.11360.0277030.023547
t1.323284‐6.563676.995892
R20.036757

Durbin
Watson
2.061111dL=1.645(FromDurbin‐
dU=1.692WatsonTables)
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WeseethattheDurbinWatsondstatisticshowsthatthereisnoautocorrelationinthefirstdifference
equation.Nowwecanbelievethevaluesofβis.
tstatisticforβ2islessthan2,soitisstatisticallyinsignificant=>USDexchangeratedoesnotaffectgold
pricesignificantly;
tstatisticforβ3ismorethan2,soitisstatisticallysignificant=>Sensexaffectsgoldpricesignificantly
andnegatively;and
tstatisticforβ4ismorethan2,soitisstatisticallysignificant=>Oilpriceaffectsgoldpricesignificantly
andpositively.
Method2:FindρfromDurbinWatsondstatistic,anduseGeneralisedLeastSquaresRegression
FromtheoriginalOLS,wegotDurbinWatsondstatisticas:0.039.
Ithasbeenestablishedthatforlargesamples,d2(1ρ).Then,ρ1d/2=10.039/2=0.98
Goldpricet=β1+β2*USDexchangeratet+β3*Sensext+β4*oilpricet
()ρ*Goldpricet1=ρ*β1+ρ*β2*USDexchangeratet1+ρ*β3*Sensext1+ρ*β4*oilpricet1
=1.645 =1.692 =2.308=2.355
d
calc
=2.061
X
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