Examining the currency-equity nexus in frontier African markets: a wavelet-based approach

Gyasi, Gene ie e; F impong, Joseph Magnus; Mi eku, Kwame
A icle
Examining he cu ency-equi y nexus in on ie A ican
ma ke s: a wa ele -based app oach
Cogen Economics & Finance
P o ided in Coope a ion wi h:
Taylo & F ancis G oup
Sugges ed Ci a ion: Gyasi, Gene ie e; F impong, Joseph Magnus; Mi eku, Kwame (2024) : Examining
he cu ency-equi y nexus in on ie A ican ma ke s: a wa ele -based app oach, Cogen Economics
& Finance, ISSN 2332-2039, Taylo & F ancis, Abingdon, Vol. 12, Iss. 1, pp. 1-19,
h ps://doi.o g/10.1080/23322039.2024.2399947
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Examining he cu ency-equi y nexus in on ie
A ican ma ke s: a wa ele -based app oach
Gene ie e Gyasi, Joseph Magnus F impong & Kwame Mi eku
To ci e his a icle: Gene ie e Gyasi, Joseph Magnus F impong & Kwame Mi eku (2024)
Examining he cu ency-equi y nexus in on ie A ican ma ke s: a wa ele -based app oach,
Cogen Economics & Finance, 12:1, 2399947, DOI: 10.1080/23322039.2024.2399947
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© 2024 The Au ho (s). Published by In o ma
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FINANCIAL ECONOMICS | REVIEW ARTICLE
Examining he cu ency-equi y nexus in on ie A ican ma ke s: a
wa ele -based app oach
Gene ie e Gyasi
a
, Joseph Magnus F impong
b
and Kwame Mi eku
b
a
Depa men o En ep eneu ship and Business Science, Uni e si y o Ene gy and Na u al Resou ces, Fiap e, Ghana;
b
Depa men o Finance, School o Business, Kwame Nk umah Uni e si y o Science and Technology, Kumasi, Ghana
ABSTRACT
This esea ch examines he co-mo emen be ween exchange a es and equi y p ices in
a selec ion o on ie A ican ma ke s (Ghana, Mau i ius, and Tunisia). The analysis
encompasses da a om 4 Janua y 2010 o 31 Ma ch 2023. Employing ad anced econo-
me ic echniques, he s udy in es iga es he in e connec edness o on ie ma ke s
and he di ec ion o ola ili y spillo e s be ween cu ency and equi y ma ke s. Ou ind-
ings e el ha Ghana, Mau i ius, and Tunisia a e cha ac e ized by s ong sensi i i y o
p ice a ia ions and high ola ili y. Mo eo e , signi ican ola ili y ansmission and spill-
o e e ec s a e obse ed ac oss he selec ed ma ke s. Finally, he analysis inds he p es-
ence o non-linea dynamics in bo h he ime and equency domains. In ligh o hese
indings, policymake s and in es o s should inco po a e he po en ial o ab up and
pe sis en changes, as well as ola ili y spillo e s, in o hei decision-making p ocesses
when conside ing in es men s in he Ghana, Mau i ius, and Tunisia ma ke s. This
esea ch is an icipa ed o con ibu e o he de elopmen o mo e obus in es men
s a egies o managing isk exposu e wi hin di e si ied po olios.
IMPACT STATEMENT
This s udy in es iga es he ela ionship be ween cu ency and equi y ma ke s in on ie
A ican economies using a wa ele -based app oach. Focusing on Ghana, Mau i ius, and
Tunisia, i unco e s signi ican ola ili y spillo e s and complex, ime- a ying dynamics.
The indings e eal non-linea ma ke beha io s, emphasizing he need o adap i e
in es men s a egies in hese ola ile egions. By o e ing deepe insigh s in o he
cu ency-equi y nexus, he esea ch p o ides aluable guidance o in es o s and policy-
make s, enabling mo e in o med decision-making and he de elopmen o esilien s a -
egies o managing isks in on ie A ican ma ke s.
ARTICLE HISTORY
Recei ed 22 May 2024
Re ised 23 Augus 2024
Accep ed 29 Augus 2024
KEYWORDS
Exchange a e; on ie
ma ke s; A ica; s ock
ma ke s; wa ele
ans o ma ion
JEL CLASSIFICATION
G10; G11; G15; O16; O11
SUBJECTS
S a is ics o Business,
Finance & Economics;
Mac oeconomics;
In e na ional Economics;
Finance; Financial
Ma hema ics; Ma hema ical
Finance; Quan i a i e
Finance; Economics
1. In oduc ion
This s udy explo es he co-mo emen be ween exchange a es and s ock ma ke pe o mance in on ie
A ican economies. We ocus on h ee ma ke s wi h signi ican capi aliza ion which a e Ghana, Mau i ius,
and Tunisia. We add ess he dea h o esea ch on he impac o he cu ency-equi y e ec on he inancial
sys ems o selec ed coun ies. These coun ies we e selec ed because hey ha e he la ges capi aliza ion
among on ie A ican economies Tunisia ($7.2BN), Mau i ius ($7.8BN), and Ghana ($7.5BN) (A ican
Secu i ies Exchanges Associa ion (ASEA) and Ox o d Business G oup (OBG), 2022). An examina ion o he
selec ed on ie economies (Mau i ius, Tunisia, and Ghana) e eals ecen dep ecia ion episodes in hei
espec i e cu encies (Mau i ian upee, Tunisian dina , and Ghanaian cedi). No ably, hese dep ecia ions
coincided wi h he mos signi ican nega i e impac obse ed on hei equi y capi al pe o mance, pa icu-
la ly du ing he pandemic. The equi y capi al ma ke ell abou 21% o Mau i ius, 9.1% o Tunisia, and
6.5% o Ghana acco ding o he Ox o d Business G oup epo (ASEA, 2022). F on ie A ican ma ke s
accoun o 60% o Sub-Saha an g oss domes ic p oduc (GDP) and popula ion (In e na ional Mone a y
CONTACT Gyasi Gene ie e [email p o ec ed] Depa men o En ep eneu ship and Business Science, Uni e si y o Ene gy
and Na u al Resou ces, Fiap e, Ghana.
