In the modern scientific literature, there are many reports about the successful application of neural network technologies for solving complex applied problems, in particular, for modeling the urban real estate market. There are neural network models that can perform mass assessment of real estate objects taking into account their construction and operational characteristics. However, these models are static because they do not take into account the changing economic situation over time. Therefore, they quickly become outdated and need frequent updates. In addition, if they are designed for a specific city, they are not suitable for other cities. On the other hand, there are several dynamic models taking into account the overall state of the economy and designed to predict and study the overall price situation in real estate markets. Such dynamic models are not intended for mass real estate appraisals. The aim of this article is to develop a methodology and create a complex model that has the properties of both static and dynamic models. Moreover, our comprehensive model should be suitable for evaluating real estate in many cities at once. This aim is achieved since our model is based on a neural network trained on examples considering both construction and operational characteristics, as well as geographical and environmental characteristics, along with time-changing macroeconomic parameters that describe the economic state of a specific region, country, and the world. A set of examples for training and testing the neural network were formed on the basis of statistical data of real estate markets in a number of Russian cities for the period from 2006 to 2020. Thus, many examples included the data relating to the periods of the economic calm for Russia, along with the periods of crisis, recovery, and growth of the Russian and global economy. Due to this, the model remains relevant with the changes of the international economic situation and it takes into account the specifics of regions. The model proved to be suitable for solving the following tasks: industrial economic analysis, company strategic and operational management, analytical and consulting support of investment, and construction activities of professional market participants. The model can also be used by government agencies authorized to conduct public cadastral assessment for calculating property taxes.
1. Introduction
The authors of many recent publications, for example [1], emphasize that artificial neural networks (ANN) as complex nonlinear systems can take into account an unlimited number of external factors and dynamic interactions. Due to this, an ANN allows for solving multiple complex real problems that could not be solved by other methods. For example, the authors of this article created the world’s first neural network lie detector [2]. The ANN technology ensured a unique diagnostic accuracy of 98 percent due to a comprehensive accounting of psychophysiological parameters of an individual such as personal data and signals coming from the sensors of a polygraph machine. The members of the same author’s team developed a neural network system that helps detectives to investigate crimes, in particular, to identify people who can be serial maniacs and murderers [3]. This objective cannot be solved by other methods due to the need to analyze a large number of parameters and factors while many of them have an insignificant impact on the diagnostic result. The same authors created a medical system based on neural network technologies [4–6]. Due to a complex mathematical formulation of the problem, this system allows not only for diagnosing cardiovascular diseases, but also for making disease development forecasts for many years to come and for selecting the optimal courses of disease treatment and prevention (https://en.kardionet.ru). One more neural network system developed by the same team has a practical value enabling users to predict the future box office of a movie based on a set of various factors that have both a direct and an indirect impact on the result of forecasting [7]. Equally important in practice is a neural network system that predicts the bank failure probability and allows you to develop recommendations for preventing such bankruptcies [8]. The book in [9] by the author of this paper provides examples of neural network intelligent systems developed under his leadership and designed to diagnose complex technical devices, the economic position of enterprises, to predict political events, to identify the business and research skills of individuals, etc. Due to their complex formulation of mathematical problems, all these neural network systems enable users not only to diagnose and predict, but also to explore the simulated domains, as well as developing measures for active management of the behavior of these rather complex areas.
As noted by the authors in [1], the cutting-edge capabilities of neural networks make it possible to successfully apply them for modeling complex multifactor nonlinear systems such as a real estate system.
Many authors draw the attention to the great urgency of developing high-precision models for carrying out the mass valuation of real estate markets. For example, [10] presents the results of an analysis of international literature and interviews with statesmen of many countries. This analysis demonstrates that systems of mass valuation and real estate taxation are an important and viable basis for increasing government revenues. The authors of [1, 11–14] also note that high-precision methods of real estate valuation are a useful decision-making tool in the taxation and urban planning sectors. Such methods can be used by investors, buyers, and governments.
As noted in [15], until 1990, five standard recognized methods were mainly used for evaluating real estate such as the comparative method (comparison), contractor’s method (cost method), residual method (development method), profits method (accounts method), and investment method (capitalization/income method).
In the 1990s, some researchers reported about successful attempts to create systems for mass appraisal of real estate objects based on a new mathematical apparatus, artificial neural networks (ANN). Apparently, one of the first papers in this direction was an article [16] published in 1991. Its author, Borst, defined a number of variables for designing an ANN-based model for evaluating New York real estate. He reported that the model can predict the price of real estate with an accuracy of up to 90%. It was a perceptron-type neural network.
In 1991, Tay and Ho in [17] reported on the use of a multilayer perceptron to determine the market price of real estate in Taiwan.
In the same year of 1991, Evans, James, and Collins in [18] reported on the use of neural networks for evaluating residential real estate in England and Wales. After testing several methods, the authors came to the conclusion that the neural network model is best suited for delivering real estate valuations.
