Mas e Deg ee P og am in
In o ma ion Managemen
Fo ecas ing models o eal es a e ma ke analysis
The case s udy o Po ugal
Ana Lúcia Ba a a Cou inho
P ojec Wo k
p esen ed as pa ial equi emen o ob aining he Mas e Deg ee P og am in In o ma ion Managemen
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
MGI
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
FORECASTING MODELS FOR REAL ESTATE MARKET ANALYSIS
THE CASE STUDY OF PORTUGAL
By
Ana Lúcia Ba a a Cou inho
P ojec Wo k p esen ed as pa ial equi emen o ob aining he Mas e ’s deg ee in In o ma ion
Managemen , wi h a specializa ion in Knowledge Managemen and Business In elligence
Supe iso (s):
João B uno Mo ais de Sousa Ja dim
Miguel de Cas o Simões Fe ei a Ne o
No embe 2023
ii
STATEMENT OF INTEGRITY
I he eby decla e ha ing conduc ed his academic wo k wi h in eg i y. I con i m ha I ha e no used
plagia ism o any o m o undue use o in o ma ion o alsi ica ion o esul s along he p ocess leading
o i s elabo a ion. I u he decla e ha I ha e ully acknowledge he Rules o Conduc and Code o
Hono om he NOVA In o ma ion Managemen School.
[Ana Lúcia Ba a a Cou inho]
[Lisbon, No embe 22nd, 2023]
iii
ACKNOWLEDGEMENTS
This esea ch would no ha e been possible wi hou he inc edible suppo o coun less people who
guided me h ough he p ocess, sha ed hei knowledge and answe ed all o my ques ions.
I would like o hank my amily o belie ing in me and i was because o hei emo ional suppo ha
hey kep my mo i a ion high h oughou he p ojec . Thanks o my iends and da a scien is s who
p o ided ad ice and eedback on he many challenges I had o o e come.
I am especially hank ul o my wo co-supe iso s Miguel de Cas o Ne o and João B uno Ja dim and
NOVA IMS o p o iding ma e ials and suppo in he essen ial con ex ha helped en ich my
knowledge and his esea ch.
i
ABSTRACT
The eal es a e ma ke is known o i s di icul ies and ola ili y, pa icula ly in de e mining p ope y
alues, which signi ican ly impac economic choices and socie al well-being. Accu a e p edic ions o
p ope y p ices can acili a e in o med decision-making and in luence in es men s a egies and
ma ke dynamics.
This s udy ocuses on p edic ing p ope y p ices in Po ugal and looks a di e en egions wi h a ocus
on Lisbon. I a emp s o use inno a i e me hods such as Decision T ee, Random Fo es , A i icial
Neu al Ne wo ks, Linea Reg ession, and K-Nea es Neighbo s.
The esea ch p o ides an in-dep h e alua ion o o ecas ing echniques by analyzing his o ical da a
and employing a ious machine lea ning algo i hms. The models a e speci ically designed o
unde s and he complex dynamics o di e en p ope y ypes in di e en egions o Po ugal. O e all,
he Random Fo es model is he bes model o p edic ing p ope y p ices, ollowed by Decision T ee
model. This o ecas is also impo an because i p o ides us wi h an insigh in o he impo ance o
ce ain ea u es in eal es a e p ope y p ices.
Using ad anced p edic i e models does no only enhance he unde s anding o eal es a e ma ke
ends bu also enables s akeholde s o make in o med decisions.
KEYWORDS
Real Es a e, Real Es a e P ope y P ices, Machine Lea ning, Random Fo es , A i icial Neu al Ne wo k,
K-Nea es Neighbo s, Decision T ee.
Sus ainable De elopmen Goals (SGD): The s udy is aligned wi h Sus ainable De elopmen
Goal 9: Indus y, Inno a ion, and In as uc u e, employing inno a i e me hods such as Decision T ee,
Random Fo es , A i icial Neu al Ne wo k, Linea Reg ession, and K-Nea es Neighbo s. Mo e
speci ically, his hesis aims o p oduce knowledge o he echnological ad ancemen o he eal es a e
ield, by in eg a ing eal es a e da a o unde s and and o ecas p ice dynamics. In such a complex and
c ucial domain, his esea ch hus p o ides one mo e con ibu ion o unde s and he eal es a e
p ope y ma ke p ices and add essing i s cu en challenges.

INDEX
1. In oduc ion .................................................................................................................. 1
2. Li e a u e e iew .......................................................................................................... 3
2.1. Mac oeconomic ..................................................................................................... 3
2.1.1. Bubbles ........................................................................................................... 4
2.1.2. Tou ism ........................................................................................................... 5
2.1.3. C ime .............................................................................................................. 5
2.2. P ice Fo ecas ........................................................................................................ 6
2.2.1. Compa a i e analysis o p edic i e models ................................................... 8
3. Me hodology .............................................................................................................. 11
3.1. Da ase Desc ip ion and modi ica ions ............................................................... 11
3.2. Model E alua ion Me ics ................................................................................... 14
3.2.1. Da a Impu a ion o he missing alues ........................................................ 16
4. Resul s and discussion ................................................................................................ 19
4.1. Explo a o y analysis ............................................................................................. 19
4.1.1. Explo ing ela ionships among key a iables ............................................... 19
4.1.2. Explo ing p ice ends in geog aphic con ex .............................................. 25
4.2. Models composi ion ............................................................................................ 30
4.3. Model esul s ....................................................................................................... 31
4.3.1. E o analysis o machine lea ning models .................................................. 34
5. Conclusions and u u e wo ks .................................................................................... 42
Bibliog aphical Re e ences .............................................................................................. 44
i
LIST OF FIGURES
Figu e 1 - Diag am ha illus a es he p ocess ha was conduc ed in his s udy .................... 2
Figu e 2 - T end o a iables o e he yea s ............................................................................ 20
Figu e 3 – P esence o absence o p ope y commodi ies o e ime ...................................... 20
Figu e 4 - Pe cen age o p ope ies ha ha e he selec ed a iable. ..................................... 21
Figu e 5 – E olu ion o P ope y Condi ion and Ene gy E iciency Ce i ica e o e ime ........ 21
Figu e 6 - Numbe o newly cons uc ed p ope ies wi h speci ic cha ac e is ics .................. 22
Figu e 7 - Numbe o newly cons uc ed p ope ies as apa men o houses ........................ 22
Figu e 8 – P ope y commodi ies analysis by p ope y ype in Ru al and Non-Rual a eas ..... 23
Figu e 9 - Dis ibu ion o p ope ies along he egions ........................................................... 24
Figu e 10 - Rela ionship be ween GBA and Numbe o bed ooms ......................................... 25
Figu e 11 - E olu ion o eal es a e p ope y p ices ................................................................ 25
Figu e 12 - E olu ion o eal es a e p ope y p ices along he egions ................................... 26
Figu e 13 - A e age p ope y selling p ices along he egions................................................. 27
Figu e 14 - A e age p ope y selling p ices in he dis ic s o Po ugal ................................... 27
Figu e 15 - A e age p ope y selling p ices in municipali y o Lisbon ..................................... 28
Figu e 16 - A e age p ope y selling p ices in he pa ish o Cascais........................................ 29
Figu e 17 - A e age p ope y selling p ices in he pa ish o Lisbon ......................................... 29
Figu e 18 - Hea map o he e olu ion o p ope y selling p ices in Lisbon's pa ishes ............. 30
Figu e 19 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices using
Random Fo es ................................................................................................................. 35
Figu e 20 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices using
Decision T ee .................................................................................................................... 36
Figu e 21 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices using KNN
.......................................................................................................................................... 36
Figu e 22 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Lisbon
using Random Fo es ........................................................................................................ 37
Figu e 23 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Lisbon
using Decision T ee .......................................................................................................... 37
Figu e 24 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in No h
using Random Fo es ........................................................................................................ 38
Figu e 25 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Cen e
using Random Fo es ........................................................................................................ 38
Figu e 26 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Alen ejo
using Random Fo es ........................................................................................................ 39
ii
Figu e 27 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Alga e
using Random Fo es ........................................................................................................ 39
Figu e 28 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Lisbon
Apa men s using Random Fo es .................................................................................... 40
Figu e 29 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Lisbon
Houses using Random Fo es ........................................................................................... 40
iii
LIST OF TABLES
Table 1 - Compa a i e analysis o p edic i e models .............................................................. 10
Table 2 - Va iables Desc ip ion ................................................................................................. 14
Table 3 - Explana ion o he me ics o ul ill missing alues ................................................... 15
Table 4 - Explana ion o he me ics selec ed o e alua ion o each o he models .............. 16
Table 5 - Explana ion o he ules applied................................................................................ 17
Table 6 - Resul s o he bes me hod o handle he missing alues ........................................ 18
Table 7 - Bes hype pa ame e s o he models ...................................................................... 31
Table 8 - Machine Lea ning Expe imen a ion o P ope y P ice P edic ion ........................... 34
6
whe he he e is a ela ionship be ween c ime a es and eal es a e p ices in Poland. The s udy led
hem o conclude ha geog aphic a eas wi h lowe alues appea ed in a eas wi h highe c ime a es.
