Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
9
PREDICTIVE MODELS FOR EVALUATING STOCK MARKET
VOLATILITY USING STATISTICAL TECHNIQUES IN TIME
SERIES ANALYSIS
M. Vasuki*, A. Dinesh Kuma **, Mbonigaba Celes in*** &
Je yson Amewo gbe Gidisu****
* S ini asan College o A s and Science (A ilia ed o Bha a hidasan Uni e si y),
Pe ambalu , Tamil Nadu, India
** Khadi Mohideen College (A ilia ed o Bha a hidasan Uni e si y), Adi ampa inam,
Thanja u , Tamil Nadu, India
*** B ainae Ins i u e o P o essional S udies, B ainae Uni e si y, Delawa e, Uni ed S a es o Ame ica
**** Kings and Queens Medical Uni e si y College, Akosombo, Eas e n Region, Ghana, Wes A ica
Ci e This A icle: M. Vasuki, A. Dinesh Kuma , Mbonigaba Celes in, Je yson Amewo gbe Gidisu.
(No embe 2025). P edic i e Models o E alua ing S ock Ma ke Vola ili y Using S a is ical Techniques in
Time Se ies Analysis. In P oceedings o he Eu opean Summi on In e disciplina y Resea ch and De elopmen
(pp. 9-20). Pe ambalu , Tamil Nadu, India: C ys al Pen Publica ion.
ISBN: 978-93-49435-80-3
Publishe Websi e: www.c ys alpen.in
Copy Righ : © 2025 C ys al Pen Publica ion (CPP). All igh s ese ed. 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 (CC BY), 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.
DOI:
Abs ac :
This s udy explo es he e ec i eness o p edic i e models in e alua ing s ock ma ke ola ili y using
s a is ical echniques in ime se ies analysis. The esea ch objec i es include assessing he accu acy o ARIMA,
GARCH, and hyb id models in o ecas ing ola ili y and analyzing he impac o ex e nal shocks such as he
COVID-19 pandemic on ma ke luc ua ions. A quan i a i e esea ch app oach was employed, u ilizing
his o ical s ock ma ke da a om 2020 o 2024 and applying s a is ical and machine lea ning models, including
LSTM ne wo ks. Findings indica e ha he GARCH model consis en ly ou pe o ms ARIMA in ola ili y
o ecas ing, wi h a lowe Mean Absolu e E o (MAE) o 4.2% and Roo Mean Squa e E o (RMSE) o 6.5% in
2020. Hyb id models, in eg a ing ARIMA wi h machine lea ning, u he imp o ed p edic i e accu acy,
educing MAE o 2.9% in 2023. The co ela ion analysis e ealed a s ong posi i e ela ionship be ween
in la ion and s ock ma ke ola ili y, peaking a 0.78 in 2022. The s udy concludes ha inco po a ing
mac oeconomic indica o s enhances p edic i e accu acy and ecommends in eg a ing hyb id models o obus
ma ke o ecas ing, ensu ing adap abili y o dynamic inancial en i onmen s.
Key Wo ds: S ock Ma ke Vola ili y, Time Se ies Analysis, GARCH Model, ARIMA Model, Machine
Lea ning in Finance
1. In oduc ion:
The dynamic na u e o s ock ma ke ola ili y has cap u ed he a en ion o inancial esea che s and
p ac i ione s, especially o e he pas i e yea s. The applica ion o s a is ical echniques in ime se ies analysis
has gained ac ion as a obus app oach o unde s and and p edic hese luc ua ions. Acco ding o Chen e al.
(2020), p edic i e models oo ed in ime se ies analysis, such as ARIMA and GARCH, ha e demons a ed high
accu acy in cap u ing he nonlinea pa e ns inhe en in s ock ma ke da a. These me hods no only enhance ou
unde s anding o ma ke beha io bu also o e ac ionable insigh s o decision-making.
The inc easing in eg a ion o ad anced compu a ional echniques, such as machine lea ning algo i hms,
has u he e olu ionized ime se ies analysis in s ock ma ke s. Recen s udies, like ha o Zhang and Li (2021),
highligh he usion o adi ional s a is ical models wi h a i icial in elligence, leading o imp o ed p edic i e
capabili ies. This end unde sco es he c i ical ole o hyb id me hodologies in enhancing he accu acy o
ma ke o ecas s, hus add essing he demands o con empo a y in es o s and policymake s.
Mo eo e , he COVID-19 pandemic has ampli ied he need o p edic i e accu acy in s ock ma ke s, as
e idenced by i s unp eceden ed impac on global inancial sys ems. Wang e al. (2022) emphasize he
impo ance o le e aging s a is ical ools o na iga e he heigh ened unce ain y and ola ili y caused by ex e nal
shocks. By ocusing on he de elopmen s om 2020 o 2024, his s udy seeks o con ibu e o he e ol ing
discou se on p edic i e modeling in inancial ma ke s.
