Article in International Journal of Entrepreneurship · December 2020 doi: 10. 4018/ijegcc. 2020070105 citations 11 reads 286 João Manuel Pereira Polytechnic Institute of Setúbal Instituto Politécnico de Lisboa 95

Table 1. The name of countries and their indices used in this paper

Index	Country
ATG	Grécia
CAC40	França
DAX30	Alemanha
FTSE100	ReinoUnido
FTSEMID	Itália
IBEX35	Espanha
ISEQ	Irlanda
PSI20	Portugal

Source: Own elaboration

x t_s ( ) = x t( ) − z t( )  (2)

Theoriginalapplicationassumesthatthetrendpresentineachoftheboxesisalinearone,i.e.

Z t( ) = at +b withsubsequentapplicationsindicatingthatitislikelytocontainotherpolynomial trends(Kantelhardt,Koscielny-Bunde,Rego,Havlin,andBunde,2001).Foreachbox,thevalueof thetrendequationisobtainedbytheleast-squaresmethod,andthentherootofthemeansquare deviationbetweenthex t( )i.e.Z t( ),x(t)seriesisestimated,withtheDFAfunctiongivenby:

F s( ) = 21N ∑t2=N1 x ts ( )2  (3)

EstimatingtheaverageofF s( ) forallboxescenteredins,thevalueof F s ( ) fluctuationsis generatedasafunctionofs .Thisestimationwillberepeatedforalldifferentvaluesofs,pendinga power-lawprocess,thatis:

F s( ) ~sα^α  (4)

RESULTS

Figure1showstheevolutionoftheCOVID-19pandemicintermsofthenumberofconfirmedcases anddeathsinaglobalcontext.AsofJuly23,2020,thenumberofconfirmedcaseshadalready exceeded15.3million,anddeathsexceeded627,000.

Figure2showstheevolutionintermsofreturnofEurope’seightfinancialmarkets.Inallseries, thereisarelativelyhighdispersionaroundtheaverageandarelativelysynchronizedbehaviorbetween thedataseries.Thereishighvolatilitythroughgraphicalanalysis,especiallyinFebruary,March, andApril2020.

Table2showsthemaindescriptivestatisticsontheprofitabilityoftheeightEuropeanfinancial marketsandtheJarque-Beraadherencetest.Analysisofdescriptivestatisticsshowthatprofitability presentsnegativedailyaverages,exceptfortheGerman(DAX30)andIreland(ISEQ)markets.The Greekmarkethasthelargeststandarddeviation,whiletheItalianmarkethasthehighestkurtosisand asymmetrylevels.Also,thecoefficientsofasymmetryandkurtosisarestatisticallydifferentfrom thoseofanormaldistribution.TheseobservationswerecorroboratedwiththeJarque-Beraadherence test,whichrejectsthenullhypothesiswitha1%significance.

Sincetimeseriesarebeingestimated,onemustexaminethestationarynatureofthedataseries forEurope’seightstockmarkets.TheLevin,Lin,andChu(2002),ADF(DickeyandFuller,1981), PP(PierrePerronandPhillips,1988)testspostulatethesamenullhypotheses.Theintersectionof unitroottestsshowsthestationarityofreturn.However,theauthorsmusthighlightthetestlags, whichsuggestthatthetimeseriesmaynotbestable.Giventhisevidence,theauthorsperformedthe testbyClementeetal.(1998)toanalyzestationaritywithstructuralbreaks.

Figure3depictsthestabilitytestscarriedoutontheresiduesoftheEuropeanstockmarkets,with thepurposeofcorroboratingthepresenceofstructuralbreaks.Thestructuralbreak’sdeterminationis relevant,asithasaneffectpotentiallysimilartothatoftheunit-roots.Throughgraphicalanalysis,the authorsassessedtheexistenceofdisturbancesinvariance.Additionally,whenexaminingthegraphs