They also examine he e ec s o gen i ica ion, a p ocess ha a ac s high-income households and
businesses, esul ing in highe incomes and educa ion le els and lowe c ime a es among his
popula ion. Thus, an inc ease in housing p ices is associa ed wi h a dec ease in c ime. “The decline in
sa e y coincides wi h he de e io a ion o he li ing condi ions o he popula ion bu also educes us
in he police and judicial sys em” (Fo yś & Pu ek-Szeląg, 2017, p. 52).
C ime educes he demand o eal es a e in ha geog aphic a ea, which educes he a ea's popula i y
and p ices. Buye s a e willing o pay mo e o li e in a eas wi h lowe c ime a es so hey can enjoy
g ea e sa e y and a be e quali y o li e (Buonanno e al., 2013).
2.2. PRICE FORECAST
The e a e many s udies ha use di e en o ecas ing me hods. We will analyze some o hem and
hei esul s o de e mine he bes me hod. Some s udies a e done using mic o a iables, as in ou
case. Va iables such as numbe o bed ooms, numbe o ba h ooms, size o he house, whe he i has
a ga age, a balcony, o e en a swimming pool a e included in his analysis.
Fu he mo e, eal es a e p ope y p ices a e a ec ed by many cha ac e is ics, some o which a e
ela ed o he cha ac e is ics o a speci ic home. The mos common a iables o he model s udied by
(Wing & Chin, 2003) include a ibu es such as ype, age o he building, numbe o bed ooms and
ba h ooms, acili ies (e.g. swimming pool), ga age, pa io, g oss a ea, and building se ices (e.g., ai
condi ional, li , e c). The applica ion o hedonic p ice o eal es a e ma ke s iden i ies a se o key
a iables o be included in he model, showing ha he e ec s o one o mo e eal es a e a ibu es
on eal es a e p ices can be obse ed, while o he ac o s being cons an . (Fle che e al., 2000)
conduc ed a s udy wi h he aim o de e mining he lis o a iables o be included in a hedonic p icing
model and ound ha , he numbe o bed ooms, ba h ooms and g oss a ea can be posi i ely ela ed
o i s p ice. In he esea ch o (My-Linh, 2020) e ealed ha he age o he building can impac p ope y
eal es a e p ices nega i ely.
To es ima e p ope y p ices (Pai & Wang, 2020) also included a iables such as dis ance o he ci y
cen e and p oximi y o he subway in his p edic ions, and used many me hods (Decision T ee, Back
P opaga ion Neu al Ne wo ks, Gene al Reg ession Neu al Ne wo ks and Leas Squa es Vec o
Reg ession) o p edic p ope y p ices. They conclude ha i is possible o p edic he p ices using
hese me hods and ha he me hod ha mos accu a ely e lec s eal es a e p ope y p ices is leas
squa es ec o eg ession. (Liu, 2022) esea ch analyses he eal es a e ma ke applying Mul iple Linea
Reg ession Model, he s udy shows a s ong co ela ion be ween he income le els wi h eal es a e
p ices e sus, he models demons a e a high accu acy wi h lowe p edic ion e o , indica ing i s
p ac icali y in o ecas ing eal es a e ma ke ends.
Random Fo es is a decision ee-based ensemble model ha uses a echnique called boo s ap
agg ega ion (o bagging) o c ea e mul iple independen eg ession models om andom samples o
he aining da a se . I is a e sa ile me hod ha can handle bo h eg ession and classi ica ion asks.
The main p ocess in ol es building a ious decision ees by andomly selec ing da a poin s and

7
ea u es du ing aining, which ul ima ely helps imp o e model accu acy (Ja’a a e al., 2021). In a
compa a i e s udy by (Čeh e al., 2018), he Random Fo es model was compa ed wi h Linea
Reg ession o p edic eal es a e p ices. The esul s show ha Random Fo es consis en ly pe o med
be e han Linea Reg ession model on a a ie y o pe o mance me ics. Fu he mo e, Random
Fo es ha e lowe e o a es in p edic ing eal es a e p ices compa ed o o he algo i hms (Shinde &
Gawande, 2018).
In a s udy conduc ed by (del Cacho, 2010), a ious models such as Naï e Neighbo s, Linea Reg ession,
Decision T ees, K-Nea es Neighbo s (KNN) and Neu al Ne wo ks we e used o p edic eal es a e
p ices. A poin o highligh ela ed o his s udy is he ac ha Naï e Neighbo s is a classi ie ha
assumes ha all a iables a e independen o each o he . The esul s we e e alua ed based on a ious
indica o s and i was ound ha he Decision T ee model p o ided he bes indica o pe o mance in
e ms o eal es a e p ices.
A i icial Neu al Ne wo k (ANN) ha e a wide ange o uses, o ecas ing is one o he pu poses so many
esea che s decided o apply his echnique. I is able o add ess p oblems ela ed o nonlinea i y and
mul icollinea i y. One o he ad an ages o his model is i s e sa ili y, i has he abili y o model
ela ionships be ween dependen and independen a iables. (Ghodsi e al., 2010) in hei esea ch o
es ima ion o I anian house p ices, in o de o o m an A i icial Neu al Ne wo king, conside ed
economic a iables including, he housing p ice index, GDP, and cos o cons uc ion ma e ials, he
esul was a success ul es ima ion o he p ices o he a iables. (Tabales e al., 2013) did o ecas ing
o he eal es a e ma ke and show ha ANN has be e p e ision esul s han econome ic models.
The s udy conduc ed by (Rahman e al., 2019) also using ANN o o ecas housing p ices, concluded
ha ANN has he po en ial o o ecas house p ices wi h high pe o mance and also con i med he
indings made by (Tabales e al., 2013), he ANN model achie ed be e esul s when es ed in a la ge
da ase . (Bahia, 2013) used wo ypes o ANN: Feed Fo wa d Back P opaga ion Neu al Ne wo k (FFBP)
and Cascade Fo wa d Back P opaga ion Neu al Ne wo k (CFBP) o p edic eal es a e p ices. The
di e ence be ween hese wo ypes is ha he second me hod, CFBP, includes a weigh ed connec ion
om he inpu o each laye and successi e laye s. The conclusion o his esea ch is ha he CFBP
me hod shows esul s ha a e closes o eal p ices since i is possible o adjus he weigh s, he esul s
we e mo e accu a e, his s udy achie ed mo e han 96% accu acy in p edic ing eal es a e p ices.
O he me hods a e also used by mo e esea che s, such as Mul iple Linea Reg ession, which we ha e
p e iously alida ed (G um & Go eka , 2016) o see he ela ionship be ween house p ices and
mac oeconomic a iables in di e en egions and cul u es (G eece, Poland, e c.), and i u ns ou ha
he e is a s ong ela ionship be ween he a iables s udied, namely he unemploymen a e and house
p ices, which accu a ely illus a es he mac oeconomic impac on his ma ke . Using mac oeconomic
a iables, GDP, house p ice index, consume index, (Li & Chu, 2017) and wi h he o ecas ing me hods
Back P opaga ion and ANN, i is concluded ha hese a iables a e no s ong enough o p edic house
p ices. Based on he inal p ice o se e al houses o e 4 yea s, (Singh e al., 2020) used h ee di e en
me hods: Random Fo es , G adien Boos ing and Linea Reg ession, in o de o p edic house p ices,
he conclusion is ha all o ecas ing models we e able o p edic p ices bu he model wi h highe
o ecas ing accu acy was he G adien Boos ing.