Types o P edic i e Models o E alua ing S ock Ma ke Vola ili y:
ARIMA (Au o Reg essi e In eg a ed Mo ing A e age) Model: ARIMA is a widely used s a is ical
model o ime se ies o ecas ing, elying on pas alues and e o s o p edic u u e ends. I is
e ec i e o sho - e m s ock ma ke ola ili y o ecas ing bu s uggles wi h high- equency
luc ua ions and long- e m accu acy.
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
10
GARCH (Gene alized Au o eg essi e Condi ional He e oskedas ici y) Model: GARCH models cap u e
ola ili y clus e ing, a key ea u e in inancial ma ke s whe e high ola ili y is ollowed by mo e
ola ili y. I pe o ms well in modeling condi ional a iance and is supe io o ARIMA in o ecas ing
s ock ma ke luc ua ions.
Hyb id ARIMA-GARCH Model: This model combines ARIMA’s end es ima ion wi h GARCH’s
abili y o model ola ili y clus e ing. I imp o es p edic i e accu acy by le e aging bo h sho - e m
ends and long- e m ola ili y cha ac e is ics.
Machine Lea ning-Based Models (LSTM and Random Fo es ): Machine lea ning echniques such as
Long Sho -Te m Memo y (LSTM) ne wo ks and Random Fo es models can iden i y complex,
nonlinea ela ionships in s ock ma ke da a. These models ou pe o m adi ional s a is ical me hods in
ola ili y o ecas ing bu equi e la ge da ase s and compu a ional esou ces.
Mon e Ca lo Simula ion: Mon e Ca lo simula ions gene a e mul iple andom scena ios based on
his o ical ola ili y pa e ns. This echnique is use ul in isk assessmen and po olio managemen bu
is compu a ionally in ensi e.
Wa ele T ans o m and F ac al Analysis Models: These models analyze ma ke cycles and sel -simila
pa e ns in ola ili y. They help in iden i ying ma ke ends a mul iple ime scales and a e pa icula ly
use ul in p edic ing ex eme p ice mo emen s.
Cu en Si ua ion o S ock Ma ke Vola ili y:
S ock ma ke ola ili y has expe ienced signi ican luc ua ions due o economic shocks, in la ion, and
in es o sen imen . The COVID-19 pandemic in 2020 esul ed in peak ola ili y le els, while subsequen yea s
saw luc ua ions d i en by in la ion c ises and geopoli ical ensions.
The his o ical ola ili y o majo s ock indices shows a clea end o economic dis up ions impac ing
ma ke s abili y. In 2020, he COVID-19 pandemic led o ola ili y peaks o 27.4% (S&P 500) and 32.1%
(NASDAQ). The ma ke s s abilized in 2021, wi h ola ili y dec easing o 15.6% and 18.5%, espec i ely.
Howe e , in 2022, in la ion conce ns caused a spike, wi h ola ili y ising o 25.3% (S&P 500) and 28.7%
(NASDAQ). By 2023 and 2024, ola ili y emained mode a e a 18.2% and 22.0%, espec i ely, bu global
economic unce ain ies con inued o in luence ma ke luc ua ions.
2. Speci ic Objec i es:
Unde s anding he signi icance o p edic i e models o s ock ma ke ola ili y is essen ial o ensu ing
in o med decision-making. This s udy aims o achie e he ollowing objec i es:
To analyze he e ec i eness o s a is ical echniques such as ARIMA and GARCH in o ecas ing s ock
ma ke ola ili y.
To e alua e he ole o hyb id models combining adi ional s a is ical app oaches wi h machine
lea ning echniques.
To in es iga e he impac o ex e nal shocks, like he COVID-19 pandemic, on s ock ma ke ola ili y
p edic ions.
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
11
3. S a emen o he P oblem:
S ock ma ke s a e expec ed o ope a e wi h a le el o p edic abili y ha allows in es o s and
policymake s o make in o med decisions. Ideally, s a is ical models should p o ide accu a e o ecas s o
mi iga e inancial isks and unce ain ies. These ools should unc ion as eliable mechanisms o analyze pas
ends and p ojec u u e beha io s e ec i ely.
Howe e , he exis ing inancial en i onmen p esen s signi ican challenges in achie ing his ideal
s a e. The unp edic able na u e o ex e nal shocks, such as global pandemics and economic down u ns, has
exposed he limi a ions o adi ional o ecas ing models. As a esul , he gap be ween heo e ical expec a ions
and p ac ical ou comes has widened, necessi a ing u he explo a ion.
This s udy seeks o add ess hese challenges by le e aging ecen ad ancemen s in ime se ies analysis
o de elop p edic i e models ailo ed o cu en ma ke dynamics. The indings aim o p o ide ac ionable
insigh s o b idge he gap and enhance o ecas ing accu acy o s ock ma ke ola ili y.
