Developing a Forecasting Model for Real Estate Auction Prices Using Artificial Intelligence

Abstract

The real estate auction market has become increasingly important in the financial, economic and investment fields, but few artificial intelligence-based studies have attempted to forecast the auction prices of real estate. The purpose of this study is to develop forecasting models of real estate auction prices using artificial intelligence and statistical methodologies. The forecasting models are developed through a regression model, an artificial neural network and a genetic algorithm. For empirical analysis, we use Seoul apartment auction data from 2013 to 2017 to predict the auction prices and compare the forecasting accuracy of the models. The genetic algorithm model has the best performance, and effective regional segmentation based on the auction appraisal price improves the predictive accuracy.

1. Introduction

In the past, the real estate industry was not recognized as an advanced industrial category. However, as a result of the informatization of the real estate industry and the linkage with financial markets, markets in financial investment instruments, such as real estate funds, Real Estate Investment Trusts (REITs) and Non-Performing Loans (NPL), have become active. Accordingly, many experts view the real estate industry as a financial field that is being explored more actively than in the past using artificial intelligence methods. A special feature of the real estate industry, the real estate auction market has played a key role in the industry’s development. Borrowers, lenders and investors are deeply involved in the real estate auction market, and the importance of the real estate auction process is increasing in the areas of finance and investment.

From January 2001 to December 2017, approximately 6.6 million real estate auctions were held in Korea nationwide, and the number of successful auctions, i.e., the number of sales, reached 2 million, while the average auction sale price rate was more than 71% of the appraisal value. Among regional markets, Seoul and the Gyeonggi province are the most active markets. The average auction sale price rate and the number of bidders in both markets are higher than the respective figures for the nationwide market. Especially looking at the apartment transaction market in Seoul, 692,397 private auctions, as well as 9435 institutional auctions, have been traded from January 2013 to December 2017. In this study, we use the data of the institutional apartment auction, which accounts for a high proportion of the total auctions in Seoul from January 2013 to December 2017. The data in the real estate auction industry are well-organized, enabling various in-depth analyses.

Considering both the real estate auction market and the capital market, the importance of related studies can be recognized. A real estate fund, which is a combination of real estate and finance, is structured to enable cooperation of many institutional participants, such as financial institutions, asset management companies and real estate management companies. This fund is a successful representative model that brought real estate to advanced financial markets; as of 2017, real estate fund assets amounted to more than 118 trillion Korean won, having grown by approximately 20% year-on-year. In other words, the real estate fund market has been expanding consistently with the growth of the capital market. For a more accurate investment in and management of this market, it is clear that there is a need for more studies of real estate using advanced techniques of data analysis and forecasting.

In this paper, we develop a forecasting model for real estate auction prices to provide forward looking auction market investors with useful information for future auction price prediction. We perform empirical analysis using artificial intelligence techniques with Korean auction market data. A recent study by Kang et al. [1] performed a chaos analysis of real estate auction sale price in Korean auction markets and confirmed that real estate auction sale price data has a deterministic structure. Therefore, it is worthwhile to develop forecasting models for real estate auction prices using various methodologies. Based on the result of Kang et al. [1], we construct forecasting models for real estate auction sale prices using artificial intelligence and a traditional statistical method; subsequently, we compare the predictive accuracy of models to identify the best model and optimization method. The artificial intelligence methods include a genetic algorithm (GA) and an artificial neural network (ANN); a statistical method of regression analysis is also used. This study is the first to consider forecasting the prices of individual real estate items using artificial intelligence methods.

The GA model is found to have the best performance. We also find that effective regional segmentation based on the auction appraisal price plays a key role in increasing the predictive accuracy of a forecasting model. These results offer valuable implications to forward looking investors at real estate auction markets, as well as managers of real estate funds. They are able to make more efficient investment strategies by using our GA model, which results in sustained economic benefits to the related stakeholder of real estate auction markets and the national economy. In this sense, the model developed in this study plays a role in sustaining economic growth.

The remainder of this paper is organized as follows. A literature review is presented in Section 2. The details of the model architecture are described in Section 3. In Section 4, the empirical analysis and results are presented. Finally, Section 5 presents the study’s conclusions.