One p oblem ha mos o he p e ious s udies ha e is he ac ha hey don’ ake in o accoun he
economic si ua ion o e ime, so, hei s udies need o be upda ed equen ly o he wise hey became
8
ou da ed. (Yasni sky e al., 2021) saw his as an oppo uni y and de eloped a mass alua ion o eal
es a e in Russia based on ixed ac o s, loca ion, and a iable ac o s, economic pa ame e s. The esul
o he model elabo a ed was ha houses in di e en geog aphical loca ions eac di e en ly o he
economic changes whe e hey a e inse ed, he olume o loans, and he GDP o he coun y. This
model is e y di e en in ha i can easily adap o he economy and he cons an changes ha exis .
(Hishamuddin e al., 2020) saw ha no many s udies combine mic oeconomic and mac oeconomic
a iables, so hey decided o conside bo h in hei pape o ha e a ision in a sho and long e m o
p ope y p ices, he me hod chosen was ANN. Using R² in e o measu emen as a basis, hey conclude
ha he pe cen age o e o is less when R² has a high alue when only mac oeconomic a iables we e
conside ed. When only mic oeconomic a iables we e used alone he esul s we e eally weak, and
when bo h a iables we e combined, he esul s we e be e han using mic oeconomic a iables alone
bu wo se han using mac oeconomics a iables alone. The e o e, i is necessa y o s udy his
combina ion o a iables in mo e de ail o a oid alue disc epancies and o ob ain a mo e eliable p ice
p edic ion. Wi h his s udy, i is possible o see ha he e is a gap in esea ch and an oppo uni y o
explo e he combina ion o hese wo mac o a iables. We need o conside bo h he mic o a iables
desc ibed abo e and he mac oeconomic a iables such as in la ion, unemploymen a e, in e es a e,
e c.
2.2.1. Compa a i e analysis o p edic i e models
The eal es a e ma ke is in luenced by se e al quan i a i e and quali a i e a iables, making p ice
o ecas ing a complex ask. To add ess his challenge, a ious p edic i e models ha e been used o ill
in he null alues ha we ha e in he da a and o es ima e eal es a e p ices. This esea ch aims o
examine and compa e se e al p edic i e models, including A i icial Neu al Ne wo k (ANN), Linea
Reg ession, Decision T ees, K-Nea es Neighbo Impu a ion (KNN), Random Fo es , and G adien
Boos ing. Each o hese models has unique s eng hs and limi a ions ha make i sui able o di e en
scena ios. By e alua ing and compa ing hese models agains each o he , we aim o p o ide aluable
insigh s in o hei pe o mance and e ec i eness. Table 1 lis s a ious o ecas ing models, each wi h a
b ie desc ip ion, s eng hs, and limi a ions. Among he au ho s who s udied p edic i e models, hose
who a e men ioned a e pa o he esea ch ca ied ou ha ga e ise o he able.
P edic i e
Model
Desc ip ion and De ini ion
S eng hs
Limi a ions
ANN
(Hush &
Ho ne, 1993)
I 's a ype o Neu al Ne wo k
algo i hm ha consis s o
in e connec ed nodes o
neu ons o ganized in o laye s,
usually including inpu , hidden,
and ou pu laye s. These
ne wo ks ake inpu da a and
p edic an ou pu based on i .
Du ing aining, neu al
ne wo ks adjus he
connec ions' weigh s o lea n
• Capable o
handling non-
linea and
complex da a.
• Sui able o big
da a applica ions
due o hei
abili y o model
in ica e
ela ionships.
• Requi es a la ge
aining da ase
o op imal
pe o mance.
• P one o
o e i ing i no
ca e ully
egula ized.
9
complex pa e ns and make
p edic ions.
Linea
Reg ession
(Mon gome y
e al., 2021)
Is a s a is ical model ha
es ablishes a linea ela ionship
be ween p edic o a iables
and he a ge a iable. I
assumes a linea combina ion
o ea u es and inds
coe icien s ha minimize he
e o be ween p edic ed and
ac ual alues.
• Simple and easy
o in e p e ,
making i a good
choice o ini ial
insigh s.
• Wide applicabili y
o a ex end o
p oblems.
• Me hod limi ed
o linea
ela ionships
be ween
a iables, which
may no cap u e
complex
pa e ns.
• Sensi i e o
ou lie s and
mul icollinea i y.
Decision
T ees
(de Ville,
2013)
A e cons uc ed by algo i hms
ha explo e di e en ways o
spli ing he da a in o dis inc
segmen s. They make decisions
based on ea u e spli s,
c ea ing a ee whe e each
node ep esen s a decision. The
ee is spli based on he
ea u e ha p o ides he bes
in o ma ion gain.
• Easily
in e p e able
models, as hey
mimic human
decision-making
p ocesses.
• Can handle bo h
nume ical and
ca ego ical da a.
• Tendency o
o e i wi h deep
ees, which
equi es p uning
o ensemble
me hods.
• Sensi i e o
small a ia ions
in he aining
da a.
KNN
(Weinbe ge
& Saul, 2009)
KNN is a non-pa ame ic
algo i hm ha p edic s a a ge
a iable based on he majo i y
class o i s k-nea es neighbo s
in a ea u e space. I
de e mines he a ge alue by
conside ing he labels o hese
neighbo s. P edic ion wi h KNN
equi es de ine he chosen
a iables, he dis ance me ic
o calcula e he dis ance
be ween obse a ions and he
numbe o neighbo s.
• Abili y o adap o
complex da a
pa e ns,
especially when
he numbe o
neighbo s (k) is
app op ia ely
chosen.
• Pe o ms well on
small da ase s
and wi h ew
ea u es.
• Sensi i e o he
choice o 'k',
which can
signi ican ly
a ec esul s.
• Is in luenced by
ou lie s in he
da a, leading o
inaccu a e
p edic ions.
Random
Fo es
(Oshi o e al.,
2012)
Random Fo es is an ensemble
me hod ha combines se e al
Decision T ees. This model is
pa icula ly known o i s abili y
o e ec i ely handle a la ge
numbe o ea u es and
• Reduces
o e i ing
h ough ensemble
a e aging. -
Handles missing
da a e ec i ely
• The ela ionship
be ween he
esponse and he
independen
a ibu es is
10
e icien ly p ocess ex ensi e
da ase s. Also imp o es
p edic ion accu acy and educe
o e i ing by agg ega ing
p edic ion om mul iple
decision ees.
wi hou
p ep ocessing.
complica ed o
unde s and.
• Tend o ha e
longe aining
imes compa ed
o o he
me hods, so is
less sui able o
eal- ime
applica ions o
e y la ge
da ase s.
G adien
Boos ing
(Has ie e al.,
2009)
Is a me hod ha sequen ially
cons uc s an ensemble o
weak lea ne s (usually decision
ees) o c ea e a s ong
p edic i e model. I builds ees
sequen ially, ocusing on he
mis akes made by p e ious
ees. This me hod gained
popula i y due o he supe io
pe o mance o Decision T ees
and led o he de elopmen o
algo i hms such as XGBoos
and Ligh GBM.
• High accu acy and
e ec i eness
ac oss many
scena ios.
• Handles missing
da a e ec i ely.
• Can be sensi i e
o ou lie s in he
aining da a.
• P one o
o e i ing,
especially when
he algo i hm is
allowed o
c ea e complex
models.
Table 1 - Compa a i e analysis o p edic i e models
11
3. METHODOLOGY
The objec i e o his s udy is o build a p ope y p ice o ecas ing model using p edic i e models.
P ope y p ice o ecas s a e designed o help homebuye s unde s and u u e p ice anges and plan
hei inances in ad ance. In addi ion, p ope y p ice o ecas s a e also bene icial o eal es a e
in es o s o unde s and he end o p ope y p ices in a pa icula egion. This s udy e e s o Po ugal
Con inen al and was a ocus on Lisbon since Lisbon is he capi al o Po ugal. Lisbon is whe e he e a e
mo e da a and exis a la ge di e ence in p ice a ia ion and whe e he di e ences be ween cul u es,
ends and li es yles a e mos p onounced, whe e is a lo o business ac i i y and ou ism, he e o e
his allows o a comp ehensi e analysis wi h abundan da a.