ß2024 The Au ho (s). Published by In o ma UK Limi ed, ading as Taylo & F ancis G oup
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/by/4.0/), which
pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. The e ms on which his a icle has been
published allow he pos ing o he Accep ed Manusc ip in a eposi o y by he au ho (s) o wi h hei consen .
COGENT ECONOMICS & FINANCE
2024, VOL. 12, NO. 1, 2399947
h ps://doi.o g/10.1080/23322039.2024.2399947
Fund (IMF), 2023). A signi ican sha e (app oxima ely wo- hi ds) o small, open economies in Sub-Saha an
A ica and No he n A ica exhibi heigh ened ulne abili y o exchange a e ola ili y. This ulne abili y
s ems om di e en ac o s, including ee- loa ing exchange a e egimes and dependence on ex e nal
economic condi ions, cu en accoun de ici s, economic slowdowns, in la iona y p essu es, and ising
in e es a es. As a consequence, A ican economies ace po en ial dis up ions o hei o e all economic
pe o mance and equi y s ock ma ke s abili y (Njindan Iyke, 2017). These a ia ions ha e in ensi ied global
isk a e sion, p omp ing a ligh o sa e-ha en asse s and a decline in in es men in lows owa d on ie
A ican ma ke s. Consequen ly, despi e hei abundan na u al esou ces, in on ie A ican coun ies, hey
con inue o display a limi ed p esence in global ade, o eign di ec in es men , and po olio in es men
(Klagge & Zademach, 2018). The cu encies o Sub-Saha an A ica’s on ie economies ha e displayed a
declining end since he 2008/2009 global inancial c isis. This decline has been expanded by ecen
e en s, including he COVID-19 pandemic and he Russia–Uk aine wa , which ha e signi ican ly a ec ed
c i ical sec o s such as inancial, supply chains, and ene gy ma ke s (Agyei e al., 2022; Amewu e al., 2022).
The inc eased ulne abili y o on ie ma ke s in Sub-Saha an and No h A ica, ep esen s an impo an
sec ion o he egion’s economic scope, highligh ing he need o mo e in es iga ion o b ing unde s and-
ing o he in e nal dynamics o A ican ma ke s.
The mul i ace ed na u e o he ela ionship be ween equi y s ock ma ke s and cu ency ma ke s is, as
seen in exis ing empi ical li e a u e wi h a signi ican e u n o co-mo emen and ola ili y spillo e ,
ound in some eme ging and on ie ma ke s while o he s ha e examined he in ica e dynamics
be ween cu ency luc ua ions and equi y ma ke pe o mance in hese ola ile egions (Bou i e al.,
2018,2019,2020; Tang & Yao, 2018).
Declines in cu ency p ices ha e o en esul ed in he all o s ock p ices as capi al ou lows inc ease
while in lows all alongside a decline in in es o con idence (Ahmad e al., 2016; Alagidede & Panagio idis,
2009; Pa o e al., 2014). Howe e , he e ec and na u e o he ela ionship a y om ade balances, o -
eign exchange ese es, and mac oeconomic policies exe ing hei in luence in some cases (Aloui e al.,
2018; Aloui & Hki i, 2014; Chkili & Nguyen, 2014). In he sho - and long- e m coun ies wi h s ong unda-
men al policies ha e displayed s ong como emen s pa e ns (Balcila e al., 2021). Also, s ock p ices a e a
con ibu ing elemen in p edic ing changes in exchange a e p ices wi h weak unidi ec ional asymme ic
causal e ec om exchange a e o s ock p ices (Xie e al., 2020). Co onado e al. (2021) ound ins an an-
eous spillo e s ac oss he e u ns o cu ency and s ock ma ke s wi h unde lying po olio di e si ica ion
o in es o s o ake ad an age in he US ma ke . Usman e al. (2022) ound he local s ock index and
SP500 index con ibu ed o he ex eme shocks in cu ency e u ns. Fu he mo e, Chkili (2012) examined
he ime- a ying ela ionship be ween exchange a es and s ock e u ns in eme ging ma ke s, highligh ing
he impac o economic and inancial c ises. In a sys ema ic e iew Obuya e al. (2024) ound exchange a e
ola ili y o ha e a posi i e e ec on s ock ma ke e u ns in de eloped coun ies.
Mo eo e , o he s udies on BRICS, Asian, and some A ican economies ha e ound he ollowing; Aydin
e al. (2023) ound a ela ionship be ween exchange a es and s ock p ices o ASEAN and BRICS coun ies
be o e COVID-19 con i ming he esul s om Na ayan e al. (2020) s udy on Japan. Using he wa ele ana-
lysis Mohamed Dahi e al. (2018) ound ha o BRICS coun ies a posi i e ela ionship exis s o B azil and
Russia, a nega i e ela ionship o Sou h A ica, and no ela ionship o China. In he wo k o Hussain e al.
(2023) exchange a e ola ili y was ound o be connec ed o s ock e u n ola ili ies du ing pandemic-
induced c ises o Russia, India, B azil, and Sou h A ica wi h weak ola ili y connec ed om China o any o
he o he coun ies in he BRICS. Using nonlinea dynamic analysis on Asian coun ies ound ola ili y
e ec s we e p esen be ween di e en asse ma ke s, showing a bi-di ec ional ela ionship be ween s ock
p ices and exchange a es (Sakemo o, 2017). Again, in Tu key, a nega i e unidi ec ional ela ionship was
ound be ween he s ock ma ke and exchange a es howe e a di e en equencies using he wa ele
cohe ence app oach (He e al., 2021). Hung (2019) examined cen al and eas e n Eu opean coun ies’ em-
po al signi ican inancial con agion be ween s ock ma ke s and exchange a e ma ke s using he GARCH-
BEKK amewo k alongside he cons an and dynamic condi ional co ela ion (CCC and DCC) models.
