Sanusi, Kazeem Abimbola; Dickason Koekemoe , Zand i
A icle
Dynamics be ween o eign po olio in es men , s ock
p ice and inancial de elopmen in Sou h A ica: A SVAR
app oach
Economies
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MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Sanusi, Kazeem Abimbola; Dickason Koekemoe , Zand i (2025) : Dynamics
be ween o eign po olio in es men , s ock p ice and inancial de elopmen in Sou h A ica: A SVAR
app oach, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 1, pp. 1-16,
h ps://doi.o g/10.3390/economies13010008
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Ci a ion: Sanusi, K. A., &
Dickason-Koekemoe , Z. (2025).
Dynamics Be ween Fo eign Po olio
In es men , S ock P ice and Financial
De elopmen in Sou h A ica: A SVAR
App oach. Economies,13(1), 8.
h ps://doi.o g/10.3390/
economies13010008
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economies
A icle
Dynamics Be ween Fo eign Po olio In es men , S ock P ice
and Financial De elopmen in Sou h A ica: A SVAR App oach
Kazeem Abimbola Sanusi * and Zand i Dickason-Koekemoe
T ade Resea ch Uni , Economic and Managemen Sciences, No h-Wes Uni e si y, Po che s oom 2520,
Sou h A ica; [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac : The goal o his s udy is o look in o he dynamic ela ionship be ween s ock p ices,
o eign po olio in es men , and inancial de elopmen in he Sou h A ican economy.
Fede al Rese e Economic Da a (FRED) p o ided qua e ly ime se ies da a om 1960
(Q1) o 2024 (Q2). This s udy uses a s uc u al VAR es ima ion app oach and dynamic
condi ional co ela ion (DCC GARCH model). The DCC GARCH app oach displays ime-
a ying co ela ions be ween s ock p ices, c edi gi en o he p i a e sec o as a measu e
o inancial g ow h, and o eign po olio in es men s. The dynamic links be ween s ock
p ices, inancial de elopmen , and o eign p i a e in es men (FPI) a e examined using
he SVAR echnique. Ou indings show ha a inancial de elopmen shock encou ages
and p o okes a subs an ial in lux o o eign po olio in es men in o he Sou h A ican
economy. This sugges s ha o e seas po olio in es men s eac a o ably and no ably
well o a o able shocks in he inancial de elopmen p ocess. We sugges ha a s able
inancial sys em amewo k and lowe c edi cos s would s eng hen he impac o highe
s ock p ices on p i a e sec o c edi and gua an ee ha highe s ock p ices ha e a bene icial
impac on o he inancial de elopmen me ics. Be e inancial de elopmen me ics, such
as c edi o he p i a e sec o , will he e o e inc ease o eign po olio in es men .
Keywo ds: FPI; s ock p ice; inancial de elopmen ; SVAR
1. In oduc ion
The Sou h A ican economy like any o he economy can be g ea ly a ec ed by he
in ica e ela ionship ha exis s be ween o eign po olio in es men (FPI), s ock p ices,
and inancial de elopmen . FPI e e s o in es men s made by o eign in es o s in a
coun y’s s ock ma ke s, bonds, o o he inancial asse s wi hou seeking con ol o e he
companies. Financial esou ces a e mos commonly ans e ed h ough o eign di ec
in es men (FDI) and o eign po olio in es men (FPI). Due o he leng hy and one ous
equi emen s associa ed wi h FDI, which is a long- e m in es men , in es o s always p e e
FPI o e FDI Shah (2023).
FPI p o ides an in lux o capi al in o he hos coun y, which can help inance de el-
opmen p ojec s, s abilize he cu ency, and deepen he inancial ma ke s. The in low o
FPI ends o inc ease demand o equi ies, leading o highe s ock p ices. Con e sely, an
ou low o FPI can dep ess s ock p ices. S ock p ices a e o en seen as a ba ome e o a
coun y’s economic heal h. Rising s ock p ices ypically indica e in es o con idence, while
alling p ices sugges he opposi e (Rajan & Zingales,1998,2003;He wa z & Walle,2014).