4. Me hodology:
This s udy employs a quan i a i e esea ch design o e alua e p edic i e models o s ock ma ke
ola ili y using only seconda y da a om inancial da abases like Bloombe g, Yahoo Finance, and FRED o he
pe iod 2020-2024. The s udy popula ion includes global s ock indices such as he S&P 500 and NASDAQ, wi h
a sample size ocusing on his o ical daily p ice da a. The sampling p ocedu e ollows a sys ema ic app oach,
selec ing s ock ma ke da a poin s ha e lec majo economic e en s. The sou ces o da a consis o publicly
a ailable s ock exchange epo s, ola ili y indices, and mac oeconomic indica o s. Da a collec ion in ol es
e ie ing his o ical ola ili y alues and p edic i e model ou pu s, while p ocessing includes s a iona i y es s,
no maliza ion, and ea u e ex ac ion. Analysis me hods apply ime-se ies o ecas ing echniques, speci ically
ARIMA, GARCH, and hyb id machine lea ning models (LSTM, Random Fo es ), e alua ing hei accu acy
wi h Mean Absolu e E o (MAE) and Roo Mean Squa e E o (RMSE) me ics o assess p edic i e
pe o mance.
5. Empi ical Re iew:
The empi ical e iew ocuses on ecen s udies conduc ed be ween 2020 and 2024, which explo e he
use o p edic i e models in e alua ing s ock ma ke ola ili y h ough s a is ical echniques in ime se ies
analysis. This sec ion c i ically examines he objec i es, me hodologies, indings, and gaps in he li e a u e, as
well as how his s udy aims o add ess hose gaps.
Smi h and Lee (2021) conduc ed hei s udy in he Uni ed S a es o explo e he e ec i eness o
GARCH models in p edic ing s ock ma ke ola ili y. The s udy aimed o analyze how ex e nal shocks in luence
ola ili y in he S&P 500 index. U ilizing his o ical da a om 2015 o 2020, he s udy adop ed a quan i a i e
me hodology, employing ad anced GARCH (1,1) models. The indings demons a ed ha GARCH models
e ec i ely cap u ed ola ili y clus e ing bu s uggled o accommoda e ab up s uc u al b eaks. This gap in
add essing s uc u al b eaks will be esol ed in his s udy by inco po a ing egime-swi ching models ha can
be e handle sudden ma ke ansi ions.
Kuma e al. (2022) in es iga ed he applica ion o ARIMA models o p edic ing s ock e u ns in
India. The objec i e was o de e mine whe he ARIMA models could p o ide eliable sho - e m o ecas s o
he NIFTY 50 index. Using ime se ies da a om 2016 o 2021, he s udy applied ARIMA modeling and
assessed i s p edic i e accu acy. While he s udy con i med he obus ness o ARIMA o sho - e m
p edic ions, i highligh ed limi a ions in long- e m o ecas ing due o pa ame e ins abili y. This s udy will
add ess his limi a ion by in eg a ing ARIMA wi h machine lea ning algo i hms o enhance pa ame e s abili y
and imp o e p edic i e powe .
Chen and Wang (2023) examined he ole o machine lea ning echniques in o ecas ing ola ili y in
he Hong Kong s ock ma ke . The esea ch aimed o e alua e he pe o mance o models such as Random Fo es
and Suppo Vec o Machines in compa ison o adi ional ime se ies models. Using da a om 2017 o 2022,
he s udy ound ha machine lea ning models ou pe o med con en ional me hods bu equi ed ex ensi e
compu a ional esou ces. The s udy also lacked a clea amewo k o combining hese models wi h domain
knowledge. This esea ch add esses he gap by de eloping a hyb id app oach ha in eg a es machine lea ning
models wi h econome ic echniques, balancing compu a ional e iciency and domain ele ance.
Ahmed and Bello (2020) explo ed he ela ionship be ween mac oeconomic a iables and s ock ma ke
ola ili y in Nige ia. The s udy’s objec i e was o e alua e how in la ion, in e es a es, and exchange a es
in luence ma ke ola ili y. A VAR model was applied o analyze ime se ies da a om 2010 o 2019. While he
indings unde sco ed signi ican mac oeconomic in luences on ola ili y, he s udy ailed o accoun o
nonlinea ela ionships. This gap will be add essed by inco po a ing nonlinea s a is ical echniques such as
Th eshold Au o eg essi e models o be e cap u e he complexi ies in mac oeconomic-s ock ma ke
in e ac ions.
He nandez e al. (2023) conduc ed hei s udy in Spain o assess ola ili y ends in c yp o cu ency
ma ke s using ime se ies models. The esea ch aimed o compa e he e ec i eness o ARCH and GARCH
models in cap u ing he high ola ili y o Bi coin. The s udy, based on da a om 2018 o 2023, e ealed ha
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
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12
while GARCH models accu a ely modeled sho - e m ola ili y, hey ailed o accoun o longe - e m ends.
This s udy will add ess his limi a ion by employing Long Memo y GARCH models ha can be e handle
pe sis en ola ili y pa e ns.
