Finance
186 2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
Mul iscale non-linea ale isk spillo e
e ec om oil o s ocks – The case o Eas
Eu opean eme ging ma ke s
Dejan Zi ko 1, Bo is Kuzman2, Na asa Papic-Blagoje ic3
1 Uni e si y o No i Sad, No i Sad School o Business, Depa men o Economics, Se bia, ORCID: 0000-0003-2357-3250,
[email p o ec ed];
2 Ins i u e o Ag icul u al Economics, Depa men o Coope a ion wi h he Economy, Se bia, ORCID: 0000-0002-8661-2993,
[email p o ec ed];
3 Uni e si y o No i Sad, No i Sad School o Business, Depa men o Economics, Se bia, ORCID: 0000-0002-1110-3414,
[email p o ec ed].
Abs ac : This pape in es iga es he mul iscale non-linea isk ansmission e ec om B en oil
o ele en Eu opean eme ging s ock ma ke s. Dynamic ex eme isk ime se ies a e c ea ed using
he FIAPARCH-CVaR app oach. The MODWT ans o ma ion is applied o make h ee wa ele
de ails ha ep esen di e en ime ho izons. In he inal s ep, he MODWT ime se ies a e i ed
in o he Ma ko swi ching model o examine he spillo e phenomenon. The esul s indica e ha
he Czech and Hunga ian s ock ma ke s endu e he spillo e e ec in c isis egime in he sho
e m, p obably because hese ma ke s a e among he mos e icien eme ging Eu opean ma ke s.
On he o he hand, a ela i ely high spillo e e ec is ound in a peace ul a he han a c isis egime
in he case o Poland. This is p obably because he Polish index lis s almos 300 s ocks, which
means ha oil shocks dispe se o a la ge numbe o di e en indus y sec o s. In small and less
de eloped ma ke s, such as Es onia, Slo enia, Bulga ia, and C oa ia, a high spillo e e ec exis s
in a anquil egime because hese coun ies ha e high oil consump ion pe capi a. Li huania and
La ia do no epo he spillo e e ec in he sho un, while his is ue o all ime ho izons
in he case o Slo akia.
Keywo ds: Ex eme isk spillo e e ec , condi ional alue-a - isk (CVaR), wa ele me hodology,
B en oil, s ock ma ke s.
JEL classi ica ion: C58, G12, G32.
APA S yle Ci a ion: Zi ko , D., Kuzman, B., & Papic-Blagoje ic, N. (2024). Mul iscale non-
linea ale isk spillo e e ec om oil o s ocks – The case o Eas Eu opean eme ging
ma ke s. E&M Economics and Managemen , 27(3), 186–200. h ps://doi.o g/10.15240/
ul/001/2024-5-015
Ea ly Access Publica ion Da e: July 25, 2024.
In oduc ion
Oil is he key s a egic ene gy sou ce ha
uns co po a e businesses a ound he wo ld.
This means ha he oil ma ke and s ock
ma ke s a e ine i ably in e connec ed, whe e
a ple ho a o li e a u e con i med his ela ion-
ship (Abakah e al., 2023; Aydin e al., 2022;
Mensi e al., 2022a). Tian e al. (2022) lis
se e al economic condui s ha connec oil and
s ock ma ke s. One o he mos impo an and
mos de imen al channels is he supply-side
shock e ec passed on o he e ec o in la ion.
In o he wo ds, an inc ease in he p ice o c ude
oil di ec ly a ec s p oduc ion by inc easing
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187
2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
he ma ginal cos s o new p oduc s. As a esul ,
in la ion inc eases due o ising oil p ices. This
lowe s spending powe o consume s and e-
duces he p o i s o companies, which causes
s ock p ices o all. On he o he hand, he so-
called agg ega e-demand e ec also occu s,
whe e pu chasing powe can be ans e ed
om oil-impo ing coun ies o oil-expo ing
coun ies. This esul s in a ise o s ock p ices
in oil-expo ing coun ies and a all o s ock
p ices in oil-impo ing coun ies.
The ecen c ises, such as he COVID-19
pandemic and he ongoing wa in Uk aine,
ha e in lic ed unp eceden ed shocks o oil and
s ocks (Gem a e al., 2022). These de elop-
men s in ensi ied he e o s o academics,
in es o s, and commodi y ade s o be e
unde s and he in e links be ween oil and
s ock ma ke s because hey ha e impo an
epe cussions o he s abili y and success ul
ope a ion o companies. The le plo in Fig. 1
clea ly shows ha he wo c ises had a e y
deep impac on he B en oil ma ke . T a el
es ic ions and lockdowns caused a s eep d op
in global oil demand, p o oking oil p ices o all
o 20 USD pe ba el in Ap il 2020. On he o he
hand, he wa in Uk aine pushed he p ice
o oil o o e 120 USD pe ba el in May 2022.