2. Literature Review

There are several previous studies related to real estate forecasting using artificial intelligence, mostly with ANN and statistical analysis. Stevenson et al. [2] examined residential sale mechanisms from an appraisal perspective and empirically tests for differences in the valuation process for auctioned and private treaty sales. They tested the hypothesis that agents use different criteria in preparing the guide prices for auctioned housing, with an element of underpricing in order to aid in the marketing of the property and found agents do adjust valuations for auctions to attract additional potential bidders. In the 1990s, mass appraisal studies of real estate, especially residential property, have been performed using ANN [3,4,5,6,7,8]. Worzala et al. [9] applied neural network technology to real estate appraisal and compared the performance of two ANN models in estimating the sales price of residential properties with a traditional multiple regression model. They were concerned about the consistency and repeatability of results and the “black box” nature of neural networks in general. Results of the study did not support previous findings that ANNs are a superior tool for appraisal analysis. Nghiep and Al [10] predicted housing values using multiple regression analysis (MRA) and ANN, and compared the predictive power of models. The researchers showed that ANN performed better than MRA when a moderate to large data sample size was used. Limsombunchao [11] analyzed two models, the hedonic price model and ANN, for housing price prediction using a randomly selected sample of 200 houses in Christchurch, New Zealand. Factors, including house size, age and type, the number of bedrooms, bathrooms, garages, and amenities around the house, as well as geographical location, were considered in the study; the result showed the potential power of ANN to predict housing prices. McCluskey et al. [12] examined the comparative performance of an ANN and several multiple regression models in terms of their predictive accuracy in the mass appraisal industry. They found that a non-linear regression model had higher predictive accuracy than the ANN and the output of the ANN was not sufficiently transparent to provide an unambiguous appraisal model. McCluskey et al. [13] assessed a number of geostatistical approaches relative to an ANN model and the traditional linear hedonic pricing model for mass appraisal valuation. They found that ANNs outperformed the traditional multiple regression models and approached the performance of spatially weighted regression models. However, ANNs retain a “black box” architecture that limits their usefulness to practitioners in the field. A relatively recent study by Núñez Tabales et al. [14] insisted on the use of ANN if there were enough statistical information and an extensive set of data spanning years. The authors considered exogenous variables and factors, such as buildings located nearby and surroundings of a house. Zhou et al. [15] tried to improve existing ANN-based prediction models and finally presented several suggestions for a mass appraisal of real estate in China.

In addition to ANN-based studies, there are several previous studies of real estate prediction using GA. Ahn et al. [16] used ridge regression with GA (GA-Ridge) to enhance real estate appraisal forecasting. The researchers performed an experimental study of the Korean real estate market and verified that GA-Ridge was effective in forecasting real estate appraisals. Del Giudice et al. [17] used GA to interpret the relationship between real estate rental prices and geographical locations of houses, and compared the results of GA and MRA to verify the potential forecasting power of GA.

Only a small number of similar studies of the Korean real estate industry have been performed. Han [18] attempted to construct a forecasting model for real estate appraisal price using GA ridge regression and compared the model to ANN and multiple regression. The study is meaningful in that it forecast a time series index related to the Korean real estate industry with a macroeconomic indicator and tried to use artificial intelligence methodologies. Kwon [19] researched a nonlinear macroeconomic time series forecasting model and is one of the empirical studies that forecast real estate prices. Unlike the past real estate forecasting models based on macroeconomic indicator data, this study designed an artificial housing market and applied GA with agent-based modeling (ABM). Chung [20] tried to construct a forecasting model for the apartment price index using ANN. The model forecast time series using the real estate price index and macroeconomic data, but had a limitation because it included a small number of variables.

3. Model Architecture

The purpose of this study is to develop forecasting models for the auction sale price. For this purpose, GA, ANN and a regression model are used (see Figure 1). In particular, this study focuses on forecasting prices of individual real estate auction items. To estimate these individual prices, sufficient data needs to be collected to construct forecasting models effectively. In addition, aspects, such as how to subdivide the analysis area (the area of Seoul in this paper) are very important.

3.1. Data Selection

The data for this study covers real estate auction cases of apartments in Seoul for the preceding five years. The data are collected from real estate auction information companies, banks, statistical offices and other related organizations. To remove insignificant factors that may pose obstacles to experiments, the results of previous studies regarding the key factors of real estate auctions are considered before an empirical study. As the format and scale of collected data vary, a standardization process is also required. The training set for constructing models and a separate testing set are assigned approximately 70% and 30%, respectively, of the entire size of data.

3.2. Grouping Process

In this step, several grouping processes for data are applied, and forecasting models are constructed for each group independently to compare the results. Theoretically, the performance will improve if the similarity within a group increases and that between groups decreases. The Seoul area is divided into 25 boroughs, which is the most segmented separation. Afterwards, grouping criteria according to the 2020 Seoul City Basic Plan are applied based on administrative and residential areas. The plan divides Seoul into five zones: The urban zone, and southeast, northeast, southwest and northwest zones (see

Table 1. Twenty-five boroughs and five zones of the Seoul area based on the 2020 Seoul City Basic Plan.

Name of Zone	Boroughs
Urban zone	Jung-gu, Jongno-gu, Yongsan-gu
Southeast zone	Gangnam-gu, Seocho-gu, Songpa-gu, Gangdong-gu
Northeast zone	Gangbuk-gu, Dobong-gu, Nowon-gu, Jungnang-gu, Gwangjin-gu, Seongdong-gu, Dongdaemun-gu, Seongbuk-gu
Southwest zone	Gangseo-gu, Yangcheon-gu, Guro-gu, Gwanak-gu, Yeongdeungpo-gu, Dongjak-gu, Geumcheon-gu
Northwest zone	Eunpyeong-gu, Seodaemun-gu, Mapo-gu

). Finally, another model is constructed using clustering based on auction appraisal prices. Based on the average auction appraisal price of each borough, all 25 boroughs are classified into several groups using the cluster analysis [21,22,23,24]. This process can be effective for improving model performance because auction appraisal price is one of the most important factors associated with a real estate auction. In other words, the classification based on auction appraisal price can increase homogeneity within groups and heterogeneity between groups [25,26,27].

