Equilib ium. Qua e ly Jou nal o Economics and Economic Policy
Volume 17 Issue 3 Sep embe 2022
p-ISSN 1689-765X, e-ISSN 2353-3293
www.economic-policy.pl
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ORIGINAL ARTICLE
Ci a ion: Kolko á, A., & Rozehnal, P. (2022). Hyb id demand o ecas ing models: p e-pandemic
and pandemic use s udies. Equilib ium. Qua e ly Jou nal o Economics and Economic Policy,
17(3), 699–725. doi: 10.24136/eq.2022.024
Con ac o co esponding au ho : And ea Kolko á, and ea.kolko a@ sb.cz
A icle his o y: Recei ed: 3.04.2022; Accep ed: 15.07.2022; Published online: 30.09.2022
And ea Kolko á
VSB - Technical Uni e si y Os a a, Czechia
o cid.o g/0000-0002-4764-3164
Pe Rozehnal
VSB - Technical Uni e si y Os a a, Czechia
o cid.o g/0000-0002-1339-9992
Hyb id demand o ecas ing models: p e-pandemic
and pandemic use s udies
JEL Classi ica ion: M21; M15; C53
Keywo ds: o ecas Hyb id; demand o ecas ing; s a is ic model; neu al ne wo ks
Abs ac
Resea ch backg ound: In business p ac ice and academic sphe e, he ques ion o which o he
p ognos ic models is he mos accu a e is cons an ly p esen . The accu acy o models based on
a i icial in elligence and s a is ical models has long been discussed. By combining he ad an ages
o bo h g oups, hyb id models ha e eme ged. These models show high accu acy. Mo eo e , he
ques ion emains whe he da a in a dynamically changing economy ( o example, in a pandemic
pe iod) ha e changed he possibili ies o using hese models. The changing economy will con in-
ue o be an impo an elemen in demand o ecas ing in he yea s o come. In business, whe e he
concep o jus in ime al eady p o es o be insu icien , i is necessa y o open new esea ch
ques ions in he ield o demand o ecas ing.
Pu pose o he a icle: The aim o he a icle is o apply hyb id models o bicycle sales e-shop
da a wi h a compa ison o accu acy models in he p e-pandemic pe iod and in he pandemic
pe iod. The pape examines he hypo hesis ha he pandemic pe iod has changed he accu acy o
hyb id models in compa ison wi h s a is ical models and models based on a i icial neu al ne -
wo ks.
Models: In his s udy, hyb id models will be used, namely he The a model and he new o e-
cas Hyb id, compa ed o he s a is ical models ETS, ARIMA, and models based on a i icial
neu al ne wo ks. They will be applied o he da a o he e-shop wi h he cycle asso men in he
pe iod om 1.1. 2019 o 5.10 2021. Whe eas he pe iod will be di ided in o wo pa s, p e-
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
700
pandemic, i.e. un il 1 Ma ch 2020 and pandemic a e ha da e. The accu acy e alua ion will be
based on he RMSE, MAE, and ACF1 indica o s.
Findings & alue added: In his s udy, we ha e concluded ha he p edic ion o he Hyb id
model was he mos accu a e in bo h pe iods. The s udy can hus p o ide a scien i ic basis o any
o he dynamic changes ha may occu in demand o ecas ing in he u u e. In o he pe iods when
he e will be ola ile demand, i is essen ial o choose models in which accu acy will dec ease he
leas . The e o e, his s udy p o ides guidance o he use o me hods in u u e pe iods as well. The
s a ed esul s a e likely o be alid e en in an in e na ional compa ison.
In oduc ion
In he academic sphe e as well as in business p ac ice, he e a e s ill discus-
sions abou models o demand o ecas ing in business economics. These
s ill used s a is ical models a e consequen ly such a s anda d solu ion o
many o ecas ing sys ems e en nowadays. In ecen yea s, models based on
a i icial in elligence ha e come o o e, p ima ily a i icial neu al ne -
wo ks, in spi e o he ac ha hese models may no always be he bes .
P ac ice shows ha he aining da a indica es g ea accu acy on he es
da a; his may no be he case (Kolko á, 2018, pp. 102–119).
The mos mode n models used in o ecas ing we e hyb id models,
which ake ad an age o bo h app oaches. As ea ly as 1969, Ba es and
G ange (2017) in oduced combined models and he ewi h p o ided he
concep ual ounda ions o he u he use o exis ing models. Hyb id mod-
els combine exis ing me hods wi h a i icial in elligence. No only hei
mu ual combina ion, bu also he possibili y o calcula ing model pa ame-
e s on a s a ic basis using a i icial in elligence.
Ini ially in M4-Compe i ion (Pe opoulos & Mak idakis, 2020, pp. 3–6),
hese models we e a ed as he mos success ul. Howe e , i is clea ha
each model has i s jus i ica ion, and i s use depends mainly on he selec ed