To make accu a e o ecas s, we need sui able ma hema ical models o es ima e how ime se ies da a
gene a e house p ices. In his con ex , CRISP-DM me hod was adap ed o his si ua ion, as discussed
by (Shea e , 2020). Analyzing cu en ends and p edic ing u u e ends is becoming inc easingly
impo an oday. P edic i e models a e gaining inc easing alue in o ganiza ions ha ace he
challenge o choosing he igh echnology o he business and unde s anding how o use exis ing da a
(Nwagwu e al., 2021).
The eal es a e ma ke is known o i s ola ili y, cha ac e ized by luc ua ions o e ime and
con inually changing ends. Gi en he complexi y o he eal es a e ma ke , which o en exhibi s non-
linea ela ionships, i becomes necessa y o le e age his o ical da a and employ machine lea ning
me hods o analysis (Han, 2018). Machine lea ning o e s he ad an age o au oma ically lea ning
pa e ns and insigh s om his o ical da a, making i well sui ed o handling he di icul ies o he eal
es a e ma ke .
Fo he cons uc ion o he p edic ion model, he p og amming language selec ed was Py hon. I is he
mos used language wo ldwide occupying he i s place in Oc obe 2023
1
, and is a use - iendly
in e ace as i is easy o unde s and and has a wide a ie y o lib a ies a ailable, which helps o inc ease
o hose uses his language sa ing p og amming ime ha would be manual.
In line o ensu e ha he in o ma ion is accu a e in his con ex , he da a we e subjec o ea men
and ules we e de ined. Be o e s a ing o de elop he model, i is necessa y o p ocess da a ha
in ol es impo ing iles in CSV o ma , Explo a ion and Da a Unde s anding, Da a P e-p ocessing,
Fea u e Selec ion, Modelling and Pe o mance Assessmen .
3.1. DATASET DESCRIPTION AND MODIFICATIONS
The s udy began by impo ing da a om wo Excel iles in o Jupy e . One o hese iles con ained he
yea o cons uc ion o he p ope ies, while he o he ile held a wide ange o a iables ha cons i u e
he da ase , such as he ype o p ope y (house o apa men ), numbe o bed ooms, ene gy e iciency
ce i ica e, g oss building a ea, p ope y’s condi ion, he p esence o ga age, swimming pool, e ace
and pa io, con ained as well a iables geog aphic ela ed, such as pa ish numbe , pos al code, la i ude
and longi ude, and las ly in o ma ion linked o eal es a e ma ke p ices, he las ma ke appea ance
da e and he selling p ice obse ed. To e i y i a p ope y had mul iple alues in he cons uc ion yea
a iable, inconsis encies we e checked, and each p ope y ID was assigned a unique cons uc ion yea .
1
TIOBE Index - TIOBE

12
A me ge ope a ion was conduc ed be ween wo Excel iles o c ea e a uni ied da ase . The da a o
his s udy consis ed o p ope ies up o he cons uc ion yea o 2024 and he e a e his o ical p ice
sales be ween 2017 and 2022.
Geog aphical in o ma ion, such as pa ish numbe and pos al code, allowed o he augmen a ion o
he da ase wi h addi ional in o ma ion. This da a was de i ed om wo ex e nal iles
2
. The ollowing
columns we e added: dis ic , zone, municipali y, and pa ish name, along wi h he u al/non- u al
designa ion. Va ious ans o ma ions we e applied o hese new a iables o make hem usable. The
p ope ies ha e been classi ied in o zones and u al and non- u al acco ding o he municipali ies,
he e a e i e zones co e ing he da ase and Po ugal, he di ision is done acco ding o he
cha ac e is ics o he zones and municipali ies, so we will ha e p ope ies in he same zone mo e
simila o each o he 2.
Two speci ic a iables ha had no signi ican alue o he da ase and only added complexi y we e
emo ed, such as la i ude and longi ude, as hei in o ma ion was ound o be edundan since hey
p o ided in o ma ion ha could be de i ed om he pos al code a iable. La i ude and longi ude
ep esen geog aphic coo dina es and a e use ul when wo king wi h map o geocoding se ices.
Howe e , in his case, he la i ude and longi ude do no change o he same pos al code, which is
ac ually inco ec , so we conside emo ing hese wo a iables and keeping he da ase concise.
Rega ding he yea o cons uc ion, he da ase compila ion e ealed se e al inconsis encies and
nonsensical yea s, including he yea 1050. As a co ec i e app oach, all p ope ies wi h a cons uc ion
yea p io o 1755 we e emo ed om he da ase . This decision was in luenced by his o ical e en s,
no ably he de as a ing ea hquake ha s uck Lisbon in 1755, leading o widesp ead des uc ion by
sunami and i e. Gi en he se e i y o he damage, i was assumed ha none o he houses
cons uc ed be o e ha yea emained habi able. Consequen ly, hese p ope ies we e excluded om
he analysis. The emo al o houses cons uc ed be o e 1755 and he handling o inconsis encies, such
as he yea 1050, ensu ed da a quali y and eliabili y in he subsequen analysis.
Se e al ans o ma ions and modi ica ions we e made o simply he da a. S a by ans o ming he
p ope y ID a iable in o nume ical o ma o acili a e u he ans o ma ions. The p ope y condi ion
a iable was ans o med in o nume ical alues anging om 1 o 4. The u al a iable was con e ed
in o a bina y o ma , wi h 0 indica ing a u al loca ion and 1 ep esen ing a non- u al loca ion. Fu he
analysis e ealed ha he EEC (Ene gy E iciency Ce i ica e) a iable could ake on nine dis inc le e s
ha signi ican ly di e en EEC le els. To simpli y his a iable, i was g ouped in o ou dis inc classes:
Class 1 includes ce i ica es A and A+, Class 2 encompasses ce i ica es B and B-, Class 3 consis s o
ce i ica es C and D, and Class 4 comp ises he emaining ce i ica es E, F, and G.
The modi ied da ase consis s o 326537 ows ep esen ing he numbe o p ope ies and includes 26
a iables ha will acili a e house p ice p edic ion modeling. Below, in able 2, is p esen ed all he 26
a iables selec ed a iables om he modi ied da ase , which will enable us o build he mos accu a e
p edic i e model. Is also p esen he wo ex a a iables du ing he o ecas .
2
h ps://www.gpp.p /images/Es a is icas_e_analises/Es a is icas/associadasmedidasapoio/Te i o ios_Ru ais.pd
h p://www.p ode .p /Resou cesUse /Documen os_Di e sos/33/PDRc_F eg_ZRu ais_NUTIIs_ e 2_co igido.pd
13
Va iable
Desc ip ion
Da a Type
P ope y ID
The unique iden i ie o he p ope ies
Objec
P ope y Type
P ope y ype. 1 i is an apa men and 2 o
a house
In ege
Nº Bed ooms
Numbe o bed ooms
In ege
EEC
Ene gy E iciency Ce i ica e: Numbe 1
includes ce i ica es A and A+, Numbe 2
ce i ica es B and B-, Numbe 3 consis s o
ce i ica es C and D, and Numbe 4
comp ises he emaining ce i ica es E, F,
and G.