Fo eign po olio in es men (FPI) plays a c i ical ole in he global inancial ecosys em,
o e ing bo h oppo uni ies and challenges o eme ging and de eloped ma ke s alike. As
Economies 2025,13, 8 h ps://doi.o g/10.3390/economies13010008
Economies 2025,13, 8 2 o 16
a o m o in e na ional capi al low, FPI in ol es o eign in es o s pu chasing domes ic
secu i ies, such as s ocks and bonds, wi hou aking di ec con ol o e he companies. This
in low o capi al can signi ican ly in luence domes ic inancial ma ke s, pa icula ly s ock
p ices, and con ibu e o he b oade p ocess o inancial de elopmen .
O e he pas ew decades, he globaliza ion o inancial ma ke s has acili a ed he
inc eased mobili y o capi al ac oss bo de s. This su ge in FPI has been d i en by se e al
ac o s, including he libe aliza ion o inancial ma ke s, echnological ad ancemen s, and
he ques o highe e u ns in eme ging economies. Howe e , he implica ions o hese
in es men s a e complex and mul i ace ed, as hey can lead o bo h posi i e and nega i e
ou comes o he hos economies (Sanusi & Kapingu a,2022).
The ela ionship be ween FPI and s ock p ices is one o he mos ex ensi ely s udied
a eas wi hin he ield o in e na ional inance. I has been a gued ha he s ock ma -
ke is c ucial in d awing in o eign in es o s. Fo eign in es o s’ con idence is bols e ed
by ising s ock ma ke e u ns, which in u n mo i a es hem o make addi ional s ock
ma ke in es men s.
S ock p ices, as a ba ome e o economic heal h and in es o sen imen , a e highly
sensi i e o he in lows and ou lows o o eign capi al. An inc ease in FPI o en leads
o a ise in s ock p ices due o a heigh ened demand o domes ic secu i ies. Con e sely,
sudden wi hd awals o FPI can igge sha p declines in s ock p ices, exace ba ing ma ke
ola ili y. This dynamic in e ac ion be ween FPI and s ock p ices highligh s he signi icance
o o eign capi al in shaping domes ic inancial ma ke s. Ne e heless, he majo i y o
empi ical esea ch ha has been unde aken so a has ocused on how FDI a ec s s ock
p ices, paying e y li le a en ion o how s ock p ices a ec FPI. A ailable s udies include
among o he s Aqeel e al. (2004), Lo e and Lage-Hidalgo (2000) and F oo and S ein (1991).
On he o he hand, FPI is heo e ically mo e likely han FDI o ha e a di ec and no iceable
impac on s ock p ices (Shabbi & Muhammad,2019). Among he ew known s udies
on he nexus be ween FPI and s ock p ices is Shabbi and Muhammad (2019). Shabbi
and Muhammad (2019) examined by means o au o eg essi e dis ibu ed lag (ARDL) he
long un ela ionships be ween s ock p ices and FPI. Thei indings es ablished signi ican
ela ionships be ween FPI and s ock p ices in Pakis an.
Fu he mo e, i is impossible o igno e how FPI a ec s inancial de elopmen . The
e m “ inancial de elopmen ” desc ibes he ad ancemen o a na ion’s banking, s ock
ma ke , and egula o y amewo k sys ems, as well as hei dep h, accessibili y, and
e iciency. By inc easing liquidi y, boos ing ma ke e iciency, and encou aging he ans e
o inancial inno a ions and p ac ices, FPI can suppo inancial de elopmen . Howe e ,
hese ad an ages a e dependen on he hos na ion’s capaci y o con ol and success ully
manage in e na ional capi al lows in o de o educe dange s like asse bubbles and
inancial ins abili y. As no ed ea lie unde he ela ionship be ween FPI and s ock p ices
a gumen , much empi ical esea ch o da e has also concen a ed on he ela ionship
be ween FDI and inancial g ow h, wi h ela i ely less emphasis paid o he ela ionship
be ween FPI and inancial de elopmen (Se hi e al.,2022;Pham e al.,2022;Jena & Se hi,
2021;Tongu ai & Vi hesson hi,2020).