3.3. Regression Model

A linear regression model determines the characteristics and relationship between independent variables and a dependent variable. A simple linear regression model incorporates one independent variable, while a multiple linear regression model incorporates multiple independent variables [28,29,30]. The linear regression analysis estimates the following linear equation that describes a plane that passes closest to each data point on a scatter plot.

$${\mathrm{Y}}_{\mathrm{n}}=a_1{x}_1+a_2{x}_2+\cdots +a_p{x}_p+{\epsilon }_n$$

(1)

This equation incorporates p independent variables. From this equation, $a_1,\cdots ,a_p$, coefficients of independent variables $x_1,\cdots ,x_p$, are estimated to forecast $y_n$ given independent variables $x_1,\cdots ,x_p$. In this paper, the forecast value is the auction sale price, and the independent variables are selected from the real estate auction procedure and macroeconomic data. In the process of estimating the coefficients, the sum of squared errors (SSE) for a linear equation is minimized; this approach is called the method of least squares [31,32,33].

3.4. Artificial Neural Network

ANN is a technique that reproduces humans’ intelligent activities [34,35,36]. An ANN model capable of expressing nonlinear relations has attracted attention as an approach to overcoming the limitations of the traditional statistical methodologies that express forecasting models through linear combinations of independent variables. The model mimics human brain cells and does not assume any linear distribution of probabilities or variables. Therefore, ANNs can be used for more varieties of data than can be traditional statistical methods [37,38,39].

An ANN consists of nodes and weights. A collection of nodes with similar properties is called a layer; typically, there are three types of layers: Input, hidden and output [34,35,36,37,38,39]. The input layer consists of input nodes that accept input values of data. The hidden layer consists of hidden nodes; each node of the hidden layer accepts output values of the previous layer as input values. The output layer consists of output nodes that represent the final output values of the network. The nodes of different layers are connected by their respective weights that are multiplied when output values of nodes are passed to other nodes. Every node of the network computes the output values by applying an activation function to input values. There are various activation functions, and we use the following sigmoid function;

$$f\left(x\right)=\frac{1}{1-\exp \left(-x\right)}$$

(2)

There are various ANN architectures, but the multi-layer perceptron is the most efficient. Multi-layer perceptron is a neural network with one or more hidden layers between the input layer and output layer. In the input layer, input data is received from the outside of the system and transmitted to the system. The hidden layer located inside the system takes input values, processes them, and generates the results. The output layer calculates the system value based on the input value and the current system state (see Figure 2). In this paper, we use the multi-layer perceptron with two hidden layers.

3.5. Genetic Algorithm

GA is an optimization methodology presented by Holland [40,41]. To search for the optimized solution, a GA uses the principles of Darwinian evolution that consists of crossover, selection and mutation [42,43]. Before searching for the optimal solution, the method represents the solutions as a binary data structure called a chromosome, and a set of chromosomes is called a population. Then, by implementing the algorithm, the fitness values of solutions increase until the specifically designated conditions are satisfied. The fitness value is calculated by the fitness function initially established to illustrate the goal of the problem. The entire process of a GA searching for the optimal solution is shown in Figure 3.

Selection is the operation of selecting two parent solutions that are more appropriate than others to determine the composition of the offspring generation based on the survival principle of the natural system. In general, chromosomes are selected with probability proportional to their fitness or from top to bottom in descending order of fitness ranking. One should choose the solution with the higher fitness. As the process of selection is repeated, it is expected that inferior solutions will be reduced, and superior solutions will survive through the generations.

Crossover is a representative operation of a GA. Crossover is a method for generating a new offspring through mixing genes in the parent chromosomes. Generally, two parent chromosomes are cut by the number of specific points, and the cut parts are exchanged with each other. In the uniform crossover, genes at randomly selected positions of one parent are exchanged with those of another parent. Using various crossover methods, the good genetic information of chromosomes of the previous generation can be preserved, and more optimized chromosomes than those observed in the past can be searched for simultaneously.

The mutation is a way to construct a new direction for finding a solution using the birth of a totally new offspring (chromosome). Crossover can bind genes in a good direction; however, it is difficult to introduce new genes that are not from parental traits. Mutation can create new chromosomes that are better than those observed in the past by randomly replacing a certain value of genes in chromosomes that already exist. However, due to randomness, crossover implies a risk of producing inferior chromosomes. By repeating these processes until the specified requirements are satisfied, the generation progresses, and the fitness of chromosomes (solutions) is improved.