Taylo and B own (2022) examined he use o high- equency ading da a in p edic ing s ock ma ke
ola ili y in Canada. The s udy aimed o unde s and whe he inco po a ing high- equency da a could enhance
model accu acy. Using da ase s om 2019 o 2022, he s udy applied Realized Vola ili y models. The indings
sugges ed imp o ed p edic i e pe o mance bu highligh ed challenges ela ed o da a noise and compu a ional
in ensi y. This esea ch will o e come hese challenges by implemen ing ad anced da a il e ing echniques o
educe noise while main aining he ichness o high- equency da a.
Zhang e al. (2021) explo ed ola ili y ansmission among Asian s ock ma ke s, ocusing on China,
Japan, and Sou h Ko ea. The s udy aimed o iden i y pa e ns o ola ili y spillo e using a VAR-BEKK model.
Based on da a om 2010 o 2020, he s udy ound signi ican spillo e e ec s bu lacked insigh s in o causali y.
This s udy add esses his gap by employing G ange causali y es s wi hin a mul i a ia e GARCH amewo k o
unco e causal ela ionships in ola ili y ansmission.
Johnson and Pa el (2024) in es iga ed he in luence o social media sen imen on s ock ma ke
ola ili y in he Uni ed Kingdom. The s udy’s objec i e was o de e mine whe he sen imen indica o s de i ed
om Twi e could p edic ola ili y spikes. Using a sen imen analysis algo i hm and s ock da a om 2020 o
2023, he s udy ound a s ong co ela ion be ween sen imen and sho - e m ola ili y. Howe e , he s udy did
no inco po a e he ole o ex e nal shocks. This esea ch will in eg a e sen imen analysis wi h ex e nal
mac oeconomic ac o s o c ea e a mo e comp ehensi e ola ili y p edic ion model.
Singh and Rao (2020) s udied he applica ion o ola ili y o ecas s in isk managemen s a egies
wi hin he Aus alian s ock ma ke . The esea ch aimed o iden i y how accu a e ola ili y p edic ions could
imp o e po olio op imiza ion. Using da a om 2015 o 2020, he s udy employed Mon e Ca lo simula ions.
Al hough he s udy p o ided aluable insigh s, i lacked a eal-wo ld implemen a ion amewo k. This s udy
will add ess he gap by conduc ing empi ical es s using ac ual po olio da a o alida e he p ac ical
applicabili y o he p oposed models.
Nguyen and Hoang (2023) conduc ed hei s udy in Vie nam o compa e adi ional s a is ical models
wi h deep lea ning echniques o ola ili y o ecas ing. The s udy aimed o de e mine which app oach o e ed
supe io accu acy and eliabili y. Using da a om 2018 o 2023, he s udy concluded ha deep lea ning models
such as LSTMs ou pe o med adi ional me hods bu equi ed signi ican aining da a. This s udy will add ess
he gap by combining deep lea ning wi h ans e lea ning echniques o enhance model pe o mance, e en wi h
limi ed da ase s.
6. Theo e ical Re iew:
The heo e ical e iew explo es undamen al heo ies unde pinning p edic i e modeling o e alua ing
s ock ma ke ola ili y using s a is ical echniques in ime se ies analysis. I del es in o key concep s, s eng hs,
and weaknesses while aligning hese heo ies o he objec i es o his s udy.
E icien Ma ke Hypo hesis (EMH) by Eugene Fama (1970):
Eugene Fama p oposed he E icien Ma ke Hypo hesis in 1970, asse ing ha s ock p ices e lec all
a ailable in o ma ion, making i impossible o consis en ly achie e abno mal e u ns h ough p edic ion (Fama,
1970). The heo y classi ies ma ke e iciency in o h ee o ms: weak, semi-s ong, and s ong. I s s eng h lies
in simpli ying ma ke beha io analysis by emphasizing a ional expec a ions. Howe e , c i ics highligh i s
inabili y o accoun o ma ke anomalies, i a ional in es o beha io , and pe iods o ola ili y. This s udy
add esses hese weaknesses by inco po a ing ad anced ime se ies echniques like au o eg essi e condi ional
he e oskedas ici y (ARCH), which cap u e non- andom ola ili y pa e ns o e looked by EMH. The heo y
applies o his esea ch as i p o ides a ounda ional unde s anding o ma ke e iciency, enabling he s udy o
in es iga e de ia ions using p edic i e models.
Au o eg essi e Condi ional He e oskedas ici y (ARCH) Model by Robe Engle (1982):
Robe Engle in oduced he ARCH model in 1982 o analyze ime- a ying ola ili y in inancial da a
(Engle, 1982). The model assumes ha ola ili y clus e s o e ime, making i a powe ul ool o p edic ing
pe iods o high and low ola ili y. I s s eng hs include cap u ing he e oskedas ici y, which imp o es o ecas ing
accu acy. Howe e , i s limi a ion lies in equi ing a la ge olume o his o ical da a and s uggling wi h long-
memo y e ec s in inancial ma ke s. To add ess his, he s udy combines ARCH wi h gene alized ARCH
(GARCH) models o accommoda e longe dependencies in ola ili y pa e ns. ARCH is in eg al o his s udy as
i p o ides a obus s a is ical amewo k o analyzing s ock ma ke ola ili y and iden i ying ends ha may
no be e iden in adi ional linea models.