da a.
This a icle uses he models ha we e e alua ed as mo e success ul in
his compe i ion. And hey we e hyb id me hods ha success ully pa ici-
pa ed in his compe i ion.
As no ed ea lie , he aim o his a icle is o apply hyb id models o bi-
cycle sales e-shop da a wi h a compa ison o accu acy models in he p e-
pandemic pe iod by con as in he pandemic pe iod. The pape examines
he hypo hesis ha he pandemic pe iod has changed he accu acy o hyb id
models in compa ison wi h s a is ical models and models based on a i icial
neu al ne wo ks.
Subsequen ly, hypo heses we e speci ied o mee he goal. The i s hy-
po hesis: ha he pandemic pe iod has changed he accu acy o hyb id
models compa ed o s a is ical models and models based on a i icial neu al
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
701
ne wo ks. The second hypo hesis hen assumes ha hyb id models we e he
mos accu a e in he p e-pandemic pe iod. The hi d hypo hesis hen im-
plies ha he mos accu a e s a is ical models emained in he pandemic
pe iod. To make ce ain hese hypo heses, s a ic models, models based on
a i icial neu al ne wo ks, and hyb id models on daily e-shop da a in he
yea s 2019–2021 we e applied.
Addi ionally, he li e a u e e iew will de ine p e ious esea ch on hy-
b id models and he applica ion o models o p ac ical da a. Hyb id models
will be desc ibed in de ail in he me hodology chap e , and a s a is ical de-
sc ip ion o he da a will be pe o med. In he esul s sec ion, he esul s o
he calcula ions will be p esen ed in he igu es and ables. These we e sub-
sequen ly commen ed on in he discussions and he achie emen o he goal
and he accep ance o e u a ion o hypo heses we e e alua ed. Finally, he
esul s will be summa ized in conclusion.
Li e a u e e iew
Hyb id models ep esen a combina ion o models based on a i icial in el-
ligence and s a is ical models (Smyl, 2020, pp. 75–85). In 2018, a la ge
compe i ion o o ecas ing models was o ganized. These compe i ions a e
e y impo an in he o ecas ing communi y. I is cu en ly a ended by
leading esea che s om all o e he wo ld. These a e no only esea che s
om he academic sphe e, bu also esea che s om business p ac ice. This
makes hese compe i ions e en mo e se ious.
The esul s o he M4 Compe i ion (Mak idakis e al., 2018, pp. 802–
808) demons a e ha he combina ion o se e al p ognos ic models gi es
he bes esul s. O he 17 models e alua ed as he mos accu a e in his
compe i ion, 12 we e mainly combina ions o s a is ical models.
The bigges su p ise o he M4 Compe i ion was he hyb id app oach.
The hyb id model was also he absolu e winne o his compe i ion. The
hyb id model in he M4 Compe i ion was p esen ed by Smyl (2020, pp. 75–
85), a da a scien is om Ube Technologies. Smyl applied a hyb id model
based on a i icial neu al ne wo ks and a s a is ical model inspi ed by expo-
nen ial smoo hing. He used exponen ial smoo hing o mulas o deseasonize
and no malize ime se ies and used ad anced neu al ne wo ks o ex apo-
la e.
He ea e he second mos accu a e model in his compe i ion was one
ha combined se en s a is ical and one machine lea ning model. The
weigh s he e we e calcula ed using a machine lea ning algo i hm. This
model was p esen ed by he Spanish Uni e si y o A Co uña and he Aus-
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
702
alian Monash Uni e si y (Mon e o-Manso e al. 2020, pp. 86–92). Ano h-
e new hyb id model was de eloped by Non apa e al. (2021), he model
uses he SARIMAX p edic ion model and an a i icial neu al ne wo k.
The esul s o he M5Compe i ion (Mak idakis e al., 2022) a e cu en -
ly being published. This compe i ion ocused on o ecas ing e ail sales, so
i was e y close o demand o ecas ing, which is also applied in his a i-
cle. Howe e , no all esul s a e cu en ly a ailable ye .
Ano he impo an o ecas ing compe i ion is p o ided by Kaggle o e-
cas ing compe i ions (Boje & Meldgaa d, 2021). He e i ollows ha mod-
els using c oss-lea ning end, decision ees and neu al ne wo ks a e s ong
p ognos ic models. As a esul , in his s udy we will supplemen neu al
ne wo ks wi h o he models and by c ea ing hyb id models we wan o ex-
amine hei usabili y.
In his con ex , i is wo hwhile o conside an in e es ing s udy on hy-
b id models in a s udy o Zougagh e al. (2021). In his s udy, con ibu ions
o hyb id p edic ion models since 2005 published in Scopus da abases ha e
been analysed; IEEE; ERIC; Google schola . A o al o 70 a icles dealing