These happenings induced huge isk in he oil
ma ke , as can be seen in he igh plo (Fig. 1),
pa o which has ce ainly been ans e ed
o s ock ma ke s.
The pape ies o es ima e uni a ia e isk
ansmission om B en oil o ele en s ock
indices o Eas Eu opean economies, which
a e membe s o he EU (Poland, Czechia,
Hunga y, Slo akia, Li huania, La ia, Es onia,
Slo enia, Romania, Bulga ia and C oa ia). Risk
ansmission be ween he ma ke s is impo an
o s udy because he oil-s ock isk in e depen-
dence is g owing s onge , whe eas he isk
ansmission mechanism is becoming mo e
complex due o he deepening o commodi y
inancializa ion and global inancial in eg a ion
(Wen e al., 2022).
In o de o measu e ex eme isk, esea ch-
e s usually conside alue-a - isk (VAR) o be
he mos amous measu e o downside isk.
Howe e , one o he majo issues o he VaR
model is i s inabili y o measu e he losses
beyond he h eshold amoun o VaR. Rocka -
ella and U yase (2002) ied o esol e his
d awback by p oposing he pa ame ic condi-
ional VaR (CVaR), which can add ess losses
beyond VaR. In o he wo ds, he pa ame ic
CVaR calcula es he a e age loss o he wo s
e u ns aking in o accoun a ce ain le el
o p obabili y (Ži ko e al., 2021). In o de
o p ope ly calcula e dynamic CVaR, empi i-
cal ime se ies need o be independen ly and
iden ically dis ibu ed, which is usually no
he case because daily ime se ies a e p one
o au oco ela ion, he e oscedas ici y, ola il-
i y clus e ing, le e age e ec s, a ails, and
long memo y. Wi h he aim o be e ecognize
he idiosync a ic ea u es o he ime se ies,
we use he FIAPARCH model because his
model p oduces he mos accu a e VaR and
expec ed sho all, acco ding o Alka he y e al.
(2022). S uden dis ibu ion is u ilized o i
Fig. 1: Empi ical dynamics o B en oil
Sou ce: own
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188 2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
he a ails o he empi ical ime se ies. Acco d-
ingly, he whi e noise esiduals o his model a e
used o c ea e he dynamic CVaR ime se ies
o B en oil and s ock indices.
Jin e al. (2023) asse ha oil p ice shocks
can impac s ock p ices in di e en ime ho i-
zons, which means ha isk spillo e s can be
obse ed a mul iple ime scales. This concep
is also impo an om he aspec o di e en
ma ke pa icipan s. In o he wo ds, sho - e m
agen s, such as a bi ageu s and specula o s
p ima ily look a empo a y happenings, such as
unusual e en s and socio-economic news
(Rösch e al., 2022). Fund manage s, as mid-
e m in es o s, a e conce ned o medium- e m
ma ke de elopmen s (Ba unik & K ehlik, 2018).
On he o he hand, policymake s and la ge
inancial ins i u ions, such as insu ance com-
panies and pension unds, a e keen o know
how he mac oeconomic en i onmen and un-
damen al ac o s unc ion (Fong e al., 2022).
To add ess he issue o he mul i- equency
spillo e e ec , we use he maximum o e lap
disc e e wa ele ans o ma ion (MODWT)
me hodology in o de o gene a e he wa ele
signals o di e en equencies ha pe soni y
sho -, medium- and long- e m ho izons.
In he inal s age o he esea ch p ocess,
we embed ele en wa ele -based oil-s ock pai s
in o he Ma ko swi ching (MS) model in a pai -
wise manne in o de o in es iga e he unidi-
ec ional oil-s ock causali y. This model is used
o cap u e shi s in economic o inancial da a
when hey canno be ully explained by a single
se o pa ame e s and assump ions. Since
we co e a ela i ely long ime span, which in-
cludes he wo c ises, i is logical o hypo hesize
ha he ela ionship is non-linea . In pa icula ,
assuming he p esence o a non-cons an
ela ionship, we allow s ock indices o ely on
he wo independen s a e egimes ha shape
he condi ional mean p ocess. Bashe e al.