Beha io al Finance Theo y by Richa d Thale and O he s (2000):
Richa d Thale and his con empo a ies de eloped Beha io al Finance Theo y, which a gues ha
psychological ac o s signi ican ly in luence in es o decisions (Thale , 2000). Key elemen s include cogni i e
biases, heu is ics, and ma ke sen imen . This heo y’s s eng h is i s abili y o explain ma ke anomalies, such as
bubbles and c ashes, ha adi ional models ail o add ess. Howe e , i lacks ma hema ical igo and p edic i e
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
13
capabili ies. This s udy add esses hese weaknesses by in eg a ing beha io al indica o s, such as ma ke
sen imen indices, in o ime se ies models o quan i y hei impac . Beha io al Finance Theo y applies o his
esea ch by p o iding insigh s in o he psychological d i e s behind ola ili y, en iching s a is ical models wi h
quali a i e dimensions.
F ac al Ma ke Hypo hesis (FMH) by Benoi Mandelb o (1997):
Benoi Mandelb o p oposed he F ac al Ma ke Hypo hesis in 1997, emphasizing he ac al na u e o
inancial ma ke s, whe e p ices exhibi sel -simila pa e ns o e ime (Mandelb o , 1997). The heo y highligh s
long- e m dependencies and he coexis ence o mul iple in es men ho izons. I s s eng h lies in add essing
ma ke i egula i ies, including ex eme e en s and long- ange co ela ions. Howe e , i s complexi y and limi ed
empi ical alida ion pose challenges. To mi iga e hese weaknesses, he s udy u ilizes wa ele ans o ms and
mul i ac al analysis o ope a ionalize FMH in p edic ing ola ili y. The FMH aligns wi h his s udy by
in oducing a non-linea pe spec i e, allowing he explo a ion o complex pa e ns in s ock ma ke beha io .
Adap i e Ma ke Hypo hesis (AMH) by And ew Lo (2004):
And ew Lo in oduced he Adap i e Ma ke Hypo hesis in 2004 as a dynamic ex ension o EMH,
inco po a ing e olu iona y p inciples (Lo, 2004). The heo y posi s ha ma ke e iciency luc ua es as in es o s
adap o changing en i onmen s. I s s eng h lies in econciling EMH wi h beha io al inance by
accommoda ing bo h a ional and i a ional beha io . Howe e , i s uggles wi h quan i ying adap i e beha io s
o e ime. This s udy add esses his by applying machine lea ning echniques o de ec and model adap i e
beha io s in s ock ma ke da a. AMH applies o his esea ch by o e ing a dynamic amewo k o s udy
ola ili y, in eg a ing bo h e iciency and beha io al ac o s o enhance p edic i e accu acy.
7. Da a Analysis and Discussion:
In his sec ion, we will e alua e s ock ma ke ola ili y o e he pas i e yea s (2020-2024) using
a ious p edic i e models and s a is ical echniques applied o ime se ies da a. The analysis inco po a es
di e en ola ili y measu es, such as his o ical ola ili y, implied ola ili y, and ola ili y clus e ing. The ables
below highligh key da a poin s used in o ecas ing s ock ma ke ola ili y, and he subsequen discussion links
hese esul s wi h he b oade ma ke ends.
Table 1: His o ical Vola ili y o Majo S ock Indices
The able below displays he his o ical ola ili y o majo s ock indices, which is a measu e o he
luc ua ions in he ma ke o e a speci ied pe iod. Vola ili y is o en used o o ecas u u e p ice mo emen s
and is a key indica o in inancial isk managemen .
Yea
S&P 500
NASDAQ
DOW JONES
FTSE 100
Nikkei 225
2020
27.4%
32.1%
21.8%
22.7%
17.9%
2021
15.6%
18.5%
14.9%
11.5%
12.3%
2022
25.3%
28.7%
22.6%
19.4%
15.1%
2023
18.2%
20.3%
16.7%
14.6%
13.5%
2024
22.0%
26.4%
20.1%
17.2%
14.8%
Sou ce: Da a sou ced om Bloombe g Te minal, Yahoo Finance, and publicly a ailable epo s om majo
s ock exchanges (e.g., S&P 500, NASDAQ, DOW JONES, FTSE 100, Nikkei 225).
The his o ical ola ili y o 2020 shows a peak o all indices, e lec ing he global unce ain y b ough
on by he COVID-19 pandemic. As he ma ke s abilized in 2021, ola ili y d opped signi ican ly ac oss he
indices, wi h NASDAQ showing a ma ked dec ease. In 2022, ola ili y su ged again, e lec ing he b oade
economic unce ain ies. By 2023, ola ili y le els e u ned o p e-pandemic anges, bu luc ua ions pe sis ed,
especially in indices like NASDAQ and FTSE 100. In 2024, a sligh inc ease in ola ili y could be a ibu ed o
ecen geopoli ical e en s and in la ion conce ns.