Kuma (2013) ound a bi-di ec ional ola ili y spillo e be ween s ock ma ke s and exchange a es among
IBSA coun ies. In Tanzania, s ock p ices ha e a unidi ec ional e ec on exchange a es (John & Kisa a,
2017). Mkhombo and Phi i (2023) ha como emen s be ween exchange a es and s ock e u ns occu du -
ing pe iods o high in la ion and lowe in e es a e mo emen s. Xu e al. (2022) used ad anced
2 G. GYASI, J. MAGNUS FRIMPONG AND K. MIREKU
econome ic models o analyze he dynamic in e ac ions be ween exchange a es, oil p ices, and s ock
ma ke s in eme ging economies, e ealing complex in e dependencies and he impac o global isk ac-
o s. Ni
,oi e al. (2018) explo ed he ime- equency co-mo emen be ween s ock ma ke s and exchange
a es in on ie ma ke s, emphasizing he signi icance o global inancial cycles and egional economic pol-
icies. Salisu e al. (2022) eme ging ma ke s ola ili y esponds posi i ely o geopoli ical isk. Sui and Sun
(2016) s udied spillo e e ec s be ween exchange a es and s ock ma ke s in eme ging economies, empha-
sizing he impac o global economic unce ain y. Fu he mo e, Bashe e al. (2012) in es iga ed he
dynamic in e ac ions be ween exchange a es, oil p ices, and s ock ma ke s in on ie ma ke s, unco e ing
complex in e dependencies and he e ec s o ex e nal shocks.
F om empi ical li e a u e, comp ehensi e s udies ha e explo ed cu ency and s ock ma ke ola ili y
in de eloped, and eme ging economies, and on ie ma ke s in o he egions whe eas he ocus on
A ican F on ie ma ke s emains limi ed (Jamil & Mobeen, 2021; Lee, 2009; Sayed & Cha e is, 2022).

Zi ko e al. (2021) commendably iden i ied he mos liquid A ican s ock ma ke s and sho - e m ola il-
i y spillo e s wi hin selec ma ke s. Howe e , hei wo k does no delinea e he op imal in es men ho i-
zon o on ie A ican ma ke s. This knowledge gap necessi a es u he in es iga ion o iden i y he
ime ame ha maximizes in es o e u ns wi hin his asse class and how hese ma ke s espond o
exchange a e luc ua ions and global e en s.
Ou pape add esses he gap by in es iga ing he nexus be ween cu ency ola ili ies and selec ed
indi idual on ie A ican equi y ma ke s (Ghana, Mau i ius, Tunisia). We employ he con inuous Mo le
wa ele ans o m (CMWT) o examine he co-mo emen s ac oss di e en ime scales (Omane-Adjepong
& D amani, 2018). This app oach seeks o cap u e bo h ime ( a ian and equency) ea u es which in
u n p o ides an unde s anding o he linkages ha exis wi hin he selec ed indi idual economies. In
using high- equency da a o examine e y sho - e m o long- e m ho izons, he CMWT p o ides unde -
s a ing aiding in in es men decision-making in he selec ed on ie A ican cu ency-equi y ma ke s.
The indings om his s udy will equip in es o s wi h a p o ound hough o he dynamic ela ionship
be ween exchange a es and s ock ma ke pe o mance in on ie A ican economies. This knowledge
will empowe hem o make in o med in es men decisions and po en ially iden i y op imal en y o exi
poin s wi hin hese ma ke s.
The a icle is sec ioned as ollows: Sec ion 2 p esen s he empi ical me hodology; Sec ion 3 p esen s
he empi ical esul s. Sec ion 4 p esen s a discussion o concluding ema ks and gi es implica ions o
he key indings.
2. Empi ical me hodology
In applying he wa ele analysis, we i s conside he linea and non-linea causal ela ionship be ween
he cu ency and equi y ma ke s by using he G ange es (G ange , 1969) as a con en ional me hod
o es ing pa ame ic linea , ime se ies model by es ima ing he condi ional mean, and he Diks and
Panchenko (2005,2006), he ea e he DP es , o de ec G ange non-causali y which is mo e consis en
and obus agains o he mean and non-linea a iance echniques (see Akosah e al., 2020). We p oceed
u he o employ he con inuous wa ele ans o m o examine co-mo emen in he cu ency-equi y
ma ke .
2.1. Linea g ange causali y amewo k
The G ange echnique (G ange , 1969) is used o explo e in o ma ional linkages be ween s ock and cu -
ency ma ke s. Gi en any wo s a iona y da a pai s, say ES and CU , say a iable ES G ange causes CU
linea ly p o ided lags o ES o e use ul in o ma ion o explaining he cu en alues o B , and ice
e sa. Whe e ES is equi y ma ke s and CU ep esen cu ency ma ke s.
