Lie symmetry analysis of the effects of urban infrastructures on residential property values

Abstract

Due to the complexity of socio-economic-related issues, people thought of housing market as a chaotic nucleus situated at the intersection of neighboring sciences. It has been known that the dependence of house features on the residential property value can be estimated employing the well-established hedonic regression analysis method in teams of location characteristic, neighborhood characteristic and structure characteristic. However, to further assess the roles of urban infrastructures in housing markets, we proposed a new kind of volatility measure for house prices utilizing the Lie symmetry analysis of quantum theory based on Schrödinger equation, mainly focusing on the effects of transportation systems and public parks on residential property values. Based on the municipal open government data regularly collected for four cities, including Boston, Milwaukee, Taipei and Tokyo, and all spatial sampling sites were featured by United States Geological Survey (USGS) National Map, transportation and park were modelled as perturbations to the quantum states generated by the feature space in response to the environmental amenities with different spatial extents. In an attempt to ascertain the intrinsic impact of the location-dependent price information obtained, the similarity functions associated with the Schrödinger equation were considered to facilitate revealing the city amenities capitalizing into house prices. By examining the spatial spillover phenomena of house prices in the four cities investigated, it was found that the mass transit systems and the public green lands possessed the infinitesimal generators of Lie point symmetries Y2 and Y5, respectively. Compared statistically with the common performance criteria, including mean absolute error (MAE), mean squared error (MSE) and, root mean squared error (RMSE) obtained by hedonic pricing model, the Lie symmetry analysis of the Schrödinger equation approach developed herein was successfully carried out. The invariant-theoretical characterizations of economics-related phenomena are consonant with the observed residential property values of the cities internationally, ultimately leading to develop a new perspective in the global financial architecture.

Continuous Symmetry Analysis of the Effects of City Infrastructures on Invariant Metrics for House Market Volatilities

“…The significant spatial spectrum features undoubtedly indicated that the entire price fluctuation was regulated by the Park, Transportation or both infrastructures marked on the maps. 3) is used to describe human perceptions [2,76,77]. As far as the symmetry behaviors of the house market fluctuation corresponding to the economic invariance are concerned, the special linear group structure is extended by embedding SO(3) ⊗ R(3) in SL(2, R).…”

“…Inspired by the principles of physics, many physicists have studied financial markets by assuming that the economic world behaves like a set of interacting particles [1]. Using the new tools of statistical physics and recent breakthroughs in understanding chaotic systems, physicists or statisticians, with the help of some serious mathematics borrowed from the study of disordered materials, are dismantling some of the puzzling economics and reducing them to some elegant general principles, e.g., symmetry and invariance [2]. One of the fundamental human needs is access to decent and affordable housing [3,4].…”

“…In our previous report, we applied a group theoretical framework utilized in the present study. We evaluated the essential Cobb-Douglas-like behavior in property price volatilities [2]. Originating from parks and transportation, the scale invariance is empirically demonstrated by plotting transaction price, distance to metro and park area percentage for these four cities, including Boston, Milwaukee, Tokyo and Taipei, globally investigated in log-log coordinates.…”

“…Incorporating the perceptual dimensions, the property price related information obtained by fusing smart city infrastructure data and open government data can be geometrically represented by points and vectors in the conceptual space. In our previous work [2], based on the infinitesimal Lie symmetry generators, The invariant solutions are derived from the mathematical model and the general [44]. We described the subgroup structure of special linear groups such as SL(2, R) in linear algebra, which is of degree two over the real number field.…”

“…The technical structure of the special linear group is illustrated in detail in the related works [45,46]. Based on the prolongation structure of the Schrödinger equation, the special linear group SL(2, R) is employed to model housing price volatility, essentially extending the special linear group structure by embedding SO(3) ⊗ R(3) in SL(2, R) [2]. The rotational invariance group leads to a Gaussian pattern, which is consistent with Shepard's universal law.…”