wi h hyb id o ecas ing models we e analysed. The esul s show ha in e -
es in hyb id models has g own signi ican ly since 2016. A i icial neu al
ne wo ks a e mos o en included in hyb id models, which we e in 41% o
models. They we e also applied in 20% au o eg essi e models (AR, ARI-
MA o ARMA). In 15%, he au ho s o hyb id models used he Gene ic
algo i hm and he suppo ec o machine was used in 13% and uzzy sys-
ems 11%.
Fu he mo e, hey deal wi h hyb id models di ec ly in demand o ecas -
ing (Siddiqui e al., 2021, pp. 1–11). A pa allel se ies hyb idiza ion o sea-
sonal in elligen -based s a is ical model o demand o ecas ing (Bah ami &
Khashei & Amindous , 2021) and a selec ed hyb id model used o demand
o ecas ing ha e been used (e.g. Zhang e al., 2021; Kolko á & Ključniko ,
2021, pp. 1063–1094).
A he same ime, he e a e s ill discussions abou whe he models based
on a i icial in elligence o s a is ical models a e mo e accu a e (Kolko á,
2020, pp. 90–105). Spilio is e al. (2022) s a e ha some machine lea ning
models p o ide be e p edic ions, bo h in e ms o accu acy. He came o
simila conclusions o Cuhada (2020, pp. 55–70), who o ecas ed ou ism
in C oa ia and concluded ha models based on a i icial neu al ne wo ks
always wo k mo e accu a ely han s a is ical models. Simila ly o Pe ei a
and Ce quei a (2021, pp. 1–18) in o ecas ing he demand o ho el se -
ices, he es ablished ha he use o machine lea ning models can educe he
mean squa e e o by up o 54% o he 1-day o ecas ho izon and by up o
45% compa ed o adi ional models o exponen ial smoo hing o a 14-day
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
703
o ecas ho izon. Balaji P abhu and Dakshayini (2020, pp. 35–47) a gue
ha he mul iple linea eg ession model and he a i icial neu al ne wo k
model a e bo h use ul, eliable, and ela i ely e ec i e ools o op imizing
he e ec s o demand p edic ion in ood ha es supply managemen o
sa is ac o ily ma ch social needs. The s udy by Abbasimeh e al. (2020, pp.
345–366) compa ed a i icial in elligence models wi h s a is ical ones. The
LSTM mul ilaye ne wo k model was he mos accu a e, he second mos
accu a e model was a i icial neu al ne wo ks, howe e , in he hi d place i
was ma ked as he mos accu a e ETS model.
Fu he mo e, scien is s and especially p ac i ione s e alua e whe he he
mos accu a e models a e always he bes o p ac ical use (Kolko á &
Na á il, 2021, pp. 123–141). Especially due o he compu a ional demand
o he p edic ion o he inancial cos o main aining such a model in eal
business ope a ions. In Kolko á and Na á il (2021, pp. 123–141) pa ame-
e s o he han accu acy we e also examined. The esul s o his s udy illus-
a ed ha models based on deep lea ning ha e p o en o be he wo s on
un ime and compu ing demand.
On he o he hand, he au ho s add ess he issue whe he o no he di -
e ences be ween he accu acy o models based on a i icial in elligence
and s a is ical models a e ela ed o he ime se ies s udied. Fold ik
Eikeland e al. (2021) conclude in hei s udy ha s a is ical models achie e
highe accu acy o e longe p edic ion ho izons compa ed o neu al ne -
wo ks, while machine lea ning app oaches wo k be e in p edic ing loads
a sho e ime in e als. On he con a y, Ma ček (2019, pp. 317–322)
showed ha all he models he applied (ARIMA, NN, SVM) a e sui able as
p edic ion models o use in p ognos ic sys ems ha commonly p edic he
alues o a iables in compe i i e ene gy ma ke s. Bui e al. (2020, pp.
382–406) ecommend new models o da a il e ing o inc ease he accu acy
o models based on a i icial neu al ne wo ks. Sudden changes in demand
can occu , especially in da a om de eloping coun ies. The esul s con-
i m ha he accu acy o hese models can be signi ican ly imp o ed by
i ue o he p oposed model o s a is ical da a il e ing.
Time-se ies esea ch, which is a ec ed by ex e nal shocks, is s ill an
impo an elemen o demand o ecas ing. P incipally in he pandemic pe i-
od, demand may ha e de eloped abno mally. In his s udy, da a a e dis ib-
u ed and he mos accu a e p ognos ic model is selec ed in a pe iod o s a-
ble de elopmen and in a pe iod o economic shocks caused by a pandemic.
Resea ch is no ye ocused on his a ea.
Da a on bicycle sales in he Czech Republic du ing he pandemic we e
selec ed o his s udy. Only a ew scien i ic wo ks deal wi h his issue. The
esul s o Habib and Anik (2022) showed ha bicycle sales inc eased sig-

Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
704
ni ican ly in he pandemic, while ca sales dec eased. The same logic un-
de lies an a icle by Ramí ez e al. (2021) whe e he au ho s ound, ia
a machine lea ning model, ha he e was a 29.76% dec ease in sales in he
au omo i e indus y in he Mexican ma ke . S udies compa ing online sales
also p o ide in e es ing esul s. Acco ding o Fai lie and Fossen (2022), i
is possible o dis inguish he ields a ec ed by he pandemic, such as ac-
commoda ion acili ies, which los up o 91% o axable sales in he place
o s udy, on he con a y, online sales o goods inc eased up o 180%.
Wang e al. (2020) decla e how he pandemic a ec ed he change in sales
s yle in he dai y indus y. Fo he ime being, he au ho s ha e no deal
wi h he analysis o me hods sui able o quan i ying he demand o bicy-
cles ye .
Resea ch me hods
We illus a e his p ocedu e o his s udy by using da a om he online
s o e wi h bicycle sales. The da a decla es
pu chases ia he e-shop. The
da a se con ains 878 alues o daily e enues and daily numbe o e-shop
o de s o he yea s 2019, 2020 and pa o he yea 2021. Exac ly, he e is
om 1.1. 2019 o 8.9.2021. The desc ip i e cha ac e is ics a e de ined in
Tab. 1.
These da a a e chosen mainly because he e has been a spike in demand
o his p oduc due o he pandemic. Such a change in consume p e e -
ences is e y likely o a ec he deg ee o accu acy o demand o ecas ing
models as well. Also, he online dis ibu ion channel is cu en ly becoming
one o he impo an dis ibu ion channels. Du ing he pandemic pe iod,
his dis ibu ion channel also sp ead among small and medium-sized en e -
p ises, and i s u he use can be expec ed in he u u e.
The es ima ed Hu s exponen o he a ec ed a iables, shown in Tab. 1,
is signi ican ly g ea e han 0.5. This sugges s ha he se ies is no andom
and is con olled by pe sis en pa e ns ( he Hu s exponen is an indica o
o andomness). I his is no acciden al, he use o p edic ion models is
jus i ied.
The minimum daily u no e and he numbe o o de s we e 0. The
maximum daily u no e was CZK 2,371,324 and he maximum numbe o
o de s placed pe day was 330. The da a on mean and median a e also
shown in Tab. 1.
The da a we e decomposed using addi i e decomposi ion. Fig. 1 shows
he b eakdown o daily u no e . This cha clea ly shows an inc ease in he
ime o he pandemic. Howe e , he seasonali y o he demand o hese
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
705
goods emains he same. Fig. 2 de ines he b eakdown o he daily numbe
o o de s, whe e a simila p og ess is e iden .
The s udy e i ies h ee hypo heses. Wi h hese hypo heses, we wan o
e i y whe he he pandemic a ec ed he o ecas ing possibili ies in e ms
o he accu acy o hyb id models in con as o s a is ical models and mod-
els based on a i icial neu al ne wo ks.
H1: The pandemic pe iod has changed he accu acy o hyb id models com-
pa ed o models based on s anda d s a is ical indica o s (he ea e s a is i-
cal models) and he neu al ne wo k model.
H2: In he p e-pandemic pe iod, hyb id models we e he mos accu a e.
H3: In he pandemic pe iod, he mos accu a e models a e s a is ical.
P io esea ch has sugges ed each model is e alua ed using accu acy.
The RMSE ( oo mean squa e e o ) coe icien was used o calcula e accu-
acy. This is de ined by Hyndman and A hanasopoulos (2018), and can be
desc ibed by o mulas (1) and (2),
 = √, (1)
whe e RMSE has he same uni as he o iginal ime se ies. The MAE indi-
ca o is also decla ed in he same uni s, which exp esses he a e age de ia-
ion o he ac ual alues om he o ecas ed ones. The median can also be
used ins ead o he mean de ia ion. We hen desc ibe bo h calcula ions as
ollows,
 =