The bi a ia e Linea G ange causali y is speci ied in a VAR sys em as ollows:
ES ¼u1þX
k
i¼1
a1iES −iþX
k
j¼1
b1iCU −jþe1 (1)
COGENT ECONOMICS & FINANCE 3

CU ¼u2þX
k
i¼1
a2iES −iþX
k
j¼1
b2iCU −jþe2 (2)
whe e u1and u2a e he cons an e ms o he sys em o he equa ion; aand bdeno e es ima ed coe i-
cien s; kis he op imal lag o de based on he Akaike In o ma ion C i e ion (AIC) and e1 and e2 ep e-
sen esiduals om he VAR model. Again, he null hypo hesis o Eq. (1) s a es ha changes in he p ice
o equi y s ock ma ke s do no G ange cause cu ency ola ili ies. In Eq. (2), cu ency ola ili ies do no
G ange cause changes in he p ice o equi y s ock ma ke s. Addi ionally, we employ he Wald es o
examine he join hypo hesis o a1i¼0 and b2j¼0:
Howe e , due o he low powe limi a ion ha cha ac e izes linea models when de ec ing non-linea
in o ma ional linkages be ween a iables, highe non-linea p edic i e powe is o en no cap u ed by
he linea model, hus we employ he non-linea model (Omane-Adjepong & Alagidede, 2019).
2.2. Non-linea g ange causali y
Among he a ious non-linea models, we employ he non-linea es by Diks and Panchenko (2005,
2006), he ea e he DP es , due o i s consis ency, lexibili y, and obus ness. This es is buil on he HJ
and ini ial nonpa ame ic es s (Baek and B ock, 1992; Hiems a and Jones, 1994). The DP es diminishes
he issue o o e - ejec ion a es ha cha ac e ize he HJ es unde he null hypo hesis.
Ou adop ion o he D&P es is, hus, no misplaced as we deno e he in o ma ion se o he lags o
ES and CU espec i ely as CX, and CY, , be o e ime ¼1; and ‘῀’ he equi alen dis ibu ion (Diks &
Panchenko, 2005,2006). Consequen ly, we he modeling sec ion o Beki os and Diks (2008) wi h he
eplacemen o X, Y, and Q o a iables ha ep esen ou selec ed a iables o in e es we assume ha
A is said o G ange cause B p o ided ha ,
ðCU þ1...,CU þkÞjðCX,1...,CY,kÞðCU þ1...,CU þkÞjCX,1(3)
whe e kis an in ege k 1, ep esen ing he o ecas ing ho izon. Fo he lag ec o s Al
¼ðES −l þ1,ES Þ
and CUls
¼ðCU −lsþ1,CU Þ, gi en (l þls1) we es he condi ional independence using a de e mina e
numbe o lags l and lsUnde a null hypo hesis o :
H0:CU þ1jðESl
:CUls
ÞCU þ1jCUls
Þ(4)
We u he educe he wo a iable ep esen a ions and use A, B, and W due o ease in modeling
adop ing he Beki os and Diks (2008) model. Conside ing ha he null hypo hesis o G ange non-causal-
i y is an asse ion abou he in a ian dis ibu ion o ðl þlsþ1Þdimensional ec o Q ¼ðAl
,Bls
,W Þ
whe e he lead ec o W ¼B þ1, he ime index is d opped and w i en as Q ¼(A, B, W) (see Beki os &
Diks, 2008).
We se l þls¼1, and k ¼1 and assume he i a ia e in Q ollows a con inuous andom a iable.
The null hypo hesis o he non-causali y in (4) may be ede ined as a join p obabili y densi y unc ion
A,B,Wða, b, wÞwi h i s ma ginal sa is ying he ollowing condi ion:
A,B,Wða, b, wÞ
BðbÞ¼ A,Bða, bÞ
BðbÞ B,Wðb, wÞ
BðbÞ(5)
Fo e e y de e mina e alue o b om ou es , he con inuous andom A and W a e independen
condi ioned on Y ¼y.
The e o e, unde he e ised null hypo hesis H0,
q¼E A,B,WA, B, W
ðÞ
BB
ðÞ
− A,BA, B
ðÞ
B,WB, W
ðÞ

(6)
The es ima e o q is exp essed based on he indica o unc ion as:
Tnԑ
ðÞ¼ð2ԑÞ−mA−2mB−mW
nðn−1Þðn−2ÞX
iX
k,k6¼iX
jj6¼iðIABW
ik IB
ij −IAB
ik IBW
ij Þ
(7)
Whe e e , IQ
ij ¼IðjjQi−Qjjj <ԑ), whe e K¼j, is no excluded explici ly as hey each con ibu e ze o o
he -s a is ic (B oock e al., 1996).
4 G. GYASI, J. MAGNUS FRIMPONG AND K. MIREKU
We ep esen he local densi y es ima o s o a mQ, a ia e as a andom ec o o Q a Qias
^
QQi
ðÞ
¼ð2ԑÞmQ
n−1XIQ
ij
jj6¼i(8)
The es s a is ic educes o:
Tnԑ
ðÞ¼n−1
ðÞ
nn−2
ðÞ
X
ið^
A,B,WAi,Bi,Wi
ðÞ
^
BBi
ðÞ
−
^
A,BAi,Bi
ðÞ
^
B,WBi,Wi
ðÞ
Þ(9)
The app op ia e sequence ԑn o bandwid h, alues should ha e es ima o s and es s a is ics ha a e
consis en and ma ch he weigh ed a e age o he local con ibu ions ^
A,B,WðA,B,WÞ^
BðBÞ−
^
A,BðA,BÞ^
B,WðB,WÞwhich end o be ze o in o he p obabili y unde he p oposed null hypo hesis.
Gi en ha mA¼mB¼mW¼1, o achie e a consis en es , he bandwid h is selec ed based on he
sample size (see Powell & S oke , 1996).
when, en¼Xn
−b o a cons an X o be posi i e (X>0) and, (be(0.25, 0.67), This will help o achie e
an asymp o ic and no mally dis ibu ed -s a is ic when he dependence be ween is absen o Qi:We
ex end his o ou ime se ies ollowing he Denke and Kelle (1983) mixing condi ions on he assump-
ion ha he co a iances be ween he local densi y es ima o s a e accoun ed o .