In this paper, GA is used to search for the optimized values of a regression model that predicts the real estate auction price after a period of time [44,45]. The GA stops when a number of generations have all evolved. The larger the population and generation, the greater the likelihood that a globally optimized solution will be obtained, but the complexity of finding optimal variables will increase exponentially. Therefore, the empirical analysis is usually carried out using a reasonable stopping condition in the process of finding an optimal solution. In this paper, the optimization process ends when the average population fitness does not improve, or the surviving chromosomes do not change after 20,000 iterations. The main parameters of the GA, such as population size, crossover rate, and mutation rate, are set to 50, 0.5, and 0.05, respectively, which are commonly used default settings. The optimized values serve as regression coefficients. The objective function of the algorithm for this model is shown by (3).

$$\mathrm{Objective}\mathrm{Function}=\frac{1}{n}{\displaystyle \sum _{i=1}^n}\left|\frac{F_i-Z_i}{Z_i}\right|$$

(3)

where $F_I$ represents the forecast values, and $I$ is the real-world value of i-th property.

4. Empirical Analysis

4.1. Data and Methodology

In this study, the auction data collected from the GG Auction Co., Ltd., Infocare Auction Co., Ltd., Bank of Korea, Kookmin Bank, Statistics Korea (KOSTAT) and Korea Exchange (KRX) were used for the empirical study. The number of data points is 9435, and the sample period of data is from January 1, 2013, to December 31, 2017. The data covers all the apartment auction items in Seoul for over five years. The reason for analyzing the Seoul area is that apartment prices in Seoul are more standardized than those in other areas.

Many previous studies of the Korean real estate industry have been limited to time series analysis of real estate prices and indices. In contrast, this study focuses on forecasting the individual prices of real estate auction items. Therefore, it is necessary to reduce the volatility of the value to be forecasted by using large amounts of data and appropriate variables. The variables affecting the real estate auction price are approximately divided into three categories: Auction characteristics, the physical properties of the real estate, and macroeconomic variables (See

Table 2. Data and variables selection.

Data	Real estate auction data
Usage/Area	All apartments in Seoul
Period	January 1, 2013–December 31, 2017
Quantity	9435 cases
Dependent variable (1)	Auction sale price
Independent variables (33)	Auction data (7)	Appraisal price, average auction sales price rate, average number of bidders, number of bids, number of views, auction period, auction index
	Physical data (14)	Exclusive area, land area, land portion, nonpayment of management fee, number of tenants, lien, priority lease, legal superficies, portion right auction, dependent right, special right, school distance, bus stop, subway distance
	Macroeconomic data (12)	Consumer price index, bill default rate, interest rate, leading economic index, stock index (construction), consumer sentiment index (Real estate), apartment (APT) sales index, APT lease index, APT sales trend index, APT lease trend index, APT buyer priority index, APT lease demand–supply index
Sources	GG Auction Co., Ltd., Infocare Auction Co., Ltd., Korea Bank, Kookmin Bank, Statistics Korea (KOSTAT) and Korea Exchange (KRX)

).

The variables classified as auction characteristics include appraisal price, average auction sales price rate, average number of bidders, number of bids, number of views, auction period, and auction index. These variables are considered important in this study because a real estate auction is the only system based on the laws of Korea, and hence, the auction characteristics inevitably have a significant impact on the auction price.

The variables classified as physical properties include exclusive area, land area, land portion, unpaid management fee, tenant, lien, priority lease, legal superficies, fractional right auction, dependent right, special right, school distance, bus stop, and subway distance. In addition, some of these the variables are classified as macroeconomic data, as shown in Table 2.

Real estate has strong individual characteristics depending on the physical, legal and economic values that differentiate properties of real estate in the same area. Therefore, the variables listed in Table 2 can be key factors that determine the prices of real estate. The detailed descriptions of all used variables and their source are shown in

Table 3. Variables description.