(2016) explain ha he Ma ko swi ching model
uses he in o ma ion om he a ying egime-
swi ching p obabili ies o being in a pa icula
egime o allow ime- a ying causali y ac oss
egimes. F om his aspec , we can ge in-
o ma ion in which ime he ho izon ex eme
isks om he oil ma ke ha e he g ea es
impac on he s ock ma ke and in which egime
his happens.
The exis ing li e a u e ound mixed esul s
ega ding he oil-s ock isk spillo e ela ion-
ship wi hou eaching a consensus, which
indica es he complexi y o his phenomenon.
Ahmed and Huo (2021) u ilized he i- a ia e
VAR-BEKK-GARCH model o examine he
dynamic nexus among commodi y ma ke s,
he Chinese s ock ma ke and global oil
p ice. They ound bidi ec ional shocks spill-
o e s be ween oil and s ock ma ke s bu
unidi ec ional ola ili y spillo e s om he oil
ma ke o he Chinese s ock ma ke . Jiang
e al. (2022) used he long-memo y Copula-
CoVaR-MODWT me hod o documen he isk
spillo e s om oil o BRICS s ock ma ke s,
add essing bo h ime and equency domains.
They showed ha signi ican isk spillo e s ex-
is wi h ime- a ying and he e ogeneous cha -
ac e is ics. The pape o Oko ie and Lin (2022)
esea ched he in o ma ion spillo e s in e u n
and ola ili y, conside ing he wo c ude oil
ma ke s (B en and WTI) and he Nige ian
s ock index (NSE) using he asymme ic VAR-
MGARCH-GJR-BEKK model. They ound a bi-
di ec ional ola ili y spillo e e ec be ween
he c ude oil ma ke s and he NSE index, and
signi ican asymme ic shocks. Chan and Qiao
(2023) in es iga ed he ola ili y in e depen-
dencies be ween oil and s ock ma ke s, aking
in o accoun he WTI oil p ice and en S&P500
sub-indices. Acco ding o hei esul s, demand
shocks o s ock ma ke s and oil cause much
s onge spillo e e ec s han supply shocks.
The main esea ch ques ion o he pape
and i s con ibu ion o he exis ing li e a u e
pe ains o whe he and how ex eme isk om
he B en ma ke spills o e o he s ock ma ke s
o Cen al and Eas e n Eu opean coun ies.
This ype o esea ch has ne e been done
be o e o his g oup o coun ies, o he bes
o ou knowledge, and his is ou mo i e
o do his s udy. Con ibu ion is also e lec ed
in he ac ha he spillo e e ec is obse ed
om he aspec o a ious ime ho izons, which
deepens he unde s anding o his phenom-
enon. The use o elabo a e me hodologies
con ibu es o he eliabili y o he esul s, which
is also a ele an cha ac e is ic o his pape .
Besides he in oduc ion, he es o he pa-
pe is s uc u ed as ollows. The i s sec-
ion explains he used me hodologies – he
FIAPARCH model, wa ele ans o ma ion, and
Ma ko swi ching model. The second sec ion
in oduces he esea ch da a and p elimina y
indings. The esul s and discussion a e p e-
sen ed in he hi d sec ion. The las sec ion is
ese ed o conclusions.
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2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
1. Used me hodologies
1.1 Long memo y GARCH and dynamic
CVaR
I a ime se ies has a slow declining au oco -
ela ion unc ion (ACF), hen i has he long
memo y p ope y, as Ding and G ange (1996)
explained. I is said ha ime se ies is a s a ion-
a y long-memo y p ocess i he au oco ela ion
unc ion (ACF), ρ(k) beha es as ρ(k) ≈ c|k|2d–1
as |k|→∞, whe e 0 < d < 0.5, and c is a posi-
i e cons an . The ACF has a e y slow a e
o decline o ze o as k s i es o in ini y and
∑∞
k=–∞|ρ(k)| = ∞. Long memo y p ope y can
be modelled by he ac ionally in eg a ed
GARCH (FIGARCH) model, which is an ex en-
sion o he classical GARCH model. I is used
o cap u e long-memo y pe sis ence in ola il-
i y, which means i accoun s o he ac ha
ola ili y ends o pe sis o e ime. In he adi-
ional GARCH model, ola ili y is modeled using
lagged squa ed e o s and lagged condi ional
a iances. Howe e , hese models assume ha
ola ili y pe sis ence is ini e. In con as , he
FIGARCH model allows o he possibili y o in i-
ni e pe sis ence, meaning ha shocks o ola il-
i y can ha e a las ing impac on u u e ola ili y.