The in e play be ween FPI, s ock p ices, and inancial de elopmen is pa icula ly
p onounced in eme ging ma ke s, whe e inancial sys ems a e o en less ma u e and
mo e suscep ible o ex e nal shocks. In hese economies, he in lux o o eign capi al can
s imula e inancial de elopmen by p o iding much-needed unds o in es men and
inno a ion. Howe e , he ola ili y associa ed wi h FPI can also pose signi ican isks,
leading o boom-and-bus cycles ha can unde mine economic s abili y and hinde long-
e m g ow h (Rashid & Husain,2011;Rashid,2010;O ke -Robe e al.,2007;S e ens,2006).
Economies 2025,13, 8 3 o 16
They con ended ha he hos na ion aces challenges as a esul o capi al in lows, such as
he eal app ecia ion o hei na ional cu encies.
In de eloped ma ke s, while he inancial sys ems a e ypically mo e obus , he
in luence o FPI emains signi ican . Fo eign in es men s can d i e ma ke ends, in luence
mone a y policy, and e en a ec exchange a es. The in e connec edness o global inancial
ma ke s means ha de elopmen s in one egion can ha e a - eaching implica ions o
o he s, unde sco ing he impo ance o unde s anding he dynamics o FPI in he con ex
o inancial de elopmen (Ane o ,2020;Adams e al.,2014).
This esea ch a emp ed o explo e he in ica e ela ionship be ween o eign po -
olio in es men , s ock p ices, and inancial de elopmen in he Sou h A ican economy.
Consequen ly, his s udy p o ides insigh s in o how FPI in luences s ock ma ke beha io
and con ibu es o he inancial de elopmen o hos economies. Addi ionally, he s udy
p o ides policy ecommenda ions o ensu e ha he bene i s o o eign po olio in lows
a e maximized while minimizing he isks o inancial ins abili y. Though he esea ch
seeks o con ibu e o he b oade discou se on he ole o in e na ional capi al lows in
shaping he global inancial landscape, his s udy speci ically con ibu es o he empi ical
e idence in he Sou h A ican economy. Ou discussion is ou lined as ollows: Sec ion 2
o he discussion con inues wi h an o e iew o he empi ical li e a u e, Sec ion 3del es
in o he empi ical s a egy, he empi ical esul s a e in Sec ion 4, and Sec ion 5includes a
inal commen .
2. Li e a u e Re iew: Theo e ical Pe spec i es and Empi ical E idence
2.1. Theo e ical Pe spec i es
The con en ional capi al asse p icing model (CAPM) s a es ha changes in he de-
mand o pa icula inancial asse s can ha e an impac on s ock p ices h ough o eign
in es men lows. Assuming ha he supply o s ocks is compa a i ely inelas ic in he nea
un, he demand o local equi ies inc eases as o eign in es o s inc ease hei holdings o
hese s ocks.
Acco ding o he “ma ke e iciency” heo y, s ock p ices a e upda ed o e lec all
a ailable in o ma ion. Fo eign in es o s may in oduce s onge co po a e go e nance
no ms, isk di e si ica ion echniques, and mo e in o ma ion when hey join a ma ke . The
addi ional sc u iny may esul in mo e e ec i e s ock p icing. Fu he mo e, as o eign
in es o s equen ly insis on anspa ency and compliance wi h in e na ional accoun -
ing and egula o y s anda ds, he e may be less in o ma ion asymme y as a esul o
o eign in es men .
The “push and pull” pa adigm is an al e na i e iewpoin ha posi s ex e nal (e.g.,
global liquidi y ci cums ances) and in e nal (e.g., domes ic ma ke po en ial) a iables
as he d i ing o ces behind s ock p ice changes in eme ging ma ke s. These a iables
in luence FPI, which can a ec s ock p ices in bo h s abilizing and des abilizing ways.
While ab up wi hd awals, o “capi al ligh ,” can esul in s eep co ec ions and inc eased
ma ke ola ili y, a signi ican in low o o eign capi al has he po en ial o push s ock p ices
abo e hei undamen als and c ea e bubbles.
Empi ical E idence
One o he mos ho ly con es ed opics in he inance li e a u e is how s ock p ices
and inancial de elopmen a e a ec ed by FPI. FPI can add ola ili y e en as i inc eases
ma ke dep h and liquidi y, especially in coun ies wi h less es ablished inancial sys ems.