Variables	Source of Variables	Description
Auction sales price	GG Auction Co., Ltd.	The highest bid price in an auction
Appraisal price	GG Auction Co., Ltd.	Appraised value of auctioned real estate
Average auction sales price rate	GG Auction Co., Ltd.	The average annual auction sale price of apartments in the same area
Average bidder number	GG Auction Co., Ltd.	The average number of bidders participating in similar real estate auctions over a year
Bid open number	GG Auction Co., Ltd.	The auction did not succeed, and the property being auctioned was scheduled to be auctioned again
View number	GG Auction Co., Ltd.	The number of people who searched for real estate at an auction website
Auction period	GG Auction Co., Ltd.	The number of days from the auction start day to the auction sale day
Auction index (APT sale price rate)	Inforcare Auction Co., Ltd.	Index of auction sale price change rate at the time of auction sale day
Exclusive area	GG Auction Co., Ltd.	Private and exclusive area of apartment
Land area	GG Auction Co., Ltd.	Land area owned by the apartment
Land portion	GG Auction Co., Ltd.	Apartment’s ratio of private area to total apartment area
Nonpayment of management fee	GG Auction Co., Ltd.	Unpaid management costs
Tenant	GG Auction Co., Ltd.	Number of tenants in the apartment
Lien	GG Auction Co., Ltd.	Number of claims on the property requiring satisfaction of outstanding obligations
Priority lease	GG Auction Co., Ltd.	Number of tenants having priority over mortgages
Legal superficies	GG Auction Co., Ltd.	Number of rights to own properties on the land of another person
Fractional right auction	GG Auction Co., Ltd.	Number of auctions for a part, but not the entirety of the apartment
Dependent right	GG Auction Co., Ltd.	Number of dependent occupancy rights during the contract period
Special right	GG Auction Co., Ltd.	Number of special rights, such as liens, legal superficies, dependent rights, etc.
School distance	GG Auction Co., Ltd.	Distance to a school from the apartment
Bus stop	GG Auction Co., Ltd.	Distance to a bus stop from the apartment
Subway distance	GG Auction Co., Ltd.	Distance to subway from the apartment
Consumer price index	National Statistical Office	Price index of fluctuations of goods and services purchased by consumers, equal to 100 for 2010
Bill default rate	Korea Bank	The percentage of bankruptcy bills, due to insufficient funds during a certain period
Interest rate	Korea Bank	Monthly standard interest rate determined by the Bank of Korea
Leading economic index	National Statistical Office	Forecasting indicators of near-term economic trends
Stock index(construction)	Korea Stock Exchange	Korea stock exchange index for construction industries
Consumer sentiment index (Real estate)	National Statistical Office	Index of the real estate market consumer behavior change and perception level
APT sales index	KB Bank	Index of a measure of the relative rate of change in the residential sale price
APT lease index	KB Bank	Index of a measure of the relative rate of change in the residential lease price
APT sales trend index	KB Bank	Trend index of the proportions of “active” and “slack” sales
APT lease trend index	KB Bank	Trend index of the proportions of “active” and “slack” leases
APT buyer priority index	KB Bank	Trend index of the proportions of “buyer advantage” and “seller advantage” sales
APT lease demand–supply index	KB Bank	Trend index of the proportions of “landlord advantage” and “tenant advantage” leases

.

Before conducting the experiment, standardization is needed because the type and scale of collected data vary. Standardization is the process of adjusting the values of each variable to a range from 0 to 1. This type of data preprocessing is known to be efficient for model construction and forecasting [46,47]. In this study, the min-max standardization method is used, as defined by Equation (4). To derive the forecast values, this formula is rearranged, as shown in Equation (5).

Standardization value = (Real value − Min) / (Max − Min)

(4)

Forecast value = Forecast ratio × (Max − Min) + Min

(5)

To develop a multiple regression model, all variables are included in the model. In the case of the ANN model, there are two hidden layers and 60 hidden nodes in each layer. The sigmoid function is adopted as the activation function because we want to forecast values between 0 and 1. Finally, coefficients in the linear regression model are optimized. For a GA model construction, the number of trials, population size, crossover rate, and mutation rate is set to 20,000, 50, 0.5 and 0.05, respectively.

The performance of models is measured by the mean absolute percentage error (MAPE), and root mean square error (RMSE) calculated by Equations (6) and (7), respectively.

$$MAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n}\left|\frac{P_i-F_i}{P_i}\right|$$

(6)

$$RMSE=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(P_i-F_i\right)}^2}{n}}$$

(7)

where $P_i$ and $F_i$ are, respectively, the real-world and forecast auction sale prices of i-th real estate, and the number of auction items is n. Without the grouping process, the training and holdout sets are composed of 6568 and 2867 auction cases, respectively. They are randomly chosen from all auction cases in Seoul.

4.2. Empirical Results

Table 4. Forecasting errors of the training set and the holdout set.

Area	Methodology	Partition	MAPE	RMSE
Seoul	GA	Training Set	8.14	0.0109
		Holdout Set	8.86	0.0060
	ANN	Training Set	20.38	0.0074
		Holdout Set	23.88	0.0067
	Regression	Training Set	16.74	0.0074
		Holdout Set	18.68	0.0061

shows the results of the proposed forecasting models using data without the grouping process. The results in Table 4 show that the GA model (MAPE is 8.86 and RMSE is 0.006) has the best performance on the holdout set among the three models.

To measure how close the forecast values are to market values, the average forecast of auction sale price rate is compared to the average of market auction sale price rate. The auction sale price rate means the ratio of the auction sale price to the auction appraisal price, calculated by Equation (8).

$$Auctionsalepricerate=\frac{Auctionsaleprice}{AuctionappraisalPrice},$$

(8)

As the auction appraisal price is fixed, the forecast price is sufficiently close to the market price if the average forecast of auction sale price rate is similar to that of market auction sale price rate.

Table 5. Comparison of auction sale price rate by model and year.

	2013	2014	2015	2016	2017	Average
Market value	0.8164	0.8765	0.9284	0.9440	0.9734	0.9306
GA	0.8277	0.8665	0.9296	0.9319	0.9645	0.9040
ANN	0.8445	0.9219	1.0753	1.0500	1.2596	1.0302
Regression	0.8302	0.9052	1.0386	1.0246	1.1363	0.9870

reports the average of market auction sale price rates and the average forecast of auction sale price rate obtained using regression, ANN and GA models. As shown in Table 5, the annual average forecast of auction sale price rates from the GA model is approximately estimated to be 83% in 2013, 87% in 2014, 93% in 2015, 93% in 2016, and 97% in 2017. These results are very close to the annual average of market auction sale price rates. In addition, the average value of the forecast auction sale price rate resulting from the GA model (0.9040) is observed to be closer than the respective values of other models to that of market auction sale price rate (0.9306).