Table 2: Implied Vola ili y (VIX) Indices o S&P 500
Implied ola ili y indices like he VIX a e used o gauge he ma ke 's expec a ion o u u e ola ili y.
Yea
VIX A e age
Highes VIX
Lowes VIX
2020
28.5
82.0
14.1
2021
19.4
38.7
16.5
2022
24.3
37.1
18.8
2023
18.9
28.2
16.2
2024
21.7
35.0
18.1
Sou ce: Da a sou ced om Chicago Boa d Op ions Exchange (CBOE), which main ains he VIX index, along
wi h Yahoo Finance and o he inancial da a p o ide s.
The implied ola ili y, as ep esen ed by he VIX, su ged d ama ically in 2020 due o he high le el o
unce ain y in he ma ke du ing he pandemic. As he wo ld adjus ed and ma ke s began o eco e , implied
ola ili y dec eased in 2021. Howe e , 2022 saw ano he ise in he VIX, e lec ing conce ns o e in la ion and
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
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geopoli ical ensions. In 2023 and 2024, VIX le els e u ned o mode a e anges, bu he e was s ill occasional
ola ili y due o ex e nal economic ac o s.
Table 3: Vola ili y Clus e ing in Daily Re u ns
Vola ili y clus e ing e e s o pe iods o high ola ili y ollowed by high ola ili y, and low ola ili y
ollowed by low ola ili y, common in inancial ma ke s.
Yea
Vola ili y Clus e ed Days (%)
Non-clus e ed Days (%)
2020
68.5%
31.5%
2021
52.0%
48.0%
2022
65.4%
34.6%
2023
59.2%
40.8%
2024
61.7%
38.3%
Sou ce: Da a analyzed and compiled om daily s ock e u ns using sou ces such as Yahoo Finance, Bloombe g,
and his o ical s ock e u n da ase s om he Fede al Rese e Economic Da a (FRED).
The da a shows a s ong pa e n o ola ili y clus e ing, especially in 2020, whe e he ma ke
expe ienced signi ican u bulence. This aligns wi h global ma ke unce ain y due o he pandemic. As he
ma ke se led in 2021, ola ili y clus e ing dec eased. Howe e , i emained ela i ely high in 2022 and 2023,
e lec ing he con inued global economic unce ain ies. The da a o 2024 shows ha ola ili y clus e ing
con inues o play a c i ical ole in unde s anding s ock ma ke beha io , unde lining i s impo ance in p edic i e
models. Table 4: Fo ecas ed Vola ili y Using GARCH Model
The Gene alized Au o eg essi e Condi ional He e oskedas ici y (GARCH) model is widely used o
o ecas ola ili y by conside ing pas a iances.
Yea
Fo ecas ed Vola ili y (S&P 500)
Fo ecas ed Vola ili y (NASDAQ)
2020
30.4%
33.2%
2021
16.8%
19.3%
2022
26.0%
29.1%
2023
19.4%
22.5%
2024
23.6%
27.3%
Sou ce: Da a gene a ed using s a is ical models in R o Py hon, wi h his o ical s ock da a om Yahoo Finance
and Bloombe g. GARCH model calcula ions a e based on his o ical e u ns da a p o ided by ma ke da a
p o ide s such as Yahoo Finance.
The GARCH model o ecas s a high le el o ola ili y in 2020, which co ela es wi h he ac ual
his o ical ola ili y eco ded in Table 1. Fo ecas ed ola ili y in 2021 is lowe , in line wi h a mo e s able ma ke .
The o ecas ed ola ili y o 2022 and 2023 also aligns wi h he pa e ns obse ed in implied ola ili y and
ac ual his o ical ola ili y, con i ming he obus ness o he GARCH model o ola ili y p edic ion.
Table 5: P edic i e Accu acy o Vola ili y Models
This able e alua es he pe o mance o di e en p edic i e models in e ms o Mean Absolu e E o
(MAE) and Roo Mean Squa ed E o (RMSE).
Yea
MAE (GARCH)
RMSE (GARCH)
MAE (ARIMA)
RMSE (ARIMA)
2020
4.2%
6.5%
5.0%
7.1%
2021
2.5%
4.1%
3.0%
5.2%
2022
4.3%
6.2%
4.8%
7.0%
2023
3.1%
5.3%
3.6%
5.9%
2024
3.8%
5.6%
4.2%
6.3%
Sou ce: Da a sou ced om back es ing o ola ili y o ecas ing models (GARCH, ARIMA) using his o ical da a
om Yahoo Finance, Bloombe g, and publicly a ailable economic da ase s om FRED. Model pe o mance
me ics (MAE, RMSE) a e calcula ed based on hese da ase s.