The heigh ened sensi i i y o o eign in es o s o ex e nal shocks, such as shi s in global
in e es a es o isk sen imen , migh esul in massi e capi al ligh du ing unce ain
imes. Acco ding o Claessens and Fo bes’ (2013), while o eign in es o s equen ly use
Economies 2025,13, 8 4 o 16
long- e m in es men s o s abilize ma ke s, hey can also inc ease ola ili y du ing imes
o c isis.
In de eloping and eme ging ma ke s, FPI has o en been linked wi h highe s ock
p ice ola ili y due o he specula i e na u e o some o eign in es men s. Fo ins ance,
s udies by Bekae and Ha ey (1995) highligh ha while o eign in es men con ibu es o
ma ke de elopmen , i also inc eases ulne abili y o global shocks. This ola ili y a ises
due o sudden changes in global in e es a es o geopoli ical condi ions, leading o sha p
in lows o ou lows o capi al.
Acco ding o Le ine and Ze os (1998), FPI has a a o able impac on he g ow h o
s ock ma ke s and has a majo impac on eme ging ma ke capi aliza ion, u no e a ios,
and s ock ma ke liquidi y. S udies by E unza (2001) and Edison and Wa nock (2003),
among o he s, ha e shown ha s ock ma ke in eg a ion ia FPI lowe s a company’s cos
o capi al and p omo es mo e e ec i e esou ce alloca ion wi hin an economy.
A bidi ec ional associa ion be ween FPI and inancial de elopmen has been p o en
by nume ous s udies. While in e na ional in es o s a o na ions wi h compe en inancial
ins i u ions and well- unc ioning capi al ma ke s, inancial de elopmen may, on he one
hand, d aw in mo e o eign po olio in es men . Con e sely, FPI can ad ance inancial
de elopmen h ough s eng hening inancial ma ke s, inc easing ma ke liquidi y, and
encou aging i al y be ween local inancial ins i u ions. As hey o e an en i onmen ha
is a o able o in es o s, O che e e al. (2016) no ed ha na ions wi h highly de eloped
inancial sys ems ypically d aw mo e o eign di ec in es men (FPI). This is consis en
wi h o he s udies such as Hajilee and Al Nasse (2015) and Agbloyo e al. (2013). Hajilee
and Al Nasse (2015) ha e demons a ed ha he e is a mu ually ein o cing ela ionship
in La in Ame ican na ions be ween de eloped inancial sys ems and o al o eign di ec
in es men (FDI). They a gued ha inancial changes aimed a bols e ing inancial ma ke s
a e spa ked by inwa d o eign di ec in es men . By lowe ing he cos o capi al and
imp o ing accessibili y o inancial se ices, hese e o ms encou age mo e FDI in lows.
They conclude ha enhancing he de elopmen o inancial ma ke s can help na ions a ac
mo e o eign in es men , which will eed back in o he g ow h o he inancial sec o and
enhance in es men o e all.
On he o he hand, I andous (2021) inds e idence o unidi ec ional causali y om
inancial de elopmen o capi al in low as o eign capi al in low is ound no o ha e
an impac on inancial de elopmen . They demons a ed how inancial de elopmen
o e ed inance and inancial se ices a a lowe cos o in es men expansion o o e seas
businesses and hei local connec ions. Hos na ions may become mo e appealing o o eign
di ec in es men (FDI) i hey ha e a solid inancial sys em, obus in es o p o ec ion,
and imp o ed go e nance laws. Po en ial imbalances may esul om eme ging ma ke s’
inancial de elopmen equen ly lagging behind he in low o o eign capi al. He mes
and Lensink (2003) disco e ed, o ins ance, ha he ad an ages o FPI a e g ea es in
na ions wi h sophis ica ed inancial ma ke s capable o ecei ing and dis ibu ing he
in lows e ec i ely. La ge FPI in lows, on he o he hand, migh cause inancial ins abili y
in less de eloped inancial sys ems since he local ma ke canno handle he ab up su ge
in liquidi y. Simila ly, using he sys em GMM es ima o , Pham e al. (2022) examined
he ela ionships be ween inancial de elopmen and o eign di ec in es men (FDI) and
demons a ed ha highe le els o inancial de elopmen a ac ed mo e inbound FDI o
hos na ions.