Some pape s ound he long memo y p o-
cess in ene gy commodi ies and s ocks (Chkili
e al., 2021; Yousse e al., 2015), so we apply
he ac ional in eg a ed asymme ic powe
ARCH model – FIAPARCH o Tse (1998) in o -
de o add ess his issue. The mean equa ion in-
cludes he i s -o de au o eg essi e e m, which
is enough o deal wi h au oco ela ion. S uden
dis ibu ion ackles a ails in he empi ical dis-
ibu ions. The mean and FIAPARCH(p, d, q)
speci ica ions look as ollows:
y = C + Θy –1 + ε ; ε ~ S (0, σ , ν) (1)
σ
δ = ω[1 – β(L)]–1 +
+ {[1 – β(L)]–1 α(L)(1–L)d } (|ε | – γε )δ
(2)
whe e: ω is cons an ; L deno es he lag-op-
e a o ; γ, δ and d a e he model pa ame e s.
Pa ame e γ is he le e age coe icien , whe e
γ < 0 means ha posi i e shocks a ec ola il-
i y mo e han nega i e shocks and ice- e sa.
Symbol δ s ands o he powe e m pa ame e ,
and i has ini e posi i e alues. When γ = 0
and δ = 2, he FIAPARCH p ocess becomes
FIGARCH(p, d, q) model. d ep esen s he ac-
ionally di e encing pa ame e measu ing
he pe sis ence o shocks o he condi ional
a iance. FIGARCH(p, d, q) model pe mi s an in-
e media e ange o pe sis ence, whe e d pa-
ame e can be ound in he scope: 0 < d < 1.
When d = 0, FIGARCH model educes o o di-
na y GARCH, whe eas when d = 1, FIGARCH is
equi alen o in eg a ed GARCH o IGARCH.
A e he es ima ion o he FIAPARCH mod-
els, we use he i ed esiduals o calcula e
he dynamic CVaR ime se ies a 5% p ob-
abili y le el. CVaR measu es he a e age
amoun o loss ha in es o could ha e in one
day wi h a ce ain p obabili y. CVaR is he in e-
g al o VaR, whe e VaR can be exp essed as
VaRα = μ  + Zασ  . μ  and σ  deno e he es ima ed
mean and s anda d de ia ion o a pa icula
asse , espec i ely, while Zα is he le quan ile
o he no mal s anda d dis ibu ion. CVaR is
calcula ed as in Equa ion (3):
(3)
1.2 MODWT ans o ma ion
A e cons uc ing he dynamic CVaR ime se-
ies o all asse s, we use wa ele me hodology
o build h ee wa ele de ails ep esen ing sho -,
medium- and long- e m ho izons. On he heo-
e ical basis, he wa ele ope a es wi h he wo
elemen a y wa ele unc ions: mo he wa ele
(ψ) and a he wa ele (ϕ). Fa he wa ele s de-
pic he low equency o smoo h pa s o a sig-
nal, ha ing an in eg al o 1. On he o he hand,
mo he wa ele s explain high- equency com-
ponen s wi h an in eg al equal o 0. The a he
(ϕJ,k( )) and mo he (ψJ,k( )) wa ele unc ions
can be p esen ed in he ollowing way:
(4)
whe e: symbol 2J s ands o he scale ac o ,
while 2k
J is he ansla ion o loca ion pa ame e .
Fo he wa ele compu a ion p ocess,
he s udy uses he non-o hogonal wa ele s,
known as he maximum o e lap disc e e wa e-
le ans o ma ion (MODWT), which has highly
edundan and non-o hogonal ans o ma ion
cha ac e is ics. Decomposed signals in he
MODWT amewo k a e p esen ed as ollows:
SJ,k ≈
∫
( )ϕJ,k ( )d (5)
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DJ,k ≈
∫
( )ψJ,k ( )d , j = 1, 2, …, J (6)
whe e: symbols SJ,k and DJ,k deno e he luc-
ua ion and scaling coe icien s, espec i ely, a
pa icula j h le el, which decomposes empi ical
signal o ime se ies in e ms o a speci ic e-
quency ( ending and luc ua ion componen s).