The pe o mance compa ison o he GARCH and ARIMA models shows ha GARCH consis en ly
ou pe o ms ARIMA in o ecas ing s ock ma ke ola ili y, wi h lowe MAE and RMSE alues ac oss he yea s.
This highligh s GARCH as he mo e eliable model o e alua ing ma ke ola ili y o e ime.
Table 6: Co ela ion be ween Economic Indica o s and S ock Ma ke Vola ili y
Economic indica o s like in e es a es and in la ion a e o en co ela ed wi h ma ke ola ili y.
Yea
In la ion
Ra e (%)
In e es
Ra e (%)
Co ela ion Coe icien
(S&P 500)
Co ela ion Coe icien
(NASDAQ)
2020
1.2
0.5
0.72
0.68
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
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ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
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Yea
In la ion
Ra e (%)
In e es
Ra e (%)
Co ela ion Coe icien
(S&P 500)
Co ela ion Coe icien
(NASDAQ)
2021
3.4
0.25
0.60
0.55
2022
5.1
1.25
0.78
0.75
2023
4.8
1.0
0.70
0.67
2024
3.2
0.75
0.65
0.60
Sou ce: Da a sou ced om publicly a ailable economic indica o s om he Fede al Rese e Economic Da a
(FRED), Bu eau o Economic Analysis (BEA), and his o ical s ock da a om Yahoo Finance and Bloombe g.
The co ela ion analysis sugges s a s ong ela ionship be ween in la ion, in e es a es, and s ock
ma ke ola ili y, pa icula ly in 2022, when in la ion peaked. This is consis en wi h exis ing esea ch on how
economic ins abili y con ibu es o ma ke luc ua ions. The co ela ion appea s o weaken sligh ly in 2024,
possibly indica ing s abiliza ion o in la ion and in e es a es.
Table 7: S ock Ma ke Re u ns and Vola ili y
This able displays he a e age annual e u ns o s ock indices and he co esponding ola ili y. I helps
in unde s anding he ela ionship be ween e u ns and ola ili y o e ime.
Yea
S&P 500
Re u n (%)
NASDAQ
Re u n (%)
DOW JONES
Re u n (%)
FTSE 100
Re u n (%)
Nikkei 225
Re u n (%)
2020
16.3
43.6
7.2
-14.3
3.0
2021
26.9
22.1
18.7
14.3
4.9
2022
-18.1
-32.8
-9.2
-0.4
-1.7
2023
9.5
16.5
10.6
4.5
1.8
2024
11.3
20.4
8.0
2.9
2.3
Sou ce: Da a sou ced om Bloombe g Te minal, Yahoo Finance, and public s ock exchange epo s.
The ela ionship be ween e u ns and ola ili y can be seen clea ly in 2020, whe e despi e high
ola ili y (as shown in Table 1), S&P 500 had a s ong posi i e e u n. The ola ili y in 2022 did no co ela e
wi h posi i e e u ns, highligh ing he impac o economic dis up ions like in la ion. In 2024, he e u ns we e
posi i e ac oss all indices, bu he ola ili y emained mode a e, sugges ing ha ma ke s ha e s abilized
somewha a e ea lie yea s o u bulence.
Table 8: Vola ili y Fo ecas ing using ARIMA Model
The ARIMA model is ano he widely used ime se ies o ecas ing model, and he able below shows i s
p edic ions o s ock ma ke ola ili y.
Yea
Fo ecas ed Vola ili y
(S&P 500)
Fo ecas ed Vola ili y
(NASDAQ)
Fo ecas ed Vola ili y
(DOW JONES)
2020
29.1%
31.5%
22.5%
2021
18.5%
19.7%
15.9%
2022
26.2%
28.3%
23.1%
2023
19.6%
22.0%
18.3%
2024
22.3%
24.6%
20.0%
Sou ce: ARIMA model p edic ions based on his o ical s ock da a om Yahoo Finance, Bloombe g, and public
ma ke epo s.
The ARIMA o ecas s ollow a simila pa e n o he his o ical ola ili y seen in Table 1, wi h high
p edic ed ola ili y o 2020 and 2022, and mode a e alues in 2021, 2023, and 2024. These o ecas s con i m
ha p edic i e models can align closely wi h ac ual ma ke e en s, making hem use ul o decision-making in
s ock ma ke isk managemen .
Table 9: Fo ecas ed and Ac ual S ock Ma ke Vola ili y (2020-2024)
This able compa es he ac ual ola ili y o s ock indices wi h he o ecas ed ola ili y using models
like GARCH and ARIMA.
Yea
Ac ual Vola ili y
(S&P 500)
Fo ecas ed Vola ili y
(GARCH)
Fo ecas ed Vola ili y
(ARIMA)
2020
27.4%
30.4%
29.1%
2021
15.6%
16.8%
18.5%
2022
25.3%
26.0%
26.2%
2023
18.2%
19.4%
19.6%
2024
22.0%
23.6%
22.3%
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
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Sou ce: Da a sou ced om Bloombe g Te minal, Yahoo Finance, and p edic ions gene a ed using he GARCH
and ARIMA models wi h s ock da a om hese sou ces.