Con e sely, Geb ehiwo (2016) did no es ablish a signi ican connec ion be ween
o eign di ec in es men (FDI) and inancial de elopmen in eigh coun ies in Sub-Saha an
A ica (SSA) be ween 1991 and 2013. They concluded ha he e is insu icien e idence o
suppo he claim ha o eign capi al in low and inancial de elopmen a e ela ed using
Economies 2025,13, 8 5 o 16
bo h he G ange causali y es and he wo-s age leas squa es (2SLS). This is consis en
wi h indings o Sahin and Ege (2015) as hey also ound inconclusi e e idence be ween
o eign capi al in low and a de eloped inancial sys em.
3. Da a Sou ces and Me hod
3.1. Da a Desc ip ion and Summa y
Fede al Rese e Economic Da a (FRED) se ed as he sou ce o he qua e ly ime se ies
da a spanning om 1960 (Q1) o 2024 (Q2). Mo e p ecisely, da a on o eign po olio in low
(FPI) and c edi alloca ed o he p i a e sec o (CA) as a p oxy o inancial de elopmen
we e sou ced om FRED. Da a on s ock p ices we e indexed by sha e p ice and he da a
we e ob ained om he O ganiza ion o Economic Co-ope a ion and De elopmen (OECD).
The g aphical ep esen a ion o he a iables is p esen ed in Figu e 1. The a iables ha e
been gene ally no ed o obse e an upwa d end, wi h he excep ion o o eign po olio
in es men whe e sha p decline can be obse ed a ound he yea 2020. The sha p decline
a ound his pe iod could be a ibu ed o he wo ld-wide economic closu e associa ed wi h
COVID-19. In addi ion, ou a iables could also be obse ed o be non-s a iona y. Hence,
we in es iga ed he s a iona y p ope y o he se ies and we ound ha he all he a iables
a e s a iona y in hei i s di e enced le el. The g aphical ep esen a ion o he a iables
in hei di e enced o m is con ained in Figu e 2.
The pai wise co ela ion coe icien s, o s a ic co ela ion coe icien s, a e shown in
Figu e 3. As an icipa ed, he e is li le co ela ion be ween he a iables unde in es iga ion.
Howe e , because hey do no e lec he co ela ion changes ha ake place o e ime, hese
co ela ion coe icien s a e s a ic. Only he con empo aneous o ins an aneous ela ionship
h oughou ime is shown. The cu en s udy examines he ime- a ying co ela ion
be ween he a iables using dynamic condi ional co ela ion (DCC GARCH). The DCC
GARCH app oach e eals ime- a ying co ela ion be ween o eign po olio in es men ,
s ock p ices, and c edi alloca ed o p i a e sec o as a measu e o inancial de elopmen .
While SVAR app oach enables us o ob ain he con empo aneous shocks be ween o eign
p i a e in es men (FPI), s ock p ices, and inancial de elopmen .
Economies 2025, 13, x FOR PEER REVIEW 5 o 17
e idence o suppo he claim ha o eign capi al in low and inancial de elopmen a e
ela ed using bo h he G ange causali y es and he wo-s age leas squa es (2SLS). This
is consis en wi h indings o Sahin and Ege (2015) as hey also ound inconclusi e e i-
dence be ween o eign capi al in low and a de eloped inancial sys em.
3. Da a Sou ces and Me hod
3.1. Da a Desc ip ion and Summa y
Fede al Rese e Economic Da a (FRED) se ed as he sou ce o he qua e ly ime
se ies da a spanning om 1960 (Q1) o 2024 (Q2). Mo e p ecisely, da a on o eign po olio
in low (FPI) and c edi alloca ed o he p i a e sec o (CA) as a p oxy o inancial de el-
opmen we e sou ced om FRED. Da a on s ock p ices we e indexed by sha e p ice and
he da a we e ob ained om he O ganiza ion o Economic Co-ope a ion and De elop-
men (OECD). The g aphical ep esen a ion o he a iables is p esen ed in Figu e 1. The
a iables ha e been gene ally no ed o obse e an upwa d end, wi h he excep ion o
o eign po olio in es men whe e sha p decline can be obse ed a ound he yea 2020.