F om he linea and non-linea G ange causali y, he use o he VAR sys em allows o he ex ac ion
o linea p edic i e powe lea ing inc emen al p edic i e powe ha could accoun o he non-linea
causali y o p edic i e powe in he se ies. On he o he hand, he non-linea Diks and Panchenko (DP)
es and G ange causali y es ace signi ican limi a ions wi h non-s a iona y ime se ies da a, p e alen
in inancial ma ke s. The DP es , designed o de ec ing non-linea dependencies, s uggles wi h s uc-
u al b eaks and a ying ola ili y, o en yielding alse posi i es o inconclusi e esul s. Simila ly, he
G ange causali y es assumes s a iona i y, leading o misleading in e ences when applied o non-s a-
iona y da a, as i iola es unde lying s a is ical assump ions. These cons ain s unde sco e he necessi y
o mo e obus me hods like wa ele -based s a egies, which e ec i ely handle non-s a iona i y by cap-
u ing localized ime- equency pa e ns, o e ing a mo e accu a e analysis o inancial ime se ies. We,
he e o e, employ he wa ele app oach as i cap u es he ime and equency ea u es o ou se ies and
o e s a obus echnique ha is use ul in examining he non-s a iona y na u e o ime se ies. In compa -
ing he wa ele app oach o ec o au o eg ession (VAR) models and dynamic condi ional co ela ion
(DCC) models espec i ely, we ind ha he VAR examines linea in e dependencies o e mul iple ime
se ies while he DCC examines ime- a ying co ela ions unde sco ing he dynamics p e alen in he
long- e m linea ela ionships and dynamic co ela ions. Again, he wa ele echnique conside s ab up
changes and a ying equencies ou pe o ming he VAR and DCC models which could lead o mislead-
ing conclusions due o he p esence o ends, ola ili y, and s uc u al b eaks unde pinning he da a i
no co ec ly examined. Ensu ing ha he ue ela ionships a e no obscu ed he wa ele app oach ho -
oughly examines he da a by iden i ying any unde lying issues such as economic cycles, and ma ke
shocks among o he s, and accu a ely models, cap u es, and ul ima ely yields obus and eliable esul s.
2.3. Con inuous wa ele ans o ma ion (CWT) and cohe ence
We employ he Mo le wa ele o examine he equency and ime-space beha io o he se ies due o
he p esence o high p ope ies in he localized equency and ime (Aloui e al., 2018; Wu e al., 2020).
We use he CWT by examining he a ia ions in non-s a iona y a iables ac oss ime and space. Fi s ly,
we decompose he ime se ies o ensu e ha localized ime- equency space and ze o means a e a unc-
ion o wa ele ans o ma ion. We u he ex ac he needed in o ma ion om he local neighbo hood
using he se ies ha has been decomposed.
The wa ele cohe ence (WC) is speci ied below as:
uu,s
ðÞ¼1
ffiffis
pw −u
s

w∙
ðÞ2L2R
ðÞ (1)
We deno e 1
ffiffis
pas he s abiliza ion elemen alida ing uni o he wa ele dispa i y. jjwu,s
ðÞ
jj2¼1;uis
he loca ion bounda y, which p esen s he exac loca ion o he wa ele .
COGENT ECONOMICS & FINANCE 5
Whe e sis he expansion le el loca ed in he bounda y, which de e mines he sp ead o he wa ele .
2.4. Mo le wa ele
uM
ðÞ¼1
p1=4eix0 e− 2=2(2)
We deno e he signi ican incidence o he wa ele by x0as 6. The con olu ion on he disc e e
sequence, scaled, and ansla ed wa ele used in he CWT is:
Wsu,s
ðÞ
¼ð1
-1
x
ðÞ1
ffiffis
pw −u
s

d (3)
Ex ac ing he wa ele wð∙Þon he ime se ies, Wsðu,sÞis ob ained.
Also, he main ad an age lies in he CWT’s abili y o decompose he se ies and ebuild i unde he
unc ion:
x
ðÞ2L2ðÞ :x
ðÞ¼1
cu
Ð1
0Ð1
0Wsu,s
ðÞ
wu,s
ðÞ
du

ds
s2,s>0
(4)
F om Eq. (4), he powe spec um is examined using he adjus ed measu emen
jj jj2¼1
cuð1
0ð1
-1jWsu,s
ðÞ
jj2du

ds
s2,s>0 (5)
In modeling ou he ed noise om he spec um se ies backg ound AR (1) p o ides he allowance.
Based on he null hypo hesis, he pocke s ound in he wa ele powe spec um (WPS) allow o he
peaks o be examined o es ablish hei signi ican le els.
The local WPS es ablished om he dis ibu ion using he Mon e Ca lo simula ion p esen s he indi-
idual ime (n) and scale (s) (see To ence and Webs e , 1999).
DWx
nsÞ2

d2
x
<p
2
43
5)1
2p 2
(6)
is ep esen ed as p , he mean spec um a Fou ie equency om he se ies. The wa ele scale is
aligned wi h he Fou ie equen ly. (s 1/ ), ¼1 is he eal wa ele , and ¼2 deno es he complex
wa ele whe e d2
xis he modi ied a iable.
The beha io o ime- equency in he cu ency-equi y ma ke is in es iga ed using he CWT o loca e
he common powe be ween he se ies (Aloui e al., 2018). The egion’s loca ion is ound using he
powe o CWT o loca e he co-mo emen s in he ime- equency dynamics.
Using a speci ic a iable se ies ( ) agains ano he (Y), he wa ele spec a o he indi idual se ies
Wx
nðsÞand Wx
nðsÞa e used in de e mining he CWT in he se ies as:
Wxy
ns
ðÞ¼Wx
nðsÞWx
nðsÞ(7)
The highes common powe om he CWT shows he a ea, ime, and space wi h WY
nðsÞas he in i-
ca e conjuga e o WY
nðsÞ:
2.5. C oss-wa ele powe
The c oss-wa ele powe jWxy
nðsÞj om he CWT indica es he co a iance is sha ed on all indi idual
le els.
