Local Real Estate Markets in Poland as a Network of Damped Harmonic Oscillators

S. Kuleszaa and M. Belej b aFaculty of Mathematics and Computer Science, Warmia and Mazury University in Olsztyn, Słoneczna 54, 10-710 Olsztyn bFaculty of Geodesy and Land Management, Warmia and Mazury University in Olsztyn, Prawocheńskiego 15, 10-720 Olsztyn

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The paper deals with time series of housing prices on local real estate markets in Warszawa (WAW), Kraków (KRK) and Poznań (POZ) from 2006 to 2013 using a model of critically-damped harmonic oscillator to study underlying system dynamics. Performed analysis reveals the presence of housing bubble in 2007 that emerge from otherwise quasi-regular evolution around the equilibrium state. Time series of housing prices are fitted numerically to estimate important parameters of the system, for example: decay constant, delay time, and price equilibrium level, which help us to chose the leading market. Obtained results show reasonable matching of the model with housing prices in WAW and POZ, but less in KRK. The latter data, however, are found to agree well with the model of under-damped harmonic oscillator, which actually suggests that some trembling might occur in that market. Nevertheless, local real estate markets can be thought of as a system of interconnected damped harmonic oscillators with leading market in WAW that is about to change under aggregate macroeconomic fluctuations (exogenous factors) triggering changes in remaining markets.

DOI: 10.12693/APhysPolA.127.A-99 PACS numbers: 05.70.Ln, 89.65.Gh, 89.75.Da