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dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t dr Sławomir Kulesza Department of Relativistic Physics PowerPoint PPT Presentation


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European Real Estate Society 19th Annual Conference 13th-16th June 2012. MODELLING THE REAL ESTATE DYNAMICS WITH THE CATASTROPHE THEORY. dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t dr Sławomir Kulesza Department of Relativistic Physics

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dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t dr Sławomir Kulesza Department of Relativistic Physics

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Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

European Real Estate Society 19th

Annual Conference 13th-16th June 2012

MODELLING THE REAL ESTATE DYNAMICS

WITH THE CATASTROPHE THEORY

dr inż. Mirosław Bełej

Department of Real Estate Management and Regional Development

dr Sławomir Kulesza

Department of Relativistic Physics

UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN

POLAND


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

POLISH REAL ESTATE MARKET

2006

1989

2004

2012

  • 1989 – SYSTEM TRANSFORMATION FROM CENTRALLY PLANNED ECONOMY (socialism) TO MARKET EKONOMY (capitalism)

  • 2004 - POLANDJOINS THE EUROPEAN UNION

  • 2006 - SUDDEN, UNEXPECTED LEVEL OF INCREASE IN REAL ESTATE PRICES IN POLAND

  • 2012 - Poland & Ukraine EURO 2012 FOOTBALL CHAMPIONSHIP

M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

POLISH REAL ESTATE MARKET

2006

1989

2004

2012

WWW.REAS.PL


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

2500 Euro

2250 Euro

2000 Euro

1750 Euro

1500 Euro

1250 Euro

1000 Euro

750 Euro

500 Euro

INSTABILITY

STABILITY

REAL ESTATE PRICES IN 2005-2011

SOURCE: M.Bełej. IDENTIFICATION OF SIMILARITIES IN REAL ESTATE TRENDS UNDER INSTABILITY CONDITIONS. Journal of Polish Real Estate Society vol.20 nr 2, 2012

WWW.TNN.ORG.PL


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

SCIENTIFIC PROBLEM

  • Significant changes in real estate prices, observed worldwide (including Poland), are not only perturbations of long-term trends, but also appear as an internal characteristic of the real estate market.

  • Changes in macroeconomic circumstances could destabilize a real estate market equilibrium, and then the system takes a series of quasi-discontinuous price changestowards a new state of balance.


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

SCIENTIFIC PROBLEM

  • - Instability of system maylead to discontinuouschanges

  • Theclassicalmethods of long-term analysis do not describeproperlydiscontinuouschangesinreal estate prices

  • The periods ofinstability, reflect an crucial feature of the real estate market, and they constitute the turning points of its development, wherethe system is looking for a new trajectory of evolution

  • The evolution path of the real estate market -under the influence of the control parameters - runs mostly over the areas of long-term stability, and occasionally enters into the instability area

M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

RESEARCH METHODOLOGY – CATASTROPHE THEORY

Catastrophe theory is a mathematical theory ofnonlineardiscontinuousphenomena.

Catastrophe theory describes how small, continuous changes in control parameters generatesdiscontinuous effects on the state of the system.

Such discontinuous, jump-like changes are called phase-transitions or catastrophes.

1972, Rene Thom: „Structural stability and morphogenesis”


Catastrophe theory morphogenesis

CATASTROPHE THEORY (MORPHOGENESIS)


Cusp catastrophe model

CUSP CATASTROPHE MODEL

Each dynamic system tends to the equilibrium state determined by the local minima of the potential function V

Potential V depends on two control parameters:

- α (asymetry coefficient),

- β (bifurcation coefficient),

and the state variable y in the form:

  • The set of all equilibrium points defines the equilibrium surface described by the equation:

M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

CUSP CATASTROPHE MODEL

  • The set of equilibrium states forms a surface with a characteristic fold

Stability area

Instability area

M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012


Case study real estate market in poland

Casestudy – Real estate market in Poland

The 4th largest province in Poland

Area of 24 000 km2(7,7% of the country’s area)

Population of 1 500 000

(3,7% of the country’s population)

THE UNIVERSITY OF WARMIA AND MAZURY

POLAND


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

HOUSING PRICES IN OLSZTYN 2003-2010


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

HOUSING PRICES IN OLSZTYN 2003-2010

TWO STATES OF EQUILIBRIUM

OF THE MARKET

STATE OF UNSTABLE EQUILIBRIUM


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

DATA ANALYSIS – 3D PLOT

Evolution path on equilibrium surface


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

DATA ANALYSIS – 2D PLOT


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

DATA ANALYSIS – MODELS COMPARSION

logLiK - (likelihood ratio test)

AIC (Akaike information criterion)

BIC - Bayesian information criterion


Conclusions

CONCLUSIONS

  • Mathematical models brought by the catastrophe theory might constitute a good description of empirical data from the real estate market under sudden price changes.

  • Sudden price changes are internal and crucial characteristicof the real estate market in the sense that they are critical points on the system evolution path towards equilibrium state.

  • Regardless of the parameters used in the fit procedure, obtained results suggest that neither linear model nor logistic one is superior to the catastrophe model.

M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012


Dr in miros aw be ej department of real estate management and regional developmen t dr s awomir kulesza department of relativistic physics

dr inż. Mirosław Bełej

Department of Real Estate Management and Regional Development

dr Sławomir Kulesza

Department of Relativistic Physics

UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN

POLAND

European Real Estate Society 19th

Annual Conference 13th-16th June 2012

MODELLING THE REAL ESTATE DYNAMICS

WITH THE CATASTROPHE THEORY

[email protected]


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