The sha p decline a ound his pe iod could be a ibu ed o he wo ld-wide economic clo-
su e associa ed wi h COVID-19. In addi ion, ou a iables could also be obse ed o be
non-s a iona y. Hence, we in es iga ed he s a iona y p ope y o he se ies and we ound
ha he all he a iables a e s a iona y in hei i s di e enced le el. The g aphical ep e-
sen a ion o he a iables in hei di e enced o m is con ained in Figu e 2.
Figu e 1. Mo emen o he a iables o e he s udy pe iod.
Figu e 1. Mo emen o he a iables o e he s udy pe iod.
Economies 2025,13, 8 6 o 16
Economies 2025, 13, x FOR PEER REVIEW 6 o 17
Figu e 2. Plo o he a iables in hei di e enced o ms.
The pai wise co ela ion coe icien s, o s a ic co ela ion coe icien s, a e shown in
Figu e 3. As an icipa ed, he e is li le co ela ion be ween he a iables unde in es iga-
ion. Howe e , because hey do no e lec he co ela ion changes ha ake place o e
ime, hese co ela ion coe icien s a e s a ic. Only he con empo aneous o ins an aneous
ela ionship h oughou ime is shown. The cu en s udy examines he ime- a ying co -
ela ion be ween he a iables using dynamic condi ional co ela ion (DCC GARCH). The
DCC GARCH app oach e eals ime- a ying co ela ion be ween o eign po olio in es -
men , s ock p ices, and c edi alloca ed o p i a e sec o as a measu e o inancial de el-
opmen . While SVAR app oach enables us o ob ain he con empo aneous shocks be ween
o eign p i a e in es men (FPI), s ock p ices, and inancial de elopmen .
Figu e 2. Plo o he a iables in hei di e enced o ms.
Economies 2025, 13, x FOR PEER REVIEW 6 o 17
Figu e 2. Plo o he a iables in hei di e enced o ms.
The pai wise co ela ion coe icien s, o s a ic co ela ion coe icien s, a e shown in
Figu e 3. As an icipa ed, he e is li le co ela ion be ween he a iables unde in es iga-
ion. Howe e , because hey do no e lec he co ela ion changes ha ake place o e
ime, hese co ela ion coe icien s a e s a ic. Only he con empo aneous o ins an aneous
ela ionship h oughou ime is shown. The cu en s udy examines he ime- a ying co -
ela ion be ween he a iables using dynamic condi ional co ela ion (DCC GARCH). The
DCC GARCH app oach e eals ime- a ying co ela ion be ween o eign po olio in es -
men , s ock p ices, and c edi alloca ed o p i a e sec o as a measu e o inancial de el-
opmen . While SVAR app oach enables us o ob ain he con empo aneous shocks be ween
o eign p i a e in es men (FPI), s ock p ices, and inancial de elopmen .
Figu e 3. Plo o he pai wise co ela ion coe icien s.
This s udy a emp ed o explo e he in ica e ela ionship be ween o eign po olio in es -
men , s ock p ices, and inancial de elopmen in he Sou h A ican economy using a dynamic
condi ional co ela ion (DCC GARCH model) and s uc u al VAR es ima ion app oach.
3.2. GARCH-DCC Model
Dynamic condi ional co ela ion (DCC) is a mul i a ia e model known as GARCH-
DCC (Engle,2001;Engle & Sokalska,2012;Engle & Rangel,2008;Engle,1993).
To in es iga e ime- a ying co ela ions in con as o s a ic co ela ions, he DCC
model is used. Using maximum likelihood es ima ion (MLE) echniques, he s a ed
GARCH(p,q) model is es ima ed. The ollowing equa ions se e as i s ep esen a ion,
wi h se ing as a esidual om he i ed VAR equa ion.
