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RafałM.Łochowski
i.e.
ln
(
S
t
+
Δ
t
/
S
t
)
hasnormaldistributionwithmean
μ
Δ
t
andvariance
σ
2
Δ
t
.
However,theempiricaldatasuggeststhatthedistributionoflogarithmicreturns
forshortertimelags
Δfailstobenormal.Inthenextsubsectionwepresent
t
testsofnormalityfordailylogarithmicreturns,correspondingto
Δt
=
1
.
1.2.Normalitytestsfordailyreturns
Intab.1wepresentresultsoftwotestsfornormalityofdailylogarithmic
stockreturnsintheanalyzedperiod1stofJanuary2011-31stofJuly2011.
ThefirsttestwastheShapiro-WilktestandthesecondwastheJarque-Beratest.
Thenullhypotesisinbothtestsassumesthenormalityofasample.Bothtest
rejectthehypothesisaboutthenormalityofthereturnsatthe
0
.
01
significance
levelforfiveanalyzedassets:GTC,KERNEL,ORLEN,TPS.A.andTVN.
Table1
Normalitytestsfordailylogarithmicreturns
intheperiod1stJanuary-31stJuly2011
ASSECO
GTC
KERNEL
KGHM
ORLEN
PKOBP
TAURON
TPSA
TVN
Asset
Shapiro-Wilktest
statistic'sp-value
<0.0001
<0.0001
0.3179
0.0007
0.0751
0.0048
0.2749
0.2460
0.0095
statistic'sp-value
Jarque-Beratest
<0.0001
<0.0001
<0.0001
<0.0001
0.7429
0.1381
0.1746
0.0033
0.0774
Whenweanalyzethewholeyear2011(moreprecisely–theperiod1st
ofJanuary2011-20thofDecember2011)thehypothesisaboutthenormality
ofthereturnsisrejectedat
0
.
01
significancelevelforallanalyzedassets(cf.
tab.2).
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