In his case, a wo- ime se ies om he W.C plo ep esen ed by ¼ n
g
and y ¼yn
g
, which is he
equency and ime gaps o he se ies co a y. This allows o he de ec ion o co-mo emen s among
he a iables showing he absolu e squa e alues om he WC plo s o he no malized WPS.
6 G. GYASI, J. MAGNUS FRIMPONG AND K. MIREKU
The coe icien o he squa e wa ele is:
R2x,y
ðÞ
¼jSðs−1Wxy u,s
ðÞ
Þj2
Sðs−1jWxu,s
ðÞ
Þj2ÞSðs−1jWyu,s
ðÞ
Þj2Þ(8)
The smoo hing pa ame e (S) balances he esolu ion and signi icance le el emo ing all issues ela ed
o WPS and he wa ele c oss-spec um (WCS).
2.6. Wa ele cohe ence
The inequali y equa ion 0 R2ðx,yÞ1 ep esen s he cohe ence wi h alues om 0 o 1. 0 ep esen s
a low co ela ion and 1 is a obus co ela ion alue. The lag oscilla ion is posi ioned in he phase o m
o he a iables as he equency wi h ;xy, explaining he phase di e ence be ween ( ) and y( ) as:
;xy ¼ an −1IWxy
n

RWxy
n

!
,;xy 2−p,p
½ (9)
The smoo hened CWT is in wo pa s when Iand R, ep esen ing he imagina y and eal pa s. The
di ec ional a ows a e also indica ed on he WC plo , wi h unique di e en phase o ms o he a iables.
The phase o ms o a( ) and b( ) whe e a ows poin o he igh (in-phase) and he le (an iphase),
downwa ds he second a iable is in lead, and upwa ds he i s a iable in lead (see b( )/a( )).
3. Empi ical esul s
We conside his o ical ime se ies da a o leading s ock on ie ma ke s wi h he highes ma ke capi al-
iza ion (as o 4 Janua y 2010) and a ela i ely leng hie da a span. In no pa icula o de o a angemen ,
s ock ma ke s; Ghana S ock Exchange Composi e Index (GSE-CI), Tunisia s ock ma ke (TUNINDEX), he
s ock exchange o Mau i ius (SEMDEX); exchange a e ma ke ; he Uni ed S a es Dolla agains he
Ghanaian Cedi (US/GHS); Tunisian dina (US/TND), Mau i ian upee (US/MUR), a e examined. The daily
s ock e u ns and local cu ency o he Uni ed S a es dolla a e da ase spans om 4 Janua y 2010 o
31 Ma ch 2023. A ican on ie ma ke s ha e expe ienced signi ican de elopmen s om 2010 o 2023,
e lec ing bo h oppo uni ies and challenges. These ma ke s, cha ac e ized by apid economic g ow h
and inc easing in es o in e es , ha e seen subs an ial changes in in as uc u e, egula o y amewo ks,
and ma ke pe o mance.
F on ie ma ke s in A ica such as Tunisia, Ghana, and Mau i ius since 2010 ha e expe ienced obus
economic g ow h d i en by he elecommunica ions indus y, banking, and na u al esou ce sec o .
Since 2012 many A ican economies ha e aken inancial, anspa ency, and e iciency, o imp o e
g ow h and de elopmen . The Secu i ies and Exchange Commission (SEC) o A ica has in oduced new
egula ions, and imp o ed co po a e go e nance, and in es o p o ec ion. These e o ms implemen ed
in capi al ma ke s ha e inc eased o eign in es men and imp o ed ma ke liquidi y. Th ough echno-
logical ad ancemen , A ican on ie ma ke s s and a chance o in luence he ans o ma ional agenda
o A ica’s capi al ma ke . Fin ech and banking solu ions ha e also inc eased inancial inclusion,
imp o ed pa icipa ion, and e olu ionized inancial ansac ions leading o ma ke de elopmen . Since
he in oduc ion o hese e o ms ma ke pe o mance has been mixed wi h signi ican gains and down-
u ns occu ing wi h in luence om ex e nal and global ac o s such as cu ency, and in e es a e luc u-
a ions, poli ical ins abili y, co up ion, inadequa e in as uc u e, global inancial c ises heal h pandemic
(COVID-19), wa s, and commodi y p ice a ia ions, among o he s. Vola ili y due o oil p ice and exchange
a e shocks has iddled some on ie ma ke s while o he s ha e shown a high le el o esilience coupled
wi h s eady g ow h due o he di e si ica ion e o s o hei espec i e go e nmen s. The in low o o -
eign in es men an impo an elemen o he de elopmen o on ie ma ke s is hinged on in es o
in e es in highe e u ns in low-yield ma ke s which A ican ma ke s o en ind hemsel es. The low
in lux o capi al h ough p i a e equi y and en u e capi al in es men s needs o g ow o suppo he
expansion o businesses and encou age s a -ups in A ican on ie ma ke s. Global dis up ions, and a
g owing need o sus ainable, en i onmen al, social, and go e nance (ESG) in in es men po olios and
COGENT ECONOMICS & FINANCE 7
4. Discussion
This in es iga ion employs wa ele analysis o comp ehensi ely examine he ime- equency dynamics o
co-mo emen be ween equi y and cu ency ma ke s in Ghana, Mau i ius, and Tunisia. Wa ele analysis
o e s a dis inc ad an age by enabling he explo a ion o how hese a iables in e ac a a ious empo al
scales and how hei in e connec edness e ol es. No ably, wa ele s excel a cap u ing non-s a iona y ea-
u es embedded wi hin he da a se ies, a limi a ion ha plagues al e na i e me hodologies. P io esea ch
has yielded con lic ing esul s (Aloui & Hki i, 2014; Rua, 2010), highligh ing he supe io i y o wa ele s in
e ec i ely cap u ing he e a ic beha io o he se ies in bo h he ime and equency domains.