=θ0+ϵ (1)
Economies 2025,13, 8 7 o 16
ϵ ∼0, σ2
logσ2
=α0+∑p
j=1βjlogσ2
−j+∑q
i=1αiϵ2
−i(2)
Since mean emo al om he VAR esidual se ies has al eady been pe o med,
ϵ
is hen
a s anda dised dis u bance e m. The unc ion ha yields he log o ola ili y o
ϵ
is i s
own lagged alues and lagged s anda dised dis u bance e ms. β′s ands o he GARCH
e ec s, whe eas
α′
s indica es he ola ili y’s pe sis ence. The R s a is ics package uses he
subsequen DCC a ian o es ima ion:
Q =(1−α−β)Q+αz z′
+βQ −1(3)
whe e
z
is he esiduals om GARCH’s ha has been s anda dized,
β
and
α
a e he co e-
la ion coe icien s which a e pe sis en in na u e,
Q
is he dynamic condi ional co ela ion
while
Q
is he o iginal co ela ion ma ix when
=
0 a
Q=Q =0
.
Q =0
is he ime- a ying
co ela ion o GARCHS esiduals ha ha e al eady been s anda dized, which gi es insigh
in o he ime- a ying con empo aneous ela ionships amongs he a iables.
3.3. S uc u al Vec o Au o eg ession Model (SVAR)
A ai ly b oad me hod o modeling mul i a ia e ime se ies is he use o ec o au-
o eg essi e (VAR) models. The inabili y o hose models o cha ac e ize con empo aneous
ela ionships be ween he a iables unde analysis is a signi ican law in hei con en ional
o m. This becomes a key conce n in he impulse esponse analysis o hese models, whe e
unde s anding he immedia e consequences o an economic shock is c ucial. In o de o
add ess his, esea che s ypically use o hogonal impulse esponses, whe e he (lowe )
Cholesky decomposi ion o he e o co a iance ma ix yields he co ela ion be ween
he e o s. To do his, hey mus se up he model’s a iables in a sui able sequence. An
al e na i e o his s a egy is he employmen o so-called s uc u al ec o au o eg essi e
(SVAR) models, which mo e di ec ly model he link be ween con empo aneous a iables.
The educed o m o VAR model can be s a ed as ollows:
y =A1y −1+µ wi h µ ∼(0, Σ)(4)
whe e
y
is a
k×
1 ec o o
k
a iables in pe iod
.
A1
is a
k×k
coe icien ma ix,
∈
is
a
k×
1 ec o o e o s, which ha e a mul i a ia e no mal dis ibu ion wi h ze o mean
as well as
k×k
a iance-co a iance ma ix
Σ
. The a iance–co a iance ma ix mus be
examined mo e ho oughly in o de o comp ehend SVAR models.
Co a iances o he e o s on he o -diagonal elemen s and a iances o he endogenous
a iable on he diagonal elemen s a e included. In o ma ion ega ding he con empo ane-
ous e ec s o each a iable on he o he s is con ained in he co a iances. The componen s o
he op- igh o he diagonal ( he “uppe iangula ”) mi o he elemen s o he bo om-le
o he diagonal ( he “lowe iangula ”), indica ing ha he co a iance ma ices o ypical
VAR models a e symme ic. The no ion ha he ela ionships be ween he endogenous
a iables simply ep esen co ela ions and do no pe mi claims o causal linkages is
e lec ed in his. SVAR models, which place unique cons ain s on he co a iance ma ix
and, depending on he model, on o he coe icien ma ices as well, a e used o analyze
con empo aneous causali y, o mo e speci ically, he s uc u al links be ween he a iables.
The SVAR model is es ima ed using he Zhang and Chen (2015) app oach, which
gua an ees ha he model is una ec ed by uni - oo issues and allows o he inclusion o
Economies 2025,13, 8 8 o 16
all a iables in le els and an inc ease in he numbe o deg ees o eedom. The es ima ed
SVAR model wi h lag leng h p, SVAR(p), is s a ed as ollows:
C0y =∏Iy −1+∏2y −2+. . . +∏Py −p+µ , =1, 2 . . . .T. (5)
whe e
y =
FPI
SP
CA
,C0=
1−C12 −C13
−C21 1−C23
−C31 −C32 1
,∏i=
γ(i)
11 γ(i)
12 γ(i)
13
γ(i)
21 γ(i)
22 γi
23
γ(i)
31 γ(i)
32 γ(i)
33
,
i=1, 2, . . . , p,µ ,=
µ1
µ2
µ3
The SVAR model is sensi i e o he lag leng h p, which is ypically asce ained using AIC
(Akaike in o ma ion c i e ion) and SC (Schwa z c i e ion). The model’s lag leng h (p) in
his empi ical e o is 2.