Acco ding o Equa ions (5–6), an empi i-
cal ime se ies y( ) can be exp essed in e ms
o hose signals as:
( ) = ∑SJ,k ϕJ,k ( ) + ∑Dj,k ψj,k ( ) +
+ ∑Dj–1,k ψj–1,k ( ) + … +∑D1,k ψ1,k ( )
(7)
1.3 Ma ko swi ching model
The scale-dependen Ma ko swi ching model
was o iginally de eloped by Gold eld and
Quand (1973), and we a e using i o esea ch
he non-linea ex eme isk spillo e e ec
be ween B en oil and s ock ma ke s in di e -
en ime ho izons. The Ma ko chain go e ns
he Ma ko swi ching model, whe e he u u e
s a e depends only on he cu en s a e and
he p obabili y o a pa icula alue (Rosen
e al., 2023). In his pape , wo s a es a e as-
sumed (S = 1, 2), whe e S is an unobse ed
s a e a iable. S = 1 depic s inc eased ola ili y
in he s ock ma ke s, while s a e S = 2 e e s
o calm ma ke condi ions. Besides he swi ch-
ing p ocess in he mean, we also pe mi
he a iance o he e o e m o swi ch be ween
he s a es. The unidi ec ional wa ele -based
Ma ko swi ching es ima ion equa ion looks
like as ollows:
SI j
i, = c j
s + ϕ j
s OIL
j + ε j
j ; ε ~ N(0,σ2
s ) (8)
whe e: SI deno es he dynamic CVaR o a pa -
icula s ock index i, and OIL is he dynamic
CVaR o B en ime se ies. Bo h cons an c
and he spillo e pa ame e ϕ a e scale-depen-
den , whe e he wa ele scale is labelled by
he symbol j. The Ma ko chain is unobse -
able by de ini ion, which means ha p obabili-
ies need o be included in o de o es ima e
an ou pu . In o he wo ds, changing egimes is
no go e ned de e minis ically bu wi h a ce -
ain p obabili y (Qian e al., 2022). The e o e,
he unobse ed s a e a iable S ollows a wo-
s a e Ma ko p ocess wi h ansi ion p obabili-
ies as in Equa ion (9):
P(S = 1│S –1 = 1) = p11
P(S = 1│S –1 = 2) = p12
P(S = 2│S –1 = 1) = p21
P(S = 2│S –1 = 2) = p22
whe e
p11 + p12 =
= p21 + p22 = 1
}
(9)
The Ma ko swi ching model is es ima ed
by he maximum likelihood unc ion, whe e
he il e ing p ocedu e o Hamil on (1990) and
he smoo hing algo i hm o Kim (1994) a e used.
2. Da ase andp elimina y indings
The pape uses daily da a o B en spo oil and
ele en s ock ma ke indices om he coun ies
o Cen al and Eas e n Eu ope: WIG (Poland),
PX (Czechia), BUX (Hunga y), SAX (Slo akia),
OMXV (Li huania), OMXR (La ia), OMXT (Es-
onia), SOBITOP (Slo enia), BET (Romania),
SOFIX (Bulga ia) and CROBEX (C oa ia).
All asse s a e collec ed om he s ooq.com
and in es ing.com websi es. The sample co -
e s he pe iod be ween Janua y 2017 and Au-
gus 2023, which includes ela i ely calm and
u bulen pe iods be o e and du ing he pan-
demic and he wa in Uk aine. All indices a e
sepa a ely combined and synch onized wi h
B en oil. Also, all ime se ies a e ans o med
in o log e u ns ( i) acco ding o he exp ession:
i = 100 × log(Pi, /Pi, −1), whe e Pi is he p ice
o a pa icula asse . I should be said ha SAX
is he leas liquid index, while B a isla a SE
is he leas de eloped s ock exchange (Baele
e al., 2015), which means ha he e was
no ading a all on a signi ican numbe o days.
This is e lec ed in he modeling and cons uc-
ion o ex eme downside and upside isks.
In o he wo ds, he c ea ed dynamic downside
isk ime se ies o SAX a e no smoo h as
in he case o o he indices (Fig. 2).
Desc ip i e s a is ics in Tab. 1 include
he i s ou momen s, he Ja que-Be a es
o no mali y, he Ljung-Box es o le el and
squa ed esiduals and he DF-GLS uni oo es .