In the next step, several grouping processes are performed to improve forecasting performance. At first, grouping according to five zones based on the 2020 Seoul City Basic Plan is used. The five zones consist of urban, southeast, northeast, southwest and northwest zones. The number of auction cases in each zone is 475 in the urban zone, 2143 in the southeast zone, 3113 in the northeast zone, 2771 in the southwest zone, and 933 in the northwest zone. The ratio of the training and holdout sets is the same as in the previous experiment.

Table 6. Comparison of forecasting models in five zones of Seoul.

Area	Performance Metric	GA	ANN	Regression
Urban zone (n = 133)	MAPE	8.27	15.89	12.34
	RMSE	0.0049	0.0086	0.0054
Southeast zone (n = 652)	MAPE	9.74	13.81	17.09
	RMSE	0.0085	0.0088	0.0090
Northeast zone (n = 957)	MAPE	7.41	18.95	17.09
	RMSE	0.0042	0.0043	0.0045
Southwest zone (n = 829)	MAPE	7.95	19.73	17.81
	RMSE	0.0036	0.0054	0.0044
Northwest zone (n = 296)	MAPE	8.20	10.09	13.63
	RMSE	0.0026	0.0028	0.0150
Average (n = 2867)	MAPE	8.33	15.69	15.59
	RMSE	0.0048	0.0060	0.0077

reports the MAPE and RMSE of the proposed forecasting models applied to the holdout set with the grouping process based on five zones.

The results in Table 6 show that the MAPE and RMSE of the GA model are the lowest among the values of the three forecasting models in all five zones of Seoul. The average values of MAPE and RMSE of the GA model for five zones are 8.31 and 0.0047, respectively. This result implies an improvement over the previous experimental results without the grouping process. Note that the values of MAPE and RMSE of the GA model applied to the holdout set without the grouping process are 8.86 and 0.0060, respectively (see Table 4).

Table 7. Comparison of auction sale price rate for five zones by model and year.

		2013	2014	2015	2016	2017	Average
Urban	Market Value	0.7780	0.8104	0.8681	0.8788	0.8869	0.8444
	GA	0.8005	0.8087	0.8684	0.8842	0.9942	0.8712
	ANN	0.7923	0.8881	0.9314	0.8641	1.0770	0.9106
	Regression	0.7893	0.8133	0.8844	0.9474	0.9254	0.8720
Southeast	Market Value	0.8231	0.8761	0.9445	0.9561	1.0095	0.9219
	GA	0.8307	0.8563	0.9441	0.9702	0.9736	0.9150
	ANN	0.8563	0.9065	0.9597	1.0281	1.0486	0.9598
	Regression	0.7200	0.8009	1.0006	1.0874	1.1559	0.9530
Northeast	Market Value	0.8178	0.8817	0.9545	0.9743	0.9619	0.9180
	GA	0.8235	0.8708	0.9689	0.9712	0.9557	0.9180
	ANN	0.8448	0.8698	1.0510	1.0206	1.2048	0.9982
	Regression	0.8501	0.8804	1.0577	1.0443	1.1223	0.9910
Southwest	Market Value	0.8148	0.8854	0.9111	0.9116	0.9854	0.9017
	GA	0.8262	0.8739	0.9181	0.9020	0.9731	0.8987
	ANN	0.8248	0.9254	1.0335	0.9422	1.1122	0.9676
	Regression	0.8308	0.9101	1.0264	0.9676	1.0292	0.9528
Northwest	Market Value	0.8119	0.8723	0.8971	0.9382	0.9759	0.8991
	GA	0.8350	0.8610	0.8821	0.9048	0.9627	0.8891
	ANN	0.8506	0.8832	0.9001	0.9305	0.9805	0.9090
	Regression	0.8310	0.8553	0.6269	0.9332	1.0372	0.8567

reports the averages of market auction sale price rate and of forecast auction sale price rate obtained using regression, ANN and GA models for five zones. The GA model shows the best performance, i.e., the average auction sale price rate obtained with the GA model is the closest to that of market auction sale price rates in all five zones.

To group data more specifically, we perform the analysis for each of 25 boroughs independently. The forecasting errors in each borough for all three models are shown in

Table 8. Comparison of forecasting models in 25 individual boroughs of Seoul.

