Logical Homologies between Housting Prices Dynamics and Damped Harmonic Oscillations

M. Bełeja, S. Kuleszab, R. Cellmera aUniversity of Warmia and Mazury in Olsztyn, Department of Spatial Analysis and Real Estate Market, ul. Prawocheńskiego 15, 10-720 Olsztyn, Poland bUniversity of Warmia and Mazury in Olsztyn, Faculty of Mathematics and Computer Science, ul. Słoneczna 54, 10-710 Olsztyn, Poland

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The aim of the article is to employ the model of a damped harmonic oscillator (DHO) and critically damped harmonic oscillator (CDHO) to study the time-dependent evolution of time series of housing prices. The study treats the housing markets as complex, adaptive dynamic systems, which develop through synergistic network responses. This assumption is based on an observation of the synergies of the trends in housing prices, despite principal differences in the geospatial attributes of the markets under study. The logical homologies between housing prices dynamics and nonlinear harmonic oscillator is drawn from observation that a steep rise in housing prices (2006-2007) is, in fact, a transient disturbance to otherwise stable price evolution and is followed by an asymptotic return to a long-term equilibrium in a series of oscillations (system relaxation). Using the model of damped oscillator, it has been shown that the housing markets are highly inert. This can be seen during periods of rapid changes, when they quickly undergo deep structural transformations, although the pace of changes during long-term evolution is slow enough to keep the systems close to the state of equilibrium. The delay in the time series relative to each other indicates the dominant role of the Warsaw market as the initiator of changes and suggests the existence of links between markets, which supports the concept of local housing markets as a network of communicating vessels.

DOI:10.12693/APhysPolA.138.89 topics: harmonic oscillations, long-term equilibrium, homologies, housing market