B en has high ku osis, which implies he p es-
ence o ex eme isk, bu all o he indices also
ha e high ku osis, which means ha high isk
is a common phenomenon in he obse ed pe-
iod, pa icula ly due o he pandemic. Au oco -
ela ion is p esen in all asse s excep B en and
WIG, whe eas all he ime se ies epo ime-
a ying a iance. These ea u es o he ime
se ies can be esol ed by some o m o he AR-
GARCH model. Besides, all he ime se ies a e
s a iona y, as he DF-GLS es indica es, which
is necessa y o he GARCH modelling.
k
k k
k

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Mean S d. de . Skewness Ku osis JB LB(Q) LB(Q2)DF-GLS
B en 0.011 1.177 −1.562 26.170 38,310.0 0.241 0.000 −8.758
WIG 0.008 0.546 −1.248 17.372 14,654.9 0.155 0.000 −6.374
PX 0.010 0.419 −1.064 15.414 10,946.7 0.000 0.000 −7.403
BUX 0.015 0.574 −1.383 15.700 11,621.9 0.000 0.000 −20.909
SAX 0.000 0.418 −0.403 14.509 8,923.4 0.001 0.000 −44.632
OMXV 0.014 0.292 −3.096 56.475 198,993.5 0.000 0.000 −16.888
OMXR 0.017 0.504 −0.777 41.551 102,095.1 0.000 0.000 −15.721
OMXT 0.014 0.363 −2.460 34.828 71,785.7 0.000 0.000 −35.429
SOBITOP 0.014 0.372 −1.785 22.859 27,887.3 0.000 0.000 −5.765
BET 0.016 0.458 −1.709 24.696 33,185.9 0.000 0.000 −10.056
SOFIX 0.005 0.346 −2.451 35.449 73,144.7 0.000 0.000 −11.661
CROBEX 0.005 0.345 −3.468 48.391 144,426.2 0.000 0.000 −2.772
No es: JB – Ja que-Be a coe icien s o no mali y; LB(Q) and LB(Q2) es s deno e p- alues o he Ljung-Box Q-s a is ics
o he le el and squa ed esiduals o 10 lags; 1% and 5% c i ical alues o DF-GLS es wi h 5 lags a e −2.566 and
−1.941, espec i ely.
Sou ce: own
Absolu e e u ns Squa ed e u ns
Lo’s R/S GPH GSP Lo’s R/S GPH GSP
B en 3.864*** 0.246*** 0.257*** 2.737*** 0.178*** 0.161***
WIG 4.400*** 0.234*** 0.235*** 2.601*** 0.161*** 0.165***
PX 4.911*** 0.305*** 0.273*** 3.248*** 0.344*** 0.290***
BUX 4.074*** 0.295*** 0.268*** 2.766*** 0.222*** 0.209***
SAX 2.591*** 0.105*** 0.153*** 1.660*** 0.071*** 0.070***
OMXV 3.301*** 0.285*** 0.271*** 1.812* 0.210*** 0.200***
OMXR 1.653 0.335*** 0.302*** 1.246 0.246*** 0.240***
OMXT 4.864*** 0.370*** 0.314*** 2.847*** 0.381*** 0.289***
SOBITOP 3.383*** 0.359*** 0.312*** 2.481*** 0.230*** 0.215***
BET 2.531*** 0.257*** 0.241*** 2.262*** 0.195*** 0.162***
SOFIX 3.274*** 0.261*** 0.249*** 1.911** 0.148*** 0.138***
CROBEX 2.601*** 0.384*** 0.322*** 2.076*** 0.285*** 0.231***
No e: *** signi icance a 1% le el, ** signi icance a 5% le el; he c i ical alues Lo’s R/S s a is ics es a e
90%: [0.861, 1.747], 95%: [0.809, 1.862] and 99%: [0.721, 2.098].
Sou ce: own
Tab. 1: Desc ip i e s a is ics o he selec ed asse s
Tab. 2: Long memo y es s
Finance
192 2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
Besides s anda d desc ip i e s a is-
ics, Tab. 2 es s he long memo y p ope y
o he uncondi ional e u ns and uncondi ional
ola ili y. Following Yousse (2015) and Alk-
a he y e al. (2022), h ee es s a e pe o med
on absolu e and squa ed e u ns. These es s
a e modi ied R/S s a is ics o Lo (1991), and
wo semipa ame ic es ima es o Hu s coe -
icien , which a e he long pe iodog am (GPH)
es ima e o Geweke and Po e -Hudak (1983)
and Gaussian semipa ame ic (GSP) es ima e
o Robinson (1995). Tab. 2 clea ly indica es
ha bo h GPH and GSP es s e i y he p es-
ence o long memo y o all asse s in absolu e
and squa ed e u ns a e y high p obabili y.