∑

− 




o  = |

| (2)
The las accu acy used is ACF1. This indica o is de ined as he au oco -
ela ion o delay e o s 1. In essence, i exp esses he deg ee o which he
cu en alue is a ec ed by p e ious alues in a ime se ies. The au oco e-
la ion unc ion o a delay o leng h k can be de ined as


=




=



!
(3)
Men ioned abo e, ETS, ARIMA, models based on a i icial neu al ne -
wo ks, a e used in his wo k. These will be compa ed wi h wo hyb id
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
706
models. The i s is he The a model, he second is he o ecas Hyb id mod-
el.
The de e minis ic model ETS (E o , T end, Seasonal) acco ding o
B own (1959); Hol (2004); Win e s (1960) can be de ined using o mulas
(4), (5), (6) and (7),


= "
#
+ %
#
+ &
#'
+ (

, (4)
whe e
"

= "
#
+ %
#
+ )(

(5)
%

= %
#
+ *(

(7)
&

= &
#'
+ +(

, (6)
whe e "

is es ima e le el, b a e es ima ed end, and s
exp ess he sea-
sonali y, ), * and + a e weigh coe icien s.
ARIMA (Au oReg essi e In eg a ed Mo ing A e age) is de ined in (Box
& Jenkins, 1976). ARIMA models use he Box-Jenkins model. The ARI-
MA model wi h he seasonal componen can be exp essed in he o m
ARIMA (p, d, q) (P, D, Q), whe e p ep esen s he deg ee o he au o-
eg essi e pa , d he deg ee o di e en ia ion, and q he deg ee o he mo -
ing a e age pa . Fo mulas can be used o calcula e ARIMA
(7) and (8),
,-./0

= 1-./(

, (7)
whe e
0

= ∆
3


(8)
This model can also be desc ibed in a special o m, ARFIMA (Au o-
Reg esi e In eg a ed Mo ing A e age). Acco ding o his model (Box &
Jenkins, 1976), i is possible o es ima e and de e mine he co ela ion in
s a iona y p ocesses e en o e y dis an andom a iables. ARFIMA in
his a icle is de ined by he ela ionship (9),
,-./-1 − ./
3