The wa ele analysis e eals ha co-mo emen s beyond a ou -yea ho izon all ou side he Cone o
In luence (COI) in he long e m. This signi ies a lack o s a is ically signi ican ela ionships a hese ime
scales, con as ing wi h p io s udies ha sugges ed pe sis en co-mo emen s beyond 2048 days (Owusu
Junio e al., 2018). On he o he hand, we ind signi ican co-mo emen s a e only no iceable wi hin he
1024 days. Fu he mo e, he obse ed co-mo emen pa e ns exhibi he e ogenei y, encompassing bo h
in-phase (posi i e co ela ion) and an i-phase (nega i e co ela ion) ela ionships. The di ec ion o causal-
i y, as indica ed by he a ows poin ing upwa ds (s ock ma ke leading) o downwa ds (exchange a e
leading), a ies ac oss he examined coun ies and ime ames.
F on ie ma ke s in Ghana, Mau i ius, and Tunisia exhibi a dynamic in e play be ween s ock ma ke luc ua-
ions and exchange a e mo emen s. Ou esea ch sugges s ha ecu en e en s can exe sho - e m p es-
su es on exchange a es, po en ially impac ing s ock ma ke pe o mance. Fu he mo e, dis up ions ha cas
doub on he sus ainabili y o u u e di idend paymen s can igge in es o isk a e sion beha io . In esponse
o such e en s, in es o s may s a egically wi hd aw capi al om he s ock ma ke and edeploy i in o longe -
e m ins umen s wi hin he on ie ma ke i sel . This po olio ealloca ion se es as a isk mi iga ion s a egy,
aiming o shield in es o weal h om he po en ial ola ili y associa ed wi h hese pe iodic e en s. Ou ind-
ings u he e eal ha in es o s in he selec ed A ican on ie ma ke s (Ghana, Mau i ius, and Tunisia) o en
cons uc di e si ied in es men po olios. This di e si ica ion s a egy is mo i a ed, in pa , by a desi e o min-
imize exposu e o sys emic isks, including he po en ial o exchange a e luc ua ions o nega i ely impac
o e all po olio e u ns. A ican on ie ma ke s examined in his s udy display he A bi age P icing heo y
dynamics. This is e iden in he p opensi y o he sho - e m ma ke s o be sensi i e o p ice ola ili y.
Howe e , he s ock p ices in hese ma ke s a e o en in equilib ium in he long- e m. These dispa i ies spu
in es o s o engage in he di e si ica ion o hei in es men po olios and implemen hedging s a egies ha
would mi iga e hei isk exposu e and inc ease e u ns (Hammami & Boujelbene, 2022;Zaiane&J ad,2020).
The esul s also d aw a en ion o he dynamic ela ionship be ween s ock ola ili y and in es o beha io as
isk-a e se in es o s on he A ican on ie educe hei ansac ion olumes du ing heigh ened ola ili y pe i-
ods. Unlike isk- ole an in es o s, who end o inc ease hei ading ac i i y du ing hese pe iods. Mo eo e ,
he ype o di e si ica ion s a egy may exe quan i iable ansac ion cos s on ma ke liquidi y.
5. Conclusion
A mul i ude o A ican on ie ma ke s ha e been bese by a con e gence o nega i e economic o ces.
These include expo dis up ions, a decline in he e ms o ade, dep ecia ion o local cu encies ela i e o
he US dolla , and a subsequen con ac ion in in es men in lows and educed compe i ion. The cumula-
i e impac o hese challenges has been a p onounced sca ci y o o eign exchange ese es, se e ely
impeding bo h ade inance ac i i ies and o eign di ec in es men . In he pas decade, a no ewo hy pol-
icy shi has been obse ed wi hin he mone a y amewo ks o many A ican on ie economies. A ansi-
ion has occu ed om ixed exchange a e egimes o mo e lexible exchange a e sys ems while ini ially
bene icial and ansi o y, has no p o ided sus ained ad an ages due o ongoing ma ke ola ili y and spill-
o e e ec s. F on ie equi y ma ke s in A ica a e pa icula ly p one o luc ua ions, de e ing bo h domes ic
and o eign in es o s and limi ing capi al mobiliza ion. The in e play o demand and supply o ces, o igi-
na ing om bo h domes ic and in e na ional ma ke s, con inues o exe a signi ican in luence on
exchange a e dynamics. This dynamic can lead o he ansmission o ola ili y and spillo e e ec s ac oss
hese selec ed A ican on ie ma ke s. F on ie equi y s ock ma ke s in Ghana, Mau i ius, and Tunisia a e
cha ac e ized by a suscep ibili y o p onounced luc ua ions and heigh ened ola ili y. These ma ke
14 G. GYASI, J. MAGNUS FRIMPONG AND K. MIREKU

dynamics ac as a signi ican disincen i e o in es o pa icipa ion, bo h domes ic and o eign, he eby con-
s aining he ma ke ’s capaci y o mobilize capi al o in es men pu poses.