The same applies o he Lo’s R/S es , excep
o he case o OMXR. This means ha he use
o he FIAPARCH model is jus i ied.
Tab. 3 shows he es ima ed pa ame e s
o he FIAPARCH model o all asse s, and
also he Ljung-Box Q-s a is ics o le el and
squa ed esiduals. The FIAPARCH model i s
well o all ime se ies, excep o he Slo a-
kian SAX index, whe e symme ic FIGARCH is
used ins ead. In all cases, δ pa ame e is
highly s a is ically signi ican , which means
ha all asse s display s ong e idence
o ola ili y asymme y.
In he se en ou o wel e cases, γ pa-
ame e is posi i e and signi ican , sugges ing
ha nega i e shocks a ec ola ili y mo e han
posi i e shocks, which is s ong e idence ha
he le e age e ec exis s in he s ock ma ke s.
In addi ion, all d pa ame e s a e highly s a is i-
cally signi ican , which means ha he long
memo y GARCH model can cap u e he long-
ange memo y phenomenon. All ν pa ame e s
a e signi ican a 99% p obabili y, indica ing ha
S uden dis ibu ion ecognizes a - ail p ope -
ies o he ime se ies e y well. The Ljung-Box
es esul s sugges ha he esiduals a e ee
o au oco ela ion and he e oscedas ici y is-
sues and a e he e o e sui able o he dynamic
CVaR calcula ion.
Fig. 2 p esen s he log e u ns o he selec -
ed asse s and he wo dynamic VaR and CVaR
isks, calcula ed a 95% p obabili y. Fig. 2 clea -
ly shows ha ex eme isk is p esen in he ob-
se ed sample, which is especially e iden
in ea ly 2020 when he pandemic e up ed and
in ea ly 2022 when he wa in Uk aine s a ed.
The pape ies o es ima e he mul iscale
spillo e e ec in di e en ime ho izons. In his
ega d, e e y dynamic downside CVaR ime
se ies is ans o med in o h ee wa ele scales:
scale 1 (2–4 days), scale 5 (32–64 days), and
scale 6 (64–128 days). We conside ed only hese
h ee scales in o de o a oid esul s o e load.
B en POL CZE HUN SLK LIT LAT EST SLO ROM BUL CRO
Panel A: Va iance equa ion
α0.248** 0.186 −0.152 0.152** 0.618*** −0.467 −0.216 0.315 0.137 0.138 −0.109 −0.001
β0.476*** 0.316*** −0.034 0.360*** 0.189 −0.409 −0.181 0.281 0.165 0.311*** −0.046 0.086
γ0.472* 0.997*** 0.518*** 0.437*** NA −0.018 0.244** −0.026 0.192*** 0.390*** 0.080 0.075
δ1.532*** 1.443*** 1.692*** 1.669*** NA 1.637*** 1.767*** 1.955*** 1.689*** 1.554*** 1.572*** 1.651***
d0.309*** 0.188*** 0.214*** 0.296*** 0.371*** 0.320*** 0.252*** 0.326*** 0.264*** 0.297*** 0.234*** 0.303***
ν4.509*** 8.034*** 5.931*** 9.991*** 2.139*** 4.089*** 3.243*** 4.150*** 4.792*** 4.836*** 4.357*** 3.881***
Panel B: Diagnos ic es s
LB(Q) 0.272 0.247 0.529 0.783 0.369 0.329 0.212 0.402 0.377 0.171 0.535 0.222
LB(Q2)0.220 0.293 0.652 0.316 0.428 0.476 0.994 0.511 0.118 0.960 0.579 0.998
No e: ***, **, * indica e signi icance a 1, 5 and 10% le el, espec i ely; LB(Q) and LB(Q2) es s deno e p- alues
o he Ljung-Box Q-s a is ics o he le el and squa ed esiduals o 10 lags.
Sou ce: own
Tab. 3: Es ima ed FIAPARCH models o he selec ed asse s
Finance
193
2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
Fig. 2: Calcula ed ex eme downside and upside isk ime se ies o he s ock indices
and B en
Sou ce: own
Fig. 3: Th ee wa ele de ails o B en oil
Sou ce: own
Finance
194 2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015
The i s scale co esponds o he sho - e m ho-
izon, whe eas he i h and six h scales a e e-
ga ded as mid- e m and long- e m, espec i ely.
Fig. 3 shows h ee ans o med wa ele ime se-
ies o B en oil using he MODWT me hodology.