In 1992, Do and Grudnitskiy [19] published a report on using a perceptron-type neural network to evaluate US real estate. Based on a test set of 105 houses, the neural network model had twice the accuracy of the predicted values as compared to the analogous regression model.
From the mid-1990s to the present, a series of research publications devoted to the development and application of neural network models for mass appraisal of real estate objects have been published. Many papers [12, 20–32] emphasize the advantages of this advanced technology as compared to regression modeling and other methods of real estate valuation.
Analyzing the papers devoted to neural network modeling of estate markets, it can be noted that few researchers (e.g., [33]) have paid attention to the specific problems of modeling this subject area and to the issues of overcoming these problems. When constructing a neural network system for assessing real estate, the authors in [33] faced the challenge of overcoming the negative impact of statistical outliers on the accuracy of the created models. For the real estate market, they tested a number of methods for detecting outliers such as Tukey’s method, standard deviation method, median method, Z-score method, MAD method, and modified Z-score method. As a result, they concluded that the median method delivers the best results.
Looking ahead, we note that in our work we used an even more effective author’s method for detecting statistical outliers [34] based on the neural network mathematical apparatus.
Summarizing the review of neural network models designed for mass real estate valuation [10, 12, 16–32], let us pay attention to their overall disadvantages:(1)Developed for a specific city, these models cannot be applied to other cities because they do not take into account mesoeconomic factors.(2)All these models quickly become outdated and require frequent updates because they do not take into account the changing economic situation in the world, some specific country, and region over time. Such models can be called static ones. This disadvantage of static models is particularly relevant for developing countries where markets are in the process of development. These markets depend on time-varying oil prices, the dollar, GDP, stock indexes, government credit policies, and so on.
It should still be noted that there is a series of research papers, for example [1, 35], devoted to the development of economic and mathematical models of real estate markets that consider many macroeconomic parameters. However, these dynamic models are intended exclusively for modeling and studying market dynamics. They are not intended for the mass assessment of apartment prices that have a large variety of static characteristics. The apartment cost indices calculated in such models (the average unit cost of apartments assigned to a square meter) can, of course, be recalculated in the cost of specific apartments taking into account their construction, operational, environmental, and other parameters. However, such a recalculation can only be made using additional methods which are not used for mass appraisal of real estate objects due to their inefficiency. The fact is that the unit prices of apartments of the same type located in the same area and even in the same house may differ. Therefore, a more differentiated approach is required in this case.
Thus, on the one hand, we have a list of static models [10, 12, 16–32], etc., for mass appraisal of real estate objects. However, these models do not take into account the changing economic situation in the world, in the country, and in the region over time. Therefore, these models quickly become outdated and require frequent updates. These models are also not suitable for the medium-term forecasting of real estate markets.
On the other hand, there are dynamic models [1, 35] taking into account the general state of the economy and designed to forecast and investigate the overall price situation in the real estate market. Nevertheless, these models are not intended for mass appraisal of real estate.
In order to overcome these shortcomings, the authors of the article offered to your attention have recently published works [36, 37], in which attempts were made to develop methods for creating complex models that have the properties of both static and dynamic models. These new models take into account both construction and operational characteristics of real estate objects as well as some parameters characterizing the changing economic situation in some region, country, and the world. Due to this, such models have become self-adaptable to time; i.e., they have learned to maintain their predictive capabilities regardless of the changing economic situation over time.
The aim of this paper is to further expand and develop the results of the previous studies [36, 37]. Our goal is to create a model that can be self-adaptive not only to time but also to space.
2. Materials and Methods
When creating a model for mass assessment and scenario forecasting of residential real estate markets in Russian cities, geographical, construction, operational, time, and macroeconomic factors were taken into account as input parameters.
The model included the following geographical factors: the city index (1: Moscow; 2: Saint Petersburg; 3: Yekaterinburg; 4: Perm; etc.), the geographical coordinates of a specific apartment house (latitude, longitude) identified using the Yandex service at an address specified, and the level of prestige of the house’s location on the geographical map of the city.
In this set of parameters, the city index, which links the estimated apartment to a specific city, is fundamentally new. The parameter that characterizes the degree of prestige of the house location on the geographical city map is also new. Let us look at this parameter in more detail, since this paper introduces it for the first time.
In order to take into account the house location prestige, professional appraisers often use the distance from a specific house to the city center. Sometimes, parameters that characterize transport accessibility, proximity to metro stations, parking lots, city squares, business and cultural centers, industrial enterprises, public toilets, etc. are considered as well. However, such parameters are subjective. For example, there are cities without some center. There are cities with several centers. Parking lots, squares, and cultural and business centers can vary in terms of their convenience and efficiency.
In this regard, we suggest using the so-called heat maps to assess the location of real estate objects. These heat maps are constructed as follows. In each city, many properties of a similar type are selected, for example, many two-room apartments of approximately the same size sold over a certain period of time. The coordinates of apartments are put on the map, and their market value is shown on the map in different colors. The zones where the most expensive apartments are located are shown in red gradually changing to colder colors as the cost of the apartment decreases. An example of a heat map of Yekaterinburg constructed in this way is shown in Figure 1.