In ege
GBA
G oss Building A ea
In ege
Pa ish
Pa ish
Objec
Pos al Code
Pos al Code
Objec
Ga age
Indica es whe he he p ope y has a ga age
o no
Bool
Te ace
Indica es whe he he p ope y has a e ace
o no
Bool
Pool
Indica es whe he he p ope y has a
swimming pool o no
Bool
Pa io
Indica es whe he he p ope y has a pa io
o no
Bool
P ope y Condi ion
The s a e o conse a ion o he house. I can
be classi ied as good, bad, new, o used. Fo
each s a e was assigned a numbe
In ege
Conse a ion S a e Ve i ied
Indica es i he conse a ion s a e was
p o ided by clien s o e i ied wi h pho os
Bool
Las Day in Ma ke
Da e o he las ma ke upda e
Da e ime
Ini ial O e Da e
Da e o he ini ial o e
Da e ime
Obse ed Selling P ice
The selling p ices ha we e obse ed by he
company
In ege
Cons uc ion Yea
Yea o cons uc ion
In ege
14
Dis ic
Dis ic
Objec
Region
Indica es one o he i e egions in o which
Po ugal was di ided (No h, Cen e , Lisbon,
Alen ejo and Alga e)
Objec
Municipali y
Municipali y
Objec
Pa ish Name
Name o he pa ish
Objec
Las Ma ke Upda e Yea
Yea o he las ma ke upda e
In ege
Ini ial O e Yea
Yea o he ini ial o e
In ege
Ru al
Indica es whe he he p ope y is loca ed in
a u al a ea o no
Bool
Decade
Decade o cons uc ion (e.g., 50’s)
Objec
Cen u y
Cen u y o cons uc ion (e.g., 20)
In ege
P edic ed Selling P ice
The selling p ices ha we e p edic ed by he
di e en models
Floa
Squa e me e P ice Di e ence
P ice pe squa e me e . Di e ence be ween
obse ed and p edic ed p ices
Floa
Table 2 - Va iables Desc ip ion
Since his da ase con ains six a iables wi h a lo o missing alues, u he ans o ma ions we e
pe o med o impu e he da a, conside ing he co ela ion be ween he a iables. Based on li e a u e
e iew, he ollowing models we e selec ed: Decision T ee Impu a ion, Random Fo es Impu a ion, K-
Nea es Neighbo Impu a ion (KNN), A i icial Neu al Ne wo k Impu a ion (ANN), and Linea
Reg ession Impu a ion. The model chosen o each a iable was he one ha ga e he bes esul s
compa ed o all he models s udied, in e ms o pe o mance me ics ( u he explained in he nex
sec ion 3.2).
3.2. MODEL EVALUATION METRICS
In his p ojec , a a ie y o e alua ion me ics ha e been employed o assess he pe o mance o
di e en models, bo h in illing missing alues and p edic ing p ope y p ices. These me ics se e as
essen ial ools o gauge he e ec i eness o he models.
To e alua e he pe o mance o da a impu a ion models, we ocus on he me ics p esen ed in able
3, based on he classi ica ion esul s.
15
Me ic
De ini ion
In e p e a ion o he esul
P ecision
Measu es he p opo ion o co ec ly impu ed
alues ( ue posi i es) ou o he o al impu ed
alues.
A high p ecision sco e indica es
ha he me hod is adep a
accu a ely illing in missing da a.
Recall
Quan i ies he a io o co ec ly impu ed
alues ( ue posi i es) o he o al ac ual
missing alues.
A highe ecall sco e implies ha
he me hod e ec i ely cap u es
missing da a.
F1-Sco e
The F1-sco e s ikes a balance be ween
p ecision and ecall, o e ing a single me ic o
assess o e all pe o mance. I combines bo h
p ecision and ecall in o a uni ied sco e,
making i aluable o assessing he o e all
quali y o da a impu a ion.
A highe F1-Sco e indica es a
be e balance be ween
p ecision and ecall, meaning a
be e pe o mance p edic ing
missing alues.
Suppo
Rep esen s he numbe o ins ances o each
class, e lec ing he dis ibu ion o missing
da a poin s ac oss di e en ca ego ies.
A highe suppo indica es ha
he model’s p edic ions a e
mo e eliable and us wo hy in
impu e missing alues.
Table 3 - Explana ion o he me ics o ul ill missing alues
These me ics a e undamen al o e alua ing he pe o mance o da a impu a ion models in
accu a ely illing missing alues. Addi ionally, hey guide us in choosing he mos e ec i e app oach o
ensu e he eliabili y and comple eness o ou da ase , which, in u n, con ibu es o mo e accu a e
p edic ions o house p ices.
Fo he p edic ion o p ope y p ices, i is impo an o e alua e he pe o mance o each model
de eloped using di e en me hods. The emphasis lies on six me ics: Accu acy, Mean Absolu e E o
(MAE), Mean Squa e E o (MSE), Roo Mean Squa e E o (RMSE), Mean Absolu e Pe cen age E o
(MAPE) and R² Sco e. Be o e using hese i e e alua ion indica o s, i is necessa y o unde s and hei
meanings and conside hei in e p e a ion wi hin he speci ic con ex o his p ojec . In able 4 is
ep esen ed an explana ion o he me ics o e alua e each o he models.
Me ic
De ini ion
In e p e a ion o he esul
Accu acy
Measu es he p opo ion o co ec ly
classi ied obse a ions ela i e o he
o al.
The highe he pe cen age, he be e
he pe o mance o he model.
MAE
Measu es he di e ence be ween wo
con inuous a iables, ansla ed in o
he a e age o he e o s o a se o
o ecas s.
A lowe alue indica es ha he models
is capable o p edic wi h accu acy he
alues.
22
As we obse e an inc ease in he numbe o newly cons uc ed p ope ies, i is impo an o analyze
he signi icance o p ope y commodi ies in hese new houses. F om Figu e 6, we can conclude ha
new p ope ies end o exhibi hese cha ac e is ics mo e no ably. Ga age a iable appea in mo e
han hal o new cons uc ions, p o iding in o ma ion abou which builde s and buye s a e inc easingly
aluing. In he Figu e 7, we can also see he di e ence be ween he numbe o p ope ies being buil
as apa men s e sus he numbe o homes, wi h mo e apa men s being cons uc ed.
Figu e 6 - Numbe o newly cons uc ed p ope ies wi h speci ic cha ac e is ics
Figu e 7 - Numbe o newly cons uc ed p ope ies as apa men o houses

23
To examine he geog aphic ela ionship be ween p ope ies in u al o non- u al a eas, analyzes we e
conduc ed o assess he beha io o p ope y commodi ies in ela ion o he p ope y ypes. In Figu e
8, he di e ence be ween he pe cen age o he numbe o p ope ies wi h and wi hou hese o
p ope y commodi ies a e no subs an ial. The mos no able di e ence can be obse ed in he
p ope y ype, apa men , o a house. The e a e mo e apa men s in non- u al a eas compa ed o u al
a eas, whe eas in u al a eas, he e is a highe p e alence o houses. The eason o his dis inc ion
can be a ibu ed o u baniza ion ends, whe e non- u al a eas o en wi ness highe popula ion
densi ies, leading o a g ea e demand o apa men s. Con e sely, u al a eas end o ha e mo e space
a ailable, which encou ages home cons uc ion.
Figu e 8 – P ope y commodi ies analysis by p ope y ype in Ru al and Non-Rual a eas
Following he geog aphical analysis o p ope y cha ac e is ics, a ho ough s udy o p ope y
commodi ies and p ope y ypes was ca ied ou o unde s and hei dis ibu ion ac oss he i e zones
in Po ugal, as shown in Figu e 9. The ga age a iable displayed a consis en pe cen age h oughou
he coun y, wi h he absence o ga ages being mo e common.
24
Rema kably, he swimming pool a iable s ood ou in he Alga e egion, whe e app oxima ely 10.73%
o p ope ies ea u ed his a iable. In he sou he nmos egions o coun y, such as Alen ejo and
Alga e, he p esence o e ace and pa io was signi ican ly mo e common.
The Lisbon egion has a lowe p opo ion o p ope ies classi ied as Houses, while he zones Cen e
and Alen ejo ha e a mo e balanced a io be ween apa men s and houses. I is no able ha he
majo i y o p ope ies in he Alen ejo a e conside ed Ru al, making i he p edominan ly u al a ea in
he coun y.
Figu e 9 - Dis ibu ion o p ope ies along he egions
25
Figu e 10 illus a es he exis ence o a mode a ely s ong posi i e ela ionship be ween he a iables
G oos Building A ea and he numbe o bed ooms. The co ela ion coe icien is 0.68, which is a
ela i ely high ela ionship, indica ing a clea end whe e an inc ease in he g oss p i a e a ea o
p ope ies co esponds o an inc ease in he numbe o ooms.
Figu e 10 - Rela ionship be ween GBA and Numbe o bed ooms
4.1.2. Explo ing p ice ends in geog aphic con ex
Con inuing he analysis o eal es a e p ope y p ices and examine hei de elopmen in di e en
con ex s.
