Multiscale non-linear tale risk spillover effect from oil to stocks – The case of East European emerging markets

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 Finance 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 Finance 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. Finance 189 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) Finance 190 2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015 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 Finance 191 2024, olume 27, issue 3, pp. 186–200, DOI: 10.15240/ ul/001/2024-5-015 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