To mi iga e his challenge, on ie economies should p io i ize he implemen a ion o a mul i ace ed
policy amewo k designed o cul i a e a mo e obus in es o appe i e o hei s ock ma ke s. Po en ial
policy in e en ions could encompass; he adop ion o s ic e egula o y amewo ks and he p omo ion
o enhanced co po a e go e nance p ac ices o os e a mo e s able and p edic able ma ke en i onmen ;
he cul i a ion o a di e si ied ange o alue-added p oduc s wi hin he domes ic economy, c ea ing
a ac i e in es men p oposi ions o bo h local and in e na ional ma ke pa icipan s; in he sho e m, a
ocus on essen ial impo s, such as medicine, ood, and uel, in sec o s whe e domes ic p oduc ion capaci y
emains limi ed; o e he medium o long e m, he p io i iza ion o policies ha os e sel -su iciency
wi hin key indus ies, wi h he ul ima e goal o educing eliance on expo s and cul i a ing a mo e di e si-
ied and esilien economic s uc u e; he in oduc ion and subsequen egula ion o inno a i e paymen
sys em echnologies o acili a e s eamlined o eign cu ency in lows in o he s ock ma ke . Again, egula-
o s and in es o s need o accoun o ola ili y spillo e s and manage isk in he ma ke . S ong and sound
s a egies om di e si ica ion, and po olio ebalancing a e impo an mechanisms o p e en ad e se
p ice mo emen s due o ex eme changes in mac oeconomic ac o s in one ma ke (Aloui e al., 2018; Cao
e al., 2020; Du e al., 2020; Kolm & Ri e , 2019), all ound ha he a ious s a egies abo e among o he s
help in balancing he e u ns du ing high ola ili y pe iods on he ma ke (Ace bi & Tasche, 2002; P lug,
2000; Rocka ella & U yase , 2002). Fu he mo e moni o ing, and implemen ing anspa ency measu es o
educe hi d-pa y isk amoun o he s can educe c oss-bo de spillo e s hey na iga ing he complex ela-
ionship be ween s ock ma ke p ices and exchange a e changes (Chen e al., 2024; OECD, 2013).
Ou s udy inds ha lexible exchange a e egimes enjoy sho -li ed ad an ages bu does no exam-
ine he limi ed long- e m bene i s o enable a gene aliza ion due o he uniqueness o each ma ke and
coun y. The e is a need o esea che s o conside explo ing he speci ic condi ions unde which ad an-
ages can be sus ained unde lexible exchange a e egimes. By add essing he sho comings and
implemen ing ecommenda ions A ican ma ke s can ake ad an age o oppo uni ies o e ec i e policy
implemen a ion o a ac in es o s.
Acknowledgmen
I acknowledge he Kwame Nk umah Uni e si y o Science and Technology, Kumasi, and he Uni e si y o Ene gy
and Na u al Resou ces, Sunyani Ghana, o hei suppo h oughou his s udy.
Au ho s’Con ibu ion
Gene ie e Gyasi was in ol ed in he concep ion and design, o analysis and in e p e a ion o he da a; he d a ing
o he pape , e ising i c i ically o in ellec ual con en ; and he inal app o al o he e sion o be published.
Joseph Magnus F impong and Kwame Mi eku we e in ol ed in he concep ion and design, e ising i c i ically o
in ellec ual con en ; and he inal app o al o he e sion o be published. All au ho s ag eed o be accoun able o
all aspec s o he wo k.
Disclosu e s a emen
No po en ial con lic o in e es was epo ed by he au ho (s).
Funding
No unding was ecei ed.
Abou he au ho s
Gene ie e Gyasi, PhD Finance, Lec u e /Resea che a he Uni e si y o Ene gy and Na u al Resou ces (UENR) in
Ghana. My cu en esea ch in e es co e s In e na ional Economics, Finance, and Econome ics opics in
De elopmen al and Financial Economics in A ica.
COGENT ECONOMICS & FINANCE 15
Joseph Magnus F impong, P o esso o Finance a Kwame Nk umah Uni e si y o Science and Technology, Kumasi,
Ghana. My esea ch in e es co e , inancial econome ics, s ock ma ke inance, p i a e sec o de elopmen , and
mac o economic a iables.
Kwame Mi eku, PhD inance, Lec u e /Resea che a Kwame Nk umah Uni e si y o Science and Technology, Kumasi,
Ghana. My in e es co e Financial li e acy, mac oeconomic a iable and de elopmen .
ORCID
Gene ie e Gyasi h p://o cid.o g/0000-0002-5144-116X
Da a a ailabili y s a emen
The da a ha suppo he indings o his s udy a e openly a ailable a in es ing.com and he Ghana S ock
Exchange. These da a we e de i ed om he ollowing esou ces a ailable in he public domain: h ps://www.in es-
ing.com/indices/ o all coun ies excep Ghana’s equi y da a which was sou ced om h ps://gse.com.gh/ ading-
and-da a/ da a a ailable on easonable eques om he co esponding au ho Gene ie e Gyasi. The da a was
ob ained om in es ing.com and he Ghana S ock Exchange da abase. Daily da a was ob ained o all h ee coun-
ies and is easily accessible. All igh s and pe missions o he da a used a e unde in es ing.com and he Ghana
S ock Exchange.
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Appendix
Table A1. Linea G ange causali y es esul s.
A ican on ie s ocks and exchange a es
Di ec ion T-s a is ics p- alue Op imal Lag
GHANA
GSE-CI6! EXC 5.8 0.45 6
EXC6!GSE-CI 3.5 0.74
MAURITIUS
SEMDEX 6! EXC 12.1 0.06 6
EXC!SAMDEX 12.4 0.054
TUNISIA
TUNINDEX !EXC 18 0.00044 3
EXC6!TUNINDEX 5.9 0.12
Table A2. Non-linea ela ionship D&P es .
A ican on ie s ocks & exchange a es
Di ec ion
e¼0.5 e¼1.5 e¼2.0
T s a is ic p- alue T s a is ic p- alue T s a is ic p- alue
GHANA
GSE-CI6! EXC 0.876 0.19058 −0.049 0.51956 −1.486 0.93135
EXC6!GSE-CI   0.377 0.35308 0.629 0.26466
MAURITIUS
SEMDEX !EXC      
EXC!SEMDEX      
TUNISIA
TUNINDEX 6! EXC 0.767 0.2215    
EXC6!TUNINDEX      
COGENT ECONOMICS & FINANCE 19