Figu e 11 p o ides an insigh in o he a e age de elopmen o p ope y p ices in he yea s conside ed.
I is e iden ha he p ices in 2018, he e was a signi ican ly inc ease compa ed wi h he p e ious yea .
Th oughou he yea s 2018 o 2020, he e we e no subs an ial luc ua ions, and om he yea 2020
onwa ds, p ices ha e consis en ly been on he ise.
Figu e 11 - E olu ion o eal es a e p ope y p ices
26
In Figu e 12, he p og ession o p ope y p ices ac oss he i e egions and he s udy yea s is
ep esen ed. The No h egion exhibi s a g adual and less p onounced g ow h, while he Alga e egion
expe iences sligh p ice luc ua ions. The Cen e and Alen ejo zones ha e main ained hei alues. In
con as , he Lisbon egion boas s he highes eal es a e p ices p ices and displays a mo e signi ican
p ice a ia ion, pa icula ly ma ked by p ice inc eases.
Figu e 12 - E olu ion o eal es a e p ope y p ices along he egions
27
In o de o o ganize he zones om he highes a e age selling p ices o he lowes , he Figu e 13 is
p esen ed. I is e iden ha Lisbon egion has he highes eal es a e p ices, closely ollowed by he
Alga e egion. The Cen e egion is cha ac e ized by mo e a o dable p ope y p ices.
Figu e 13 - A e age p ope y selling p ices along he egions
I is impo an o ha e a sense o he p ice dispa i ies among he dis ic s o Po ugal. Con i ming he
p e ious in o ma ion, Figu e 14, illus a es ha he Lisbon dis ic has he highes a e age p ope y
p ices, closely ollowed by he Fa o dis ic . In con as , he Gua da dis ic eme ges as he mos
budge - iendly op ion. Rema kably, he a e age housing p ice in Lisbon is o e h ee imes highe
han ha in Gua da. In e ms o p icing wi hin his ma ke , Lisbon is 37% mo e expensi e han he
second mos populous dis ic in he coun y, which is Po o.
Figu e 14 - A e age p ope y selling p ices in he dis ic s o Po ugal

28
Gi en ha Lisbon is he dis ic wi h he highes eal es a e p ope y p ices, i becomes impo an o
na ow down he geog aphical analysis. Consequen ly, he Lisbon municipali y was examined, and
Figu e 15 appea s. Among he municipali ies wi hin he dis ic , Cascais s ands ou wi h he highes
a e age housing p ices, closely ollowed by he Lisbon municipali y, wi h li le di e ence be ween he
wo alues. In con as , Azambuja, a municipali y in he Lisbon dis ic , has he lowes a e age housing
p ices, wi h a alue ha is o e h ee imes cheape compa ed o Cascais.
Figu e 15 - A e age p ope y selling p ices in municipali y o Lisbon
Since Cascais and Lisbon we e he municipali ies wi h he highes eal es a e selling p ices, Figu es 16
and 17 ep esen he p ices wi hin he espec i e pa ishes. In Cascais, he di e ence be ween he
pa ish wi h he highes and he lowes p ices is app oxima ely he double. In Lisbon, he di e ences
a e e en g ea e , wi h p ices a ying by almos ou imes om he pa ish wi h he highes a e age
p ices o he one wi h he lowes .
29
Figu e 16 - A e age p ope y selling p ices in he pa ish o Cascais
Figu e 17 - A e age p ope y selling p ices in he pa ish o Lisbon
30
As we can see, eal es a e p ope y p ices in Lisbon a e highe and he di e ences be ween pa ishes
a e e y no iceable. To be e unde s and how p ices de elop in his pa ish, he as shown in Figu e 18
we e c ea ed. I is possible o examine he p ice e olu ion and maximum p ice spikes in each pa ish o
Lisbon.
In he yea 2017, p ope ies wi h he highes p ices we e loca ed in he San a Ma ia Maio and San o
An ónio pa ishes. In 2018, he A enidas No as pa ish expe ienced a signi ican p ice inc ease,
becoming he pa ish wi h he highes eal es a e p ope y p ices. In 2019, he Pa que das Nações pa ish
doubled in alue compa ed o 2017, now anking among he pa ishes wi h he highes housing p ices,
consis en ly inc easing in p ice o e he yea s.
By 2022, we can conclude ha he op i e pa ishes wi h he highes p ope y p ices, in descending
o de , a e A enidas No as, Pa que das Nações, San o An ónio, Belém, and Campolide. The pa ishes
wi h lowe p ices ha ha e emained compa a i ely mo e a o dable include Ajuda, San a Cla a, Bea o,
Penha da F ança, and Ma ila.
Figu e 18 - Hea map o he e olu ion o p ope y selling p ices in Lisbon's pa ishes
4.2. MODELS COMPOSITION
The inal da ase ep esen s a culmina ion o he bes models p e iously es ed o ul ill missing alues.
Wi h hese e ined a iables now in eg a ed, he da ase s ands p epa ed o he accu a e p edic ion
o p ope y p ices. Nex , we pe o m a igo ous compa ison o models o disce n hei e ec i eness in
he eal es a e con ex . Th ough sys ema ic e alua ion and ca e ul analysis based on he p e iously
men ioned me ics, we aim o iden i y he model ha pe o ms bes o he eal es a e p ice
o ecas ing ask and he exis ing di e ences when analyzed in di e en geog aphic con ex .
31
Fo all he p edic ing me hods, he da ase was di ided in o wo se s, he aining se , and he es se .
The o iginal da ase was also spli in o independen and dependen a iables, as his spli is essen ial
o e alua ing model pe o mance using p e iously unseen da a. The spli be ween aining and es ing
da ase was explo ed o he di e en scena ios. The spli used was 80% - 20%, which means 20% o
he da a is used o he es ing da ase and he emaining 80% o he da a in he aining.
A e aining, p edic ions we e made on he es basis. These o ecas s ep esen es ima es o he
dependen a iable based on he independen a iable.
In all models, he analysis o ea u e impo ance was conduc ed, and hese ea u es we e ca e ully
chosen o c ea e he o ecas ing inpu s. The main ocus is o include ea u es ha ha e a s ong
co ela ion wi h he a ge a iable and show a signi ican impac on p ope y selling p ice. Du ing
model es ing and alida ion, he consequences o including o excluding ce ain ea u es we e
e alua ed. A ibu es ha signi ican ly imp o ed p edic i e pe o mance o he models we e
inco po a ed in o he inal inpu . This delibe a e selec ion ensu es ha he o ecas s a e op imized, as
i ocuses on he ea u es ha exe he mos signi ican impac on he p edic ions, enhancing he
o e all accu acy and eliabili y o he models.
To de e mine he pe o mance me ics o he eg ession models, se e al me ics we e e alua ed. A e
aining he model wi h he di e en o ecas models, add he p ice p edic ion o he da abase by
c ea ing a new column "P edic ed Selling P ice".
To op imize he pe o mance o ou machine lea ning models, an ex ensi e expe imen was conduc ed
o e alua e a ious combina ions o hype pa ame e s. The objec i e was o iden i y he op imal
se ings o each algo i hm, ensu ing ha he models we e well- uned and highly accu a e. Table 7
highligh s he speci ic hype pa ame e s used in he p edic ion model.
Machine Lea ning Models
Bes Hype pa ame e s
Random Fo es
Random S a e: 42. N es ima o s: 100. Min Samples Spli : 2. Min
Samples Lea : 2. Max Fea u es: sq . C i e ion: MSE. Boo s ap: T ue
Decision T ees
Spli e : bes . Random S a e: 42. Min Samples Spli : 5. Min Samples
Lea : 2. Max Fea u es: sq . C i e ion: MSE
KNN
Weigh s: uni o m. N neighbo s: 5. Me ic: minkowski. Lea size: 16.
Algo i hm: kd_ ee
Table 7 - Bes hype pa ame e s o he models
4.3. MODEL RESULTS
P edic ed eal es a e p ices s a wi h all p ope ies in he da ase and use h ee di e en o ecas
models: Random Fo es , Decision T ee and KNN. The esul s a e shown in Table 8.
