Realistische Unsicherheitsschätzung des Verkehrs wertes durch ein Fuzzy-Bayes-Vergleichswertverfahren

authored by
H. Alkhatib, A. Weitkamp, S. Zaddach, I. Neumann

The real estate and finance crisis in 2007/2008 has shown the importance of real estate valuation: The market value has to satisfy high objective quality requirements. Besides, the German jurisdiction demands a maximum dispersion of ±20 [%] of the market value. The sales comparison approach as one of the valuation methods is from a mathematical-statistical point of view based on a multiple linear regression analysis. Since decades, it has been considered as a standard procedure for analysing the real estate market and to determine the current market value. The estimated comparative value is in particular depending on the number and the type of influencing variables which are considered within the regression model. Nevertheless, the uncertainty estimation of this approach has not been extended since its introduction. The uncertainty here results from the inherent uncertainty of the observations on the one hand, on the other hand from the selected model as imperfect realisation of the reality. The aim of this research is to develop and enhance the uncertainty estimation in the used regression analysis by dividing the uncertainty budget in epistemic and aleatoric parts. While the aleatoric components describe random variability, which can be modelled by means of Bayesian inferences, the epistemic components characterise systematic and/or deterministic influences which result from unsatisfactory knowledge, assumptions, simplifications and linguistic formulations. Epistemic components can be modelled by selected approaches from fuzzy theory. This paper introduces a Fuzzy-Bayesian approach, which is able to consider the uncertainty of the market value affected by the above described characteristics and thus to quantify its impact on the market value. As starting point for this investigation, the data basis is prepared: The market value affecting attributes, which have a significant influence on the valuation approaches, were listed and categorised for showcase samples of different spatial and objective partial markets. The establishment of the advanced mathematical approach should allow predicting any real estate values for objects within the selected spatial and objective submarket. The methodology is tested on a real data set. It can be concluded, that this approach should provide more precise and appropriate uncertainty estimations of predicted values without changing the market value itself.

Geodetic Institute
ZFV - Zeitschrift fur Geodasie, Geoinformation und Landmanagement
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