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7/29/2019 Raunak Jain R Presentation
http://slidepdf.com/reader/full/raunak-jain-r-presentation 1/11
STATISTICALMETHODSINFINANCE FLOWCHARTOFTHEPROCESS
7/29/2019 Raunak Jain R Presentation
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STATIONARYMean(Testformean0)
Variance(Takelogdifference)
ADFtestforStaonarity.
MODELIDENTIFICATIONACF,PACFplot
MODELESTIMATION
ARIMA,
GARCH.
MODELADEQUACYBoxTestfor
serialcorrelaon.
FORECASTING
1 2 3
4 5
THEPROCESSUNDERTAKEN
STATISTICALMETHODSINFINANCE FLOWCHARTOFTHEPROCESS
7/29/2019 Raunak Jain R Presentation
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• Ttestshowsmeannotzeroof
theclosingprices.
• p-value<2.2e-16
• alternavehypothesis:
• truemeanisgreaterthan0
• Since the mean is not zero,
wedifferencethedata.
20
40
60
80
closing [2007−01−03/2012−07−06]
Last 14.14
Jan 03
2007
Jan 02
2008
Jan 02
2009
Jan 04
2010
Jan 03
2011
Jan 03
2012
STATISTICALMETHODSINFINANCE
MeanZero
7/29/2019 Raunak Jain R Presentation
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• TheaugmentedDickey–Fuller(ADF)stasc, used in the test, is anegave number. The more
negave it is, the stronger therejecon of the hypothesis thatthereisaunitrootatsomelevelofconfidence.
• Dickey-Fuller = -12.2629, Lag order=11,
• p-value=0.01
• alternavehypothesis:staonary
• Conclusion: Since p value<0.05,reject null of non staonarity,thereforedataisstaonary
• A model that includes a constant
andametrendisesmatedusingsample of 50 observaons andyieldsthe stascof−4.57.Thisismore negave than the tabulatedcricalvalueof−3.50,soatthe95percentlevelthenullhypothesisofaunitrootwillberejected.
−10
−5
0
5
dtest [2007−01−04/2012−07−06]
Last −0.0199999999999996
Jan 04
2007
Jan 02
2008
Jan 02
2009
Jan 04
2010
Jan 03
2011
Jan 03
2012
STATISTICALMETHODSINFINANCE
ADFTEST:Sta@onarity
7/29/2019 Raunak Jain R Presentation
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Jarque-BeraNormalalityTest
TestResults:
X-squared:58437.3676,
PVALUE:<2.2e-16
theJarque–Beratestisagoodness-of-fittest of whether sample data have the
skewness and kurtosis matching a
normaldistribuon.
Thenullhypothesisisajointhypothesis
of the skewness being zero and theexcesskurtosisbeingzero.
Hence,weconcludethatthedatadoes
nothaveanormaldistribu@on.
STATISTICALMETHODSINFINANCE NORMALITYTEST
BasicSTATS
MS.Close
nobs1385.000000NAs0.000000
Mean-0.001226
Variance0.002144
Stdev0.046308
Skewness1.393276Kurtosis31.649301
Gaussianity refers to the probability
distribu@onwithrespecttothevalue,in
thiscontexttheprobabilityofthesignal
reaching an amplitude, while the term
'white' refers to the way the signal
powerisdistributedover@meoramong
frequencies.
7/29/2019 Raunak Jain R Presentation
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STATISTICALMETHODSINFINANCE MODELIDENTIFICATION
SAMPLEACFINTERPRETATIONS
7/29/2019 Raunak Jain R Presentation
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0 10 20 30 40 − 0 . 2
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
Series: y
LAG
A C F
0 10 20 30 40 − 0 . 2
0 . 0
0 . 2
0 . 4
0
. 6
0 . 8
1 . 0
LAG
P A C F
STATISTICALMETHODSINFINANCE ACF,PACFPLOT
• There is no clear indicaon of a
AR(p) or MA(q) process here, as
neithertheACFnorthePACFhasa
gradualdeclineatconsecuvelagsnordotheyhavespikesatcertain
lags.
• Secondmethodofp,qes@ma@on.
best.order<-c(0,0,0)
best.aic<-Inf
for(iin0:4)for(jin0:3){
fit.aic<-AIC(arima(resid(arma)
,order=c(i,0,j)))
if(fit.aic<best.aic){best.order<-c(i,0,j)
best.arma<-arima(resid(arma1)
,order=best.order)
best.aic<-fit.aic}}
7/29/2019 Raunak Jain R Presentation
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• ARIMA(1,0,1),AIC=-5.141276
• ARIMA(3,0,1),AIC=-5.165905
• Box-Ljung test (H0: The data are
independentlydistributed)
X-squared=41.8899,df=12,p-value=
3.476e-05
• Sincep<0.05,werejectthenullandsay
dataisdependent.
• Here an ARIMA p=1,3 and q=1 with
d=0(asdataisstaonary)hasbeenfied
to the data without indicaons of
removal of serial correlaons between
the square of residuals. We find arelaon between the variance of the
residuals signifying that the data was
not totally characterizedby the ARIMA
models usedhere andmore analysis is
neededtogetawhitenoiseintheend.
0 10 20 30 40
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
Series: armaresi4^2
LAG
A C F
0 10 20 30 40
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
LAG
P A C F
STATISTICALMETHODSINFINANCE Fi\ngARMA
7/29/2019 Raunak Jain R Presentation
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7/29/2019 Raunak Jain R Presentation
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STATISTICALMETHODSINFINANCE COMPARISONBETWEENDIFFERENTMODELS
GARCH(1,1),
t
ARMA(3,1)+GARCH(1,1),
normal
ARMA(3,1)+GARCH(1,1),
t
ARMA(3,1)+GARCH(1,1),
skewedt
AIC -4.134258 -4.040692 -4.134697 -4.133303
Ar1 0 0.55364 0.7038 0.70338
ar2 0 0.01263 0.01662 0.16594
ar3 0 -0.069487 -0.04825 -0.48111
ma1 0 -0.58672 -0.7336 -0.73270
alpha 0.13389 0.13272 0.1189 0.12188
beta 0.85514 0.85570 0.8843 0.88402
7/29/2019 Raunak Jain R Presentation
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STATISTICALMETHODSINFINANCE FINALGARCHMODEL
Rt = 0.703Rt≠1 + ‘t ≠ 0.7336‘t≠1
‘t =Ô ht÷t with
ht = 0.1189‘t≠1 + 0.8843ht
Where,ŋshouldbeWN(0,1).ButsinceourGARCHdoesnotcaptureallthe
characteris@csofthemodelitisnotinthiscase.