Random Fo es model achie ed he highes R² sco e, 82,34% which indica es ha app oxima ely 82%
o housing p ices can be explained by he co ela ed a iables. By compa ing he p ice be ween
“Obse ed Selling P ice” and he model p edic ed p ice, and e alua ing his p ice compa ison using he
MAE me ic, i is ound ha he MAE be ween he es ima ed p ice and he p edic ed p ice is 21.969€.
38
Figu e 24 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in No h using
Random Fo es
Figu e 25 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Cen e using
Random Fo es

39
Figu e 26 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Alen ejo using
Random Fo es
Figu e 27 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Alga e using
Random Fo es
The sca e plo in Figu es 22 o 27 demons a es uni o mi y along he egions, exhibi ing simila
pa e ns o each egion, wi h he Alga e egion displaying a highe dispe sion o poin s, pa icula ly
hose de ia ing om he diagonal line. His og ams in Figu es 22 o 27, o di e en egions illus a e
a ying dis ibu ions. The Alen ejo egion p esen s highe densi y wi h mul iple columns concen a ed
nea ze o, whe eas he o he egions p edominan ly exhibi a p ima y column nea ze o,
complemen ed by smalle ba s a ound his cen al poin . These obse a ions sugges ha he model
po en ially showcases highe accu acy and consis ency in p edic ing p ope y p ices wi hin he
Alen ejo egion compa ed o o he egions.
40
4.3.1.3. Model pe o mance o e iew in he p ope y ypes
Figu e 28 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Lisbon Apa men s
using Random Fo es
Figu e 29 - Sca e plo and His og am o esiduals o p edic ing eal es a e p ices in Lisbon Houses
using Random Fo es
F om he sca e plo in Figu es 28 and 29 o apa men s and houses, i is appa en ha bo h exhibi
simila cha ac e is ics wi h a concen a ion o poin s a ound ze o and an alignmen along he diagonal
line. The his og am in Figu es 28 and 29 o apa men s e eals wo signi ican ly all columns
concen a ed a ound ze o. On he o he hand, in he case o houses, a p ominen column cen e ed a
ze o is ollowed by smalle columns in he icini y o ze o. This implies ha p edic ions o apa men s
and houses a e mos ly close o he ac ual alues, showcasing highe accu acy in p edic ions o bo h
p ope y ypes. The mo e p ominen columns a ound ze o signi y a highe equency o p edic ions
close o he ac ual p ices, demons a ing mo e consis en pe o mance in p edic ing p ope y p ices,
in bo h models, wi h a signi ican ly lowe e o .
41
This s udy shows ha among he h ee eal es a e p ope y p ice p edic ion models analyzed (Random
Fo es , Decision T ee and KNN), he Random Fo es model becomes he i s choice o eal es a e
p ice p edic ion. The esul s o he sca e plo and his og am analysis show ha he p edic ion
pe o mance o he wo p ope y ypes, apa men s, and houses, is consis en , wi h de ia ions close
o ze o. Alignmen along he diagonal shows ha he p edic ed and ac ual alues o he wo models
a e in good ag eemen . These g aphical obse a ions a e consis en wi h he s a is ical esul s
p esen ed in able 8, whe e he Random Fo es model has he lowes e o ma gin, ollowed by he
Decision T ee model, while he KNN model has ela i ely high p edic ion e o s.
Co ela ing hese g aphical obse a ions wi h he s a is ical me ics p esen ed ea lie , in able 8, i is
clea ha Random Fo es models consis en ly ou pe o m Decision T ee and KNN models. The poin s
a ound he ze o poin in he sca e plo and he highe columns in he his og am a e signi ican ly
concen a ed, especially in he case o Random Fo es , con i ming he high p edic ion accu acy. This is
consis en wi h he esul s o he pe o mance able and suppo s he conclusion ha he Random
Fo es model has a lowe e o a e compa ed o o he models, making i he mos eliable model o
p edic ing p ope y eal es a e p ices.
42
5. CONCLUSIONS AND FUTURE WORKS
The pu pose o his s udy was o p edic eal es a e p ope y p ices and gain a deepe unde s anding
o he Po uguese p ope y ma ke . To achie e his goal, a ho ough in es iga ion was conduc ed in o
he mos app op ia e me hods o handling he da a a hand, conside ing he na u e and his o ical
con ex o he da a. The li e a u e e iew plays a c ucial ole in selec ing he di e en me hods ha
bes sui he esea ch objec i es.
Da a p ep ocessing includes da a cleaning, explo a o y da a analysis, and examina ion o ends and
co ela ions o e ime. This allowed us o calcula e p ope y p ices ac oss Po ugal and analyze
di e ences be ween egions, highligh ing he impac o di e en a iables and geog aphical ea u es
on p ice dispa i ies.
The esul s ob ained om he p edic i e models demons a ed he e ec i eness o he chosen
app oach. These models show ex emely high accu acy, wi h ew, ela i ely mino e o s, which may
ha e limi ed impac wi hin he con ex o he eal es a e ma ke .
This main ad an age o his s udy is he abili y o p edic u u e de elopmen s and p o ide cus ome s
wi h aluable insigh s o make in o med decisions. This ou come is consis en wi h he main objec i es
o he p ojec .
Despi e i s impo an indings, his wo k has ce ain limi a ions ha mus be acknowledged. Some ha e
o do wi h he da ase i sel . In pa icula , he lack o ce ain cha ac e is ics, such as he numbe o
ba h ooms, he p esence o an ele a o o he loo s o he p ope y, c ea es challenges in de e mining
he p ice o a p ope y. Due o he omission o hese a iables and he lack o clea co ela ions in he
da a se , hese ea u es we e no added.
Fu he mo e, he da ase con ains a la ge numbe o missing alues, making da a impu a ion a
complex and less eliable p ocess. While po en ially aluable, excluding la i ude and longi ude da a
can p o ide p ecise geog aphic coo dina es ha allow you o de e mine he exac loca ion o a
p ope y. In many cases, his in o ma ion can be de i ed om pos al codes al eady included in he
da a se . Howe e , i is impo an o no e ha pos al codes co e la ge a eas and di e en p ope ies
wi hin he same pos al code may ha e di e en coo dina es. Fo example, wo houses wi h he same
zip code bu loca ed on opposi e sides o a s ee o in di e en buildings will ha e di e en la i ude
and longi ude coo dina es. The e o e, he accu acy o la i ude and longi ude in his da ase is
inconsis en . Fu u e wo k should ocus on using coo dina es o imp o e accu acy.
Economic, poli ical, and social ac o s also ha e a signi ican impac on he eal es a e ma ke o e
ime. Models based on his o ical da a may no accu a ely p edic such changes. Fu he mo e, he
skewed p ice dis ibu ion o he da ase a ec s o ecas accu acy, especially in ex eme cases.
This s udy ma ks an impo an s ep in ully unde s anding he Po uguese dynamic eal es a e ma ke .
By using he powe o p edic i e models and geospa ial da a, is possible o p o ide aluable insigh s
o cus ome s and s akeholde s o shape a mo e well-known eal es a e ma ke .
In iew o hese limi a ions, i is impo an o ealize ha his s udy ep esen s a snapsho o he
dynamic eal es a e ma ke and p o ides he ounda ion o u u e wo k and imp o emen .
43
Realizing his wo k b ings i close o he ul ima e goal: o help indi iduals, companies and in es o s
make da a-o ien ed decisions in dynamic and changing eal es a e landscape. I hope his esea ch can
suppo and encou age u he esea ch in his ield.

44
BIBLIOGRAPHICAL REFERENCES
Agnello, L., & Schuknech , L. (2011). Booms and bus s in housing ma ke s: De e minan s and
implica ions.
Ahmad, N., Menegaki, A. N., & Al-Muha ami, S. (2020). Sys ema ic Li e a u e Re iew o
Tou ism G ow h Nexus: An O e iew o he Li e a u e and a Con en Analysis o 100
Mos In luen ial Pape s. Jou nal o Economic Su eys, 34(5), 1068–1110.
h ps://doi.o g/10.1111/joes.12386
Ahn, J. J., Byun, H. W., Oh, K. J., & Kim, T. Y. (2012). Using idge eg ession wi h gene ic
algo i hm o enhance eal es a e app aisal o ecas ing. Expe Sys ems wi h Applica ions,
39(9), 8369–8379. h ps://doi.o g/10.1016/j.eswa.2012.01.183
Akinsomi, O. K., Mkhabela, N., & Tade e a, M. (2018). The ole o mac o-economic indica o s
in explaining di ec comme cial eal es a e e u ns: E idence om Sou h A ica.