District	Performance metric	GA	ANN	Regression
Gangnam-gu (n = 201)	MAPE	11.39	13.94	14.65
	RMSE	0.0115	0.0124	0.0111
Gangdong-gu (n = 133)	MAPE	8.00	10.18	9.89
	RMSE	0.0039	0.0036	0.0035
Gangbuk-gu (n = 45)	MAPE	4.92	6.79	6.12
	RMSE	0.0012	0.0014	0.0013
Gangseo-gu (n = 172)	MAPE	7.04	10.02	20.86
	RMSE	0.0024	0.0023	0.0040
Gwanak-gu (n = 85)	MAPE	6.61	25.70	11.54
	RMSE	0.0021	0.0064	0.0030
Gwangjin-gu (n = 64)	MAPE	10.49	19.72	17.39
	RMSE	0.0071	0.0103	0.0114
Guro-gu (n = 127)	MAPE	8.24	14.72	11.55
	RMSE	0.0016	0.0025	0.0016
Geumcheon-gu (n = 52)	MAPE	4.934	10.45	5.50
	RMSE	0.0012	0.0020	0.0013
Nowon-gu (n = 304)	MAPE	6.98	15.18	16.68
	RMSE	0.0018	0.0028	0.0035
Dobong-gu (n = 159)	MAPE	7.05	7.21	9.13
	RMSE	0.0014	0.0014	0.0014
Dongdaemun-gu (n = 96)	MAPE	17.62	27.30	19.17
	RMSE	0.0018	0.0025	0.0018
Dongjak-gu (n = 86)	MAPE	9.18	11.83	11.69
	RMSE	0.0030	0.0035	0.0030
Mapo-gu (n = 103)	MAPE	6.18	8.35	6.99
	RMSE	0.0029	0.0032	0.0031
Seodaemun-gu (n = 69)	MAPE	8.64	10.14	12.72
	RMSE	0.0021	0.0025	0.0028
Seocho-gu (n = 130)	MAPE	9.84	13.06	11.80
	RMSE	0.0091	0.0079	0.0079
Seongdong-gu (n = 78)	MAPE	5.93	18.96	18.01
	RMSE	0.0063	0.0124	0.0162
Seongbuk-gu (n = 116)	MAPE	5.63	16.07	5.75
	RMSE	0.0017	0.0064	0.0016
Songpa-gu (n = 188)	MAPE	8.39	19.02	9.56
	RMSE	0.0064	0.0150	0.0056
Yangcheon-gu (n = 186)	MAPE	9.62	18.05	14.09
	RMSE	0.0050	0.0046	0.0045
Yeongdeungpo-gu (n = 121)	MAPE	6.84	9.62	7.26
	RMSE	0.0060	0.0049	0.0051
Yongsan-gu (n = 85)	MAPE	8.49	12.63	13.50
	RMSE	0.0054	0.0074	0.0064
Eunpyeong-gu (n = 124)	MAPE	10.32	10.61	17.88
	RMSE	0.0026	0.0029	0.0175
Jongno-gu (n = 18)	MAPE	11.87	28.65	16.64
	RMSE	0.0031	0.0083	0.0049
Jung-gu (n = 30)	MAPE	9.78	17.93	12.29
	RMSE	0.0039	0.0064	0.0041
Jungnang-gu (n = 95)	MAPE	5.65	8.03	11.89
	RMSE	0.0013	0.0018	0.0024
Average (n = 2867)	MAPE	8.39	14.57	12.50
	RMSE	0.0038	0.0054	0.0052

. The GA model shows the lowest MAPE in all boroughs, whereas, the regression and the ANN model show lower values of RMSE than those of the GA model in some boroughs. On average, the GA model shows the best performance among three models with the lowest average values of MAPE (8.70) and RMSE (0.0040). Figure 3 shows the MAPE values of the GA model in 25 boroughs. In Figure 4, no regularity and homogeneity of MAPE are observed for boroughs. For instance, the GA model has a high forecasting power in Seongdong-gu (MAPE is 5.93) and a relatively poor forecasting power (MAPE is 17.62) in nearby Dongdaemun-gu. This result indicates that the auction market in each borough of Seoul has its unique characteristics.

Finally, the 25 boroughs of the Seoul area are grouped based on the auction appraisal price to reflect characteristics of the auction market. In this experiment, only the GA model is constructed because the GA algorithm is superior to others, as shown by both previous experimental results. The 25 boroughs are grouped into 3 to 6 groups in the descending order of the auction appraisal price, i.e., zone 1 is the group with the highest average auction appraisal price. The GA models are constructed for each group independently.

Table 9. Segmentation of boroughs by auction appraisal price.

