Forecasting models for real estate market analysis The case study of Portugal

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. 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