= 1-./(

(9)
Equilib ium. Qua e ly Jou nal o Economics and Economic Policy, 17(3), 699–725
707
A i icial neu al ne wo ks a e inspi ed by p ocesses in he human b ain.
The ou pu o a neu on is calcula ed when he sum o he inpu s o he neu-
on xi mul iplied by hei speci ic weigh s w
i
exceeds a ce ain alue, which
we call he dis o ion. The neu on can be desc ibed in his way
.
5
= 67∑8
9
∙ 0
5,9
− %
5
'
9
<, (10)
whe e x
i
is he speci ic alue on he i- h inpu , w
j,i
a e he weigh s o his
inpu , b
j
is bias, m is he o al numbe o inpu s, is a ans o ma ion unc-
ion, and he ou pu alues o y. P ocess a i icial neu al ne wo ks is shown
in Figu e 3. In his a icle, he Nna (p,k) model is used, whe e k is he num-
be o hidden nodes. The inpu s a e o lags 1 o p.
This model ends o be e y accu a e on aining da a, bu is usually less
accu a e on es da a. Howe e , i usually achie es good accu acy.
The i s selec ed hyb id model o ecas Hyb id is de ined in Shaub and
Ellis (2020). This model combines ARIMA, ETS, and The a, Tba s ( he
name his model is an ac onym deno ing i s salien ea u es T o igono-
me ic eg esso s o model mul iple-seasonali ies, B o Box-Cox ans o -
ma ions, A o ARMA e o s, T o end and S o seasonali y, and a i i-
cial neu al ne wo ks). The whole o ecas Hyb id model is hen de ined by
o mula (11),
-=/=∑0
'
∙ 6
'
-=/