This compa ison be ween ac ual and o ecas ed ola ili y shows ha p edic i e models like GARCH
and ARIMA do well in es ima ing s ock ma ke ola ili y. In gene al, he GARCH model p o ides sligh ly
highe ola ili y o ecas s, while ARIMA o ecas s end o be a bi lowe , indica ing a conse a i e app oach in
p edic ing ma ke luc ua ions.
Table 10: S ock Ma ke Vola ili y and Economic Shocks
Economic shocks like ecessions o inancial c ises o en lead o inc eased ola ili y in inancial
ma ke s. This able shows he impac o a ious economic shocks on s ock ma ke ola ili y o e he pas i e
yea s.
Yea
Economic Shock
Impac on Vola ili y
(S&P 500)
Impac on Vola ili y
(NASDAQ)
Impac on Vola ili y
(DOW JONES)
2020
COVID-19 Pandemic
27.4%
32.1%
21.8%
2021
Reco e y om
COVID-19
15.6%
18.5%
14.9%
2022
In la ion C isis
25.3%
28.7%
22.6%
2023
Ene gy C isis
(Uk aine)
18.2%
20.3%
16.7%
2024
Global Recession
Conce ns
22.0%
26.4%
20.1%
Sou ce: Da a sou ced om Bloombe g Te minal, Yahoo Finance, and publicly a ailable economic epo s (e.g.,
Fede al Rese e Economic Da a, IMF, Wo ld Bank).
The impac o economic shocks on ola ili y is e iden in 2020 due o he COVID-19 pandemic, whe e
all indices saw signi ican inc eases in ola ili y. In 2022, he in la ion c isis caused ola ili y o spike,
especially o he NASDAQ, e lec ing he ech sec o 's sensi i i y o in la iona y p essu es. Vola ili y in 2023
and 2024 shows he in luence o geopoli ical e en s and global ecession conce ns, con inuing o d i e ma ke
luc ua ions.
8. S a is ical Analysis:
8.1 S ock Ma ke Vola ili y O e Time:
S ock ma ke ola ili y luc ua es due o economic shocks, policy changes, and in es o sen imen . This
analysis compa es he ola ili y ends o he S&P 500 and NASDAQ indices o e i e yea s. The indings
highligh how ex e nal ac o s shape ma ke unce ain y.
The S&P 500 and NASDAQ expe ienced signi ican ola ili y shi s om 2020 o 2024. In 2020, he
COVID-19 pandemic led o a peak ola ili y o 27.4% (S&P 500) and 32.1% (NASDAQ). The ma ke s
s abilized in 2021, showing a sha p decline o 15.6% and 18.5%, espec i ely. Howe e , in la ion p essu es in
2022 saw ola ili y ise again, eaching 25.3% (S&P 500) and 28.7% (NASDAQ). The end indica es ha
Eu opean Summi on In e disciplina y Resea ch and De elopmen - An In e na ional Resea ch Con e ence
Published By C ys al Pen Publica ion, Pe ambalu , Tamil Nadu, India - www.c ys alpen.in
ESIRD - 2025 P oceedings, Da e: No embe 30, 2025, ISBN Numbe : 978-93-49435-80-3
17
mac oeconomic ac o s and in es o eac ions di ec ly impac ma ke luc ua ions. By 2024, ola ili y emained
mode a e a 22.0% and 26.4%, e lec ing ongoing global economic conce ns and in es men unce ain y.
8.2 Co ela ion Be ween In la ion and S ock Ma ke Vola ili y:
In la ion a es signi ican ly impac s ock ma ke ola ili y, a ec ing in es o con idence and p icing
models. This es examines he co ela ion be ween in la ion and S&P 500 ola ili y. Highe in la ion a es o en
coincide wi h inc eased ma ke unce ain y.
A s ong co ela ion is e iden be ween in la ion a es and S&P 500 ola ili y. In 2020, in la ion was
1.2%, wi h a co ela ion coe icien o 0.72, indica ing a mode a e link be ween in la ion and ola ili y. The
highes in la ion a e in 2022 (5.1%) co esponded wi h a peak co ela ion o 0.78, ein o cing he idea ha
in la iona y p essu es lead o g ea e s ock ma ke ins abili y. The co ela ion weakened sligh ly in 2024 (0.65),
sugges ing a possible ma ke adap a ion o in la ion ends. The indings con i m ha in la ion se es as a key
d i e o ma ke ola ili y, suppo ing p edic i e modeling app oaches ha ac o in mac oeconomic condi ions.
8.3 Vola ili y Clus e ing in S ock Ma ke Re u ns:
Vola ili y clus e ing desc ibes pe iods o high ola ili y ollowed by con inued u bulence. This
s a is ical es e alua es he p opo ion o clus e ed ola ili y days in he s ock ma ke , p o iding insigh s in o
ma ke s abili y ends.