Jou nal o P ope y Resea ch, 35, 1 o 28.
h ps://doi.o g/10.1080/09599916.2017.1402071
Alhowaish, A. K. (2016). Is Tou ism De elopmen a Sus ainable Economic G ow h S a egy
in he Long Run? E idence om GCC Coun ies. Sus ainabili y, 8(7), A icle 7.
h ps://doi.o g/10.3390/su8070605
Alkali, M., Sipan, I., & Razali, M. (2018). An O e iew o Mac o-Economic De e minan s o
Real Es a e P ice in Nige ia. In e na ional Jou nal o Enginee ing and
Technology(UAE), 7, 484–488. h ps://doi.o g/10.14419/ije . 7i3.30.18416
Bada inza, C., & Ramado ai, T. (2018). Home away om home? Fo eign demand and London
house p ices. Jou nal o Financial Economics, 130(3), 532–555.
h ps://doi.o g/10.1016/j.j ineco.2018.07.010
Ba oe-Bonnie, J. (1998). The Dynamic Impac o Mac oeconomic Agg ega es on Housing
P ices and S ock o Houses: A Na ional and Regional Analysis. The Jou nal o Real
45
Es a e Finance and Economics, 17(2), 179–197.
h ps://doi.o g/10.1023/A:1007753421236
Bahia, I. S. H. (2013). A Da a Mining Model by Using ANN o P edic ing Real Es a e Ma ke :
Compa a i e S udy. In e na ional Jou nal o In elligence Science, 3(4), A icle 4.
h ps://doi.o g/10.4236/ijis.2013.34017
Ba on, K., Kung, E., & P ose pio, D. (2021). The E ec o Home-Sha ing on House P ices
and Ren s: E idence om Ai bnb. Ma ke ing Science, 40(1), 23–47.
h ps://doi.o g/10.1287/mksc.2020.1227
Biagi, B., B andano, M. G., & Lambi i, D. (2015). Does Tou ism A ec House P ices?
E idence om I aly. G ow h and Change, 46(3), 501–528.
h ps://doi.o g/10.1111/g ow.12094
B zezicka, J. (2020). Towa ds a Typology o Housing P ice Bubbles: A Li e a u e Re iew.
Housing, Theo y and Socie y, 38, 1–23.
h ps://doi.o g/10.1080/14036096.2020.1758204
Buonanno, P., Mon olio, D., & Raya-Vílchez, J. M. (2013). Housing p ices and c ime
pe cep ion. Empi ical Economics, 45(1), 305–321. h ps://doi.o g/10.1007/s00181-012-
0624-y
Čeh, M., Kiliba da, M., Lisec, A., & Baja , B. (2018). Es ima ing he Pe o mance o Random
Fo es e sus Mul iple Reg ession o P edic ing P ices o he Apa men s. ISPRS
In e na ional Jou nal o Geo-In o ma ion, 7(5), A icle 5.
h ps://doi.o g/10.3390/ijgi7050168
Cellme , R., & T ojanek, R. (2020). Towa ds Inc easing Residen ial Ma ke T anspa ency:
Mapping Local Housing P ices and Dynamics. ISPRS In e na ional Jou nal o Geo-
In o ma ion, 9(1), A icle 1. h ps://doi.o g/10.3390/ijgi9010002
46
Cheng, I.-H., & Xiong, W. (2014). Financializa ion o Commodi y Ma ke s. Annual Re iew o
Financial Economics, 6(1), 419–441. h ps://doi.o g/10.1146/annu e - inancial-
110613-034432
Cocola-Gan , A., & Gago, A. (2021). Ai bnb, buy- o-le in es men and ou ism-d i en
displacemen : A case s udy in Lisbon. En i onmen and Planning A: Economy and
Space, 53(7), 1671–1688. h ps://doi.o g/10.1177/0308518X19869012
C owe, C., Dell’A iccia, G., Igan, D., & Rabanal. (2012). Policies o Mac o inancial S abili y:
Managing Real Es a e Booms and Bus s.
Cunha, A. M., & Lobão, J. (2021). The e ec s o ou ism on housing p ices: Applying a
di e ence-in-di e ences me hodology o he Po uguese ma ke . In e na ional Jou nal
o Housing Ma ke s and Analysis, 15(4), 762–779. h ps://doi.o g/10.1108/IJHMA-04-
2021-0047
de Ville, B. (2013). Decision ees: Decision ees. Wiley In e disciplina y Re iews:
Compu a ional S a is ics, 5(6), 448–455. h ps://doi.o g/10.1002/wics.1278
Dehesh, A., & Pugh, C. (2000). P ope y Cycles in a Global Economy. U ban S udies, 37(13),
2581–2602. h ps://doi.o g/10.1080/00420980020080701
del Cacho, C. (2010, Decembe 11). A compa ison o da a mining me hods o mass eal es a e
app aisal [MPRA Pape ]. h ps://mp a.ub.uni-muenchen.de/27378/
Fama, E. F. (1991). E icien Capi al Ma ke s: II. The Jou nal o Finance, 46(5), 1575–1617.
h ps://doi.o g/10.1111/j.1540-6261.1991. b04636.x
Fle che , M., Gallimo e, P., & Mangan, J. (2000). He e oscedas ici y in hedonic house p ice
models. Jou nal o P ope y Resea ch, 17(2), 93–108.
h ps://doi.o g/10.1080/095999100367930
47
Fo yś, I., & Pu ek-Szeląg, E. (2017). THE IMPACT OF CRIME ON RESIDENTIAL
PROPERTY VALUE - ON THE EXAMPLE OF SZCZECIN. Real Es a e Managemen
and Valua ion, 25(3), 51–61. h ps://doi.o g/10.1515/ ema -2017-0022
Ghodsi, R., Boos ani, A., & Faghihi, F. (2010). Es ima ion o Housing P ices by Fuzzy
Reg ession and A i icial Neu al Ne wo k. 2010 Fou h Asia In e na ional Con e ence
on Ma hema ical/Analy ical Modelling and Compu e Simula ion, 81–86.
h ps://doi.o g/10.1109/AMS.2010.29
Goodha , C., & Ho mann, B. (2008). House P ices, Money, C edi and he Mac oeconomy.
G um, B., & Go eka , D. K. (2016). In luence o Mac oeconomic Fac o s on P ices o Real
Es a e in Va ious Cul u al En i onmen s: Case o Slo enia, G eece, F ance, Poland and
No way. P ocedia Economics and Finance, 39, 597–604.
h ps://doi.o g/10.1016/S2212-5671(16)30304-5
Han, J. H. (2018). Compa ing Models o Time Se ies Analysis. Wha on Resea ch Schola s.
h ps:// eposi o y.upenn.edu/wha on_ esea ch_schola s/162
Has ie, T., F iedman, J., & Tibshi ani, R. (2009). The Elemen s o S a is ical Lea ning.
Sp inge . h ps://doi.o g/10.1007/978-0-387-21606-5
Hishamuddin, M., Ali, H., Achu, K., Bin i, R., Abdul Jalil, R., Folake, A., & Yakub, A. (2020).
Jou nal o C i ical Re iews THE EFFECT OF ADOPTING MICRO AND MACRO-
ECONOMIC VARIABLES ON REAL ESTATE PRICE PREDICTION MODELS
USING ANN: A SYSTEMATIC LITERATURE REVIEW. Jou nal o C i ical
Re iews, 7, 2020. h ps://doi.o g/10.31838/jc .07.11.88
Housing p ice s a is ics—House p ice index. (2023). h ps://ec.eu opa.eu/eu os a /s a is ics-
explained/index.php? i le=Housing_p ice_s a is ics_-_house_p ice_index
Hush, D. R., & Ho ne, B. G. (1993). P og ess in supe ised neu al ne wo ks. IEEE Signal
P ocessing Magazine, 10(1), 8–39. h ps://doi.o g/10.1109/79.180705