3. Resul s and discussion
3.1 Resul s
This sec ion p esen s he esul s o he es-
ima ed wa ele -based wo-s a e Ma ko
swi ching model. S a e 1 (2) e e s o he c isis
( anquil) pe iod, espec i ely. Tab. 4 shows
he esul s o egime-dependen ϕ pa ame e s,
ansi ion p obabili ies, a e age expec ed du-
a ion o each egime and egime-speci ic e -
o a iances. All hese alues a e calcula ed
in espec o he h ee wa ele de ails. I can be
seen ha he egime pa ame e s a e di e en
ac oss he egimes, wa ele scales and coun-
ies, which jus i ies he use o he wa ele -
based MS model.
Mos o he egime-dependen pa ame e s
a e highly s a is ically signi ican , which means
ha he ex eme isk spillo e phenomenon ex-
is s om B en oil o s ock ma ke s in CEECs.
On he o he hand, he s a is ically signi ican
pa ame e s a e posi i e and in line wi h logic
in mos cases, which sugges s ha when ex-
eme isk ises in he oil ma ke , he ise o isk
in s ock ma ke s ollows. Only in a ew cases,
we ind s a is ically signi ican nega i e pa ame-
e s, which means ha ising isk in he oil ma -
ke ac ually dec eases ex eme isk in he s ock
ma ke . Howe e , hese pa ame e s a e e y
low, indica ing ha his coun e in ui i e phe-
nomenon is e y weak and almos non-exis en .
Obse ing Panel A in Tab. 4, which po ays
he sho - e m ho izon, i can be seen ha ela-
i ely s ong spillo e e ec exis s in bo h c isis
and anquil egimes. I is in e es ing o no e ha
almos always, one egime pa ame e is sig-
ni ican ly highe han he o he , sugges ing ha
he spillo e e ec happens dominan ly in one
egime. In pa icula , ela i ely high s a is ically
signi ican pa ame e s a e ound in Czechia,
Hunga y and Romania in he c isis egime,
POL CZE HUN SLK LIT LAT EST SLO ROM BUL CRO
Panel A: D1 wa ele scale
ϕ10.003 0.114*** 0.195*** −0.009 0.091 −0.037 −0.010 0.018*** 0.309*** 0.008 0.042***
ϕ20.170*** −0.002 0.000 −0.280 −0.004 0.024*** 0.324*** 0.436*** −0.004 0.273*** 0.484***
P11 0.920 0.840 0.710 0.900 0.750 0.760 0.930 0.930 0.850 0.930 0.960
P22 0.750 0.920 0.920 0.790 0.970 0.950 0.770 0.700 0.800 0.730 0.720
ED112.300 6.300 3.500 9.700 4.000 4.100 15.000 14.100 1.200 15.100 23.800
ED24.000 12.200 11.900 4.800 32.000 18.50 4.400 3.300 5.000 3.700 3.600
σ2
1−3.980*** −2.410*** −2.110*** −3.030*** −1.530*** −1.280*** −3.360*** −3.570*** −1.790*** −3.980*** −3.840***
σ2
2−2.410*** −4.220*** −3.800*** −0.980*** −3.860*** −3.150*** −1.480*** −1.740*** −3.780*** −2.350*** −1.840***
Panel B: D5 wa ele scale
ϕ10.163*** 0.370*** −0.002 −0.076*** 0.256*** 0.296*** 0.323*** 0.313*** 0.114*** 0.250*** 0.330***
ϕ20.351*** 0.091*** 0.500*** 0.018 −0.005 0.059*** 0.094*** 0.012** 0.449*** −0.027*** 0.014***
P11 0.980 0.940 0.980 0.970 0.950 0.950 0.940 0.950 0.760 0.950 0.950
P22 0.930 0.980 0.950 0.960 0.980 0.990 0.980 0.980 0.240 0.970 0.980
ED148.400 17.700 41.100 36.300 20.300 21.800 16.300 20.600 4.200 20.100 20.800
ED215.100 41.000 19.600 26.800 50.800 74.100 41.400 62.800 1.300 31.000 66.200
σ2
1−2.960*** −1.520*** −3.070*** −3.510*** −1.920*** −1.120*** −1.600*** −1.750 −2.720*** −2.380*** −1.600***
σ2
2−1.530*** −3.180*** −1.340*** −2.060*** −3.890*** −2.970*** −3.290*** −3.570 −1.370*** −4.100*** −3.510***
Tab. 4: Es ima ed wa ele -based Ma ko swi ching models – Pa 1