'
, (11)
whe e 0
'
is weigh o each m o he n model, 6
'
-=/ indi idual model o
ime ho izon i. This model is called o ecas Hyb id and is published in
a package in he s a is ical p og am R (Shaub & Ellis, 2020).
The The a model was c ea ed by Assimakopoulos and Nikopoulos
(2000, pp. 521–530). The model is based on he concep o modi ica ion o
local luc ua ions o he ime se ies using he coe icien The a (deno ed by
he G eek le e θ). This coe icien is applied o he second di e ence o
he ime se ies, in ac acco ding o he ela ion,
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Acknowledgmen s
The a icle was suppo ed by SGS p ojec o VŠB-TUO, Facul y o Economics
wi h p ojec numbe SP2022/74.
Annex
Table 1. S a is ical desc ip ion
Da a Min. Max. Mean Median S anda d
de ia ion
Hu s
exponen
Re enues 0 Kč 2 371 324 Kč 260 993 Kč 168 619 Kč 296 840.9421 0.9378
Numbe o
o de s
0 Kč 330 64 46 56.3552 0.9591
2019
Re enues 0 Kč 918 742 Kč 138 705 Kč 102 916 Kč 131 155.9072 0.8812
Numbe o
o de s
0 Kč 118 35 31 23.1490
1.0096
2020–2021
Re enues
0 Kč
2 371 324 Kč
330 113 Kč
232 863 Kč
339 065.7547
0.8597
Numbe o
o de s
0 Kč
330
81
63
62.4749
0.8812
Table 2. Accu acy esul s acco ding o he ETS model
da a
RMSE
MAE
ACF1
Re enues o ecas : p e
-
pandemic da a
123660.7
91029.67
0.0251
Re enues o ecas : pos
-
pandemic da a
220112.3
158069.3
0.1134
Numbe o o de s:
p e
-
pandemic da a
20.2868
15.8643
0.0650
Numbe o o de s: pos
-
pandemic da a
37.4864
27.7062
0.1247
Table 3. Accu acy esul s acco ding o he ARIMA model
da a
RMSE
MAE
ACF1
Re enues o ecas : p e
-
pandemic da a
123645.3
90951.2
0.0243
Re enues o ecas : pos
-
pandemic da a
218015
158084.5
0.0020
Numbe o o de s: p e
-
pandemic da a
20.2256
15.7006
0.0027
Numbe o o de s: pos
-
pandemic da a
37.0503
27.5582
0.0007
Table 4. Accu acy esul s acco ding o he neu al ne wo k model
da a
RMSE
MAE
ACF1
Re enues o ecas : p e
-
pandemic da a
123660.7
91029.67
0.0251
Re enues o ecas : pos
-
pandemic da a
220112.3
158069.3
0.1134
Numbe o o de s:
p e
-
pandemic da a
20.2868
15.8643
0.0650
Numbe o o de s: pos
-
pandemic da a
37.4864
27.7062
0.1247
Table 5. Accu acy esul s acco ding o he o ecas Hyb id
da a
RMSE
MAE
ACF1
Re enues o ecas : p e
-
pandemic da a
109151.6
79836.51
0.0252
Re enues o ecas : pos
-
pandemic da a
183004.4
133228.9
0.0842
Numbe o o de s: p e
-
pandemic da a
17.8029
13.7436
0.0356
Numbe o o de s: pos
-
pandemic da a
33.2794
25.0714
0.0460
Table 6. Accu acy esul s acco ding o he The a
da a
RMSE
MAE
ACF1
Re enues o ecas : p e
-
pandemic da a
123642.7
91222.12
0.0260
Re enues o ecas : pos
-
pandemic da a
220112.3
158064.1
0.1135
Numbe o
o de s: p e
-
pandemic da a
20.2868
15.8640
0.0650
Numbe o o de s: pos
-
pandemic da a
37.4864
27.7061
0.1247
Table 7. Decline in model accu acy du ing he pandemic
The a o ecas Hyb id Nna ARIMA ETS
e enues 77.09% 70.07% 77.87% 91.77% 77.87%
numbe o o de s 47.87% 22.61% 47.87% 74.07% 47.87%
Table 8. O de o models acco ding o accu acy
O de o models acco ding o accu acy
To al
o de
RMSE MAE ACF1
The a
Re enues o ecas : p e-pandemic da a
2
4
4
4
Re enues o ecas : pos -pandemic da a
3
2
4
3
o ecas Hyb id Re enues o ecas : p e-pandemic da a
1
1
3
1
Re enues o ecas : pos -pandemic da a
1
1
2
1
NNAR Re enues o ecas : p e-pandemic da a
4
3
2
3
Re enues o ecas : pos -pandemic da a
3
3
3
3
ARIMA Re enues o ecas : p e-pandemic da a
3
2
1
2
Re enues o ecas : pos -pandemic da a
2
4
1
3
ETS Re enues o ecas : p e-pandemic da a
4
3
2
3
Re enues o ecas : pos -pandemic da a
3
3
3
3
The a
Numbe o o de s: p e-pandemic da a
3
3
3
3
Numbe o o de s: pos -pandemic da a
3
3
3
3
o ecas Hyb id Numbe o o de s: p e-pandemic da a
1
1
2
1
Numbe o o de s: pos -pandemic da a
1
1
2
1
Table 9. Con inued
O de o models acco ding o accu acy
To al
o de
RMSE MAE ACF1
NNAR Numbe o o de s: p e-pandemic da a
3
3
3
3
Numbe o o de s: pos -pandemic da a
3
3
3
3
ARIMA Numbe o o de s: p e-pandemic da a
2
2
1
2
Numbe o o de s: pos -pandemic da a
2
2
1
2
ETS Numbe o o de s: p e-pandemic da a
3
3
3
3
Numbe o o de s: pos -pandemic da a
3
3
3
3
Figu e 1. Decomposi ion o addi i e ime se ies daily e enues

Figu e 2. Decomposi ion o addi i e ime se ies daily numbe o o de s
Figu e 3. A i icial neu al ne wo ks
Sou ce: own p ocessing acco ding o Hyndman and A hanasopoulos (2021).
Figu e 4. ETS Fo ecas
Figu e 5. ARIMA o ecas
Figu e 6. Neu al ne wo ks o ecas