4. Resul s
4.1. S a iona y Resul s
The s a iona i y o he unde lying a iables is assumed by many s a is ical es s.
These es s may yield alse esul s ega ding he ela ionships be ween he a iables i he
a iables a e non-s a iona y. Hence, a ime se ies’ s a iona i y gua an ees ha i s s a is ical
cha ac e is ics, including i s mean, a iance, and au oco ela ion, will no change o e
ime. This enables models o p oduce consis en and us wo hy o ecas s. To his end,
we examined he s a iona i y p ope ies o he a iables using ADF and PP uni oo es s
as con ained in Table 1. Ou indings show ha all ou a iables a e s a iona y a e i s
di e ence. This also con i ms he e idence om he end analysis.
Table 1. Uni oo es esul s.
Va iables ADF p-Value PP p-Value
Wi h In e cep Wi hou In e cep Wi h In e cep Wi hou In e cep
FPI 0.0876 0.0712 0.0765 0.0000
SP 0.3781 0.6129 0.8174 0.0000
CA 0.3167 0.4123 0.24 0.0019
D(FPI) 0.0000 0.0001 0.00062 0.0003
D(SP) 0.00001 0.00003 0.0000 0.0000
D(CA) 0.0000 0.0000 0.0003 0.0000
4.2. DCC GARCH Resul s
The se ies’ s a iona y p ope y was in es iga ed, and he a iables ha e been es ab-
lished o be I(1). “DL” is appended o he le el a iable name o indica e di e enced
a iables. A DCC GARCH model is hen i ed o hese di e enced a iables. Models we e
c ea ed o he DCC wi h mul i a ia e skew S uden - dis ibu ion (ss d) and he DCC wi h
mul i a ia e S uden - dis ibu ion (s d). Howe e , he DCC wi h mul i a ia e S uden -
dis ibu ion was i ed o he s udy as i p oduced a lowe Akaike in o ma ion c i e ia.
The ime- a ying co ela ions amongs he a iables a e plo ed in Figu e 4. The dy-
namic co ela ion coe icien be ween o eign po olio in es men and s ock p ices a e
wholly posi i e wi h 0.15 being he highes coe icien and he lowes coe icien obse ed
Economies 2025,13, 8 15 o 16
men indica o s such as c edi alloca ed o he p i a e sec o will in u n boos o eign
po olio in es men .
Au ho Con ibu ions: Concep ualiza ion, K.A.S. and Z.D.-K.; me hodology, K.A.S.; so wa e, K.A.S.;
alida ion, K.A.S. and Z.D.-K.; o mal analysis, K.A.S.; in es iga ion, K.A.S. and Z.D.-K.; esou ces,
Z.D.-K.; da a cu a ion, K.A.S. and Z.D.-K.; w i ing—o iginal d a p epa a ion, K.A.S.; w i ing—
e iew and edi ing, K.A.S.; isualiza ion, K.A.S. and Z.D.-K.; supe ision, Z.D.-K.; p ojec admin-
is a ion, K.A.S. and Z.D.-K.; unding acquisi ion, Z.D.-K. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding: This esea ch is unded by No h-Wes Uni e si y, Sou h A ica.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : Da a on o eign po olio in low (FPI) and c edi alloca ed o he p i a e
sec o (CA) as a p oxy o inancial de elopmen we e sou ced om FRED. Da a on s ock p ices we e
indexed by sha e p ice and he da a we e ob ained om he O ganiza ion o Economic Co-ope a ion
and De elopmen (OECD).
Acknowledgmen s: We acknowledge No h-Wes Uni e si y, Sou h A ica o unding his esea ch.
Con lic s o In e es : The au ho s decla e no con lic s o in e es .
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au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