Number of Groups	Label	The Boroughs Belonging to The Zone
3	Zone 1	Gangnam, Seocho, Yongsan, Songpa, Gwangjin, Jongno, Jung, Yeongdeungpo
	Zone 2	Yangcheon, Mapo, Seongdong, Dongjak, Gangdong, Gwanak, Dongdaemun, Gangseo
	Zone 3	Seongbuk, Seodaemun, Eunpyeong, Guro, Jungnang, Gangbuk, Nowon, Geumcheon, Dobong
4	Zone 1	Gangnam, Seocho, Yongsan, Songpa, Gwangjin, Jongno, Jung
	Zone 2	Yeongdeungpo, Yangcheon, Mapo, Seongdong, Dongjak, Gangdong
	Zone 3	Gwanak, Dongdaemun, Gangseo, Seongbuk, Seodaemun, Eunpyeong
	Zone 4	Guro, Jungnang, Gangbuk, Nowon, Geumcheon, Dobong
5	Zone 1	Gangnam, Seocho, Yongsan, Songpa, Gwangjin
	Zone 2	Jongno, Jung, Yeongdeungpo, Yangcheon, Mapo
	Zone 3	Seongdong, Dongjak, Gangdong, Gwanak, Dongdaemun
	Zone 4	Gangseo, Seongbuk, Seodaemun, Eunpyeong, Guro
	Zone 5	Jungnang, Gangbuk, Nowon, Geumcheon, Dobong
6	Zone 1	Gangnam, Seocho, Yongsan, Songpa
	Zone 2	Gwangjin, Jongno, Jung, Yeongdeungpo
	Zone 3	Yangcheon, Mapo, Seongdong, Dongjak
	Zone 4	Gangdong, Gwanak, Dongdaemun, Gangseo
	Zone 5	Seongbuk, Seodaemun, Eunpyeong, Guro
	Zone 6	Jungnang, Gangbuk, Nowon, Geumcheon, Dobong

shows the segmentation of boroughs based on the auction appraisal price. The forecasting results of a GA model for every zone are reported in

Table 10. GA model performance with grouping based on auction appraisal price.

Segmentation	Area	Average MAPE (RMSE)	MAPE	RMSE
Auction Appraisal Price	Zone 1	8.40 (0.0048)	9.43	0.0086
	Zone 2		8.88	0.0040
	Zone 3		6.88	0.0017
	Zone 1	7.94 (0.0042)	9.72	0.0087
	Zone 2		7.90	0.0044
	Zone 3		7.36	0.0023
	Zone 4		6.76	0.0015
	Zone 1	8.16 (0.0042)	9.84	0.0089
	Zone 2		7.83	0.0042
	Zone 3		9.22	0.0041
	Zone 4		7.02	0.0021
	Zone 5		6.91	0.0015
	Zone 1	7.83 (0.0042)	9.66	0.0087
	Zone 2		8.06	0.0060
	Zone 3		8.40	0.0045
	Zone 4		7.08	0.0030
	Zone 5		6.86	0.0019
	Zone 6		6.91	0.0015

. The average MAPE (RMSE) in Table 10 indicates that the GA model with the six-group clustering based on auction appraisal price shows the best performance among other segmentation methods. The average MAPE (7.83) of the GA model with the six-group clustering based on auction appraisal price in Table 10 is observed to be superior to that based on 25 individual boroughs (8.70) in Table 8. This result implies that clustering based on appraisal price and constructing the GA forecasting models for each cluster improves the average performance. Accordingly, auction appraisal price is likely to play a more significant role in increasing homogeneity within a group of auction cases than that of locations of real estate. It is also noted that the MAPE and RMSE for zones classified as having lower auction appraisal prices are lower than those for zones classified as having higher auction appraisal prices in all segmentation methods. In other words, the lower the auction appraisal price is, the better the performance of the GA model is.

As the final step, we perform the paired t-test of the forecast values of all models to verify results from our experiments using various grouping processes.

Table 11. p-values of the paired t-test for three models without grouping.

Area		GA	ANN	Regression
Whole of Seoul (n = 2867)	GA	-	0.000 *	0.000 *
	ANN	-	-	0.000 *

* refers to the significance at the 5% level.

shows p-values of the paired t-test for three forecasting models without a grouping process. The results indicate significant differences in performance by all pairs of models [16,30,48]. Similarly, the paired t-test for models with grouping based on five zones is performed. Results in

Table 12. p-values of the paired t-test for three models with grouping based on five zones.

Area		GA	ANN	Regression
Urban zone (n = 133)	GA	-	0.000 *	0.005 *
	ANN	-	-	0.006 *
Southeast zone (n = 652)	GA	-	0.001*	0.000 *
	ANN	-	-	0.004 *
Northeast zone (n = 957)	GA	-	0.000 *	0.000 *
	ANN	-	-	0.118
Southwest zone (n = 829)	GA	-	0.000*	0.000 *
	ANN	-	-	0.001 *
Northwest zone (n = 296)	GA	-	0.094	0.325
	ANN	-	-	0.447

* refers to the significance at the 5% level.

show that all zones except the northwest zone have significant p-values, implying a better performance of the GA model than that of other models. When we construct models with grouping based on 25 boroughs, results of the paired t-test are inconsistent. As shown in

Table 13. p-values of the paired t-test for three models with grouping based on 25 boroughs.

Area	Comparison Target	GA	ANN	Regression
Gangnam-gu (n = 201)	GA	-	0.019 *	0.183
	ANN	-	-	0.126
Gangdong-gu (n = 133)	GA	-	0.635	0.827
	ANN	-	-	0.808
Gangbuk-gu (n = 45)	GA	-	0.233	0.218
	ANN	-	-	0.728
Gangseo-gu (n = 172)	GA	-	0.220	0.000 *
	ANN	-	-	0.000 *
Gwanak-gu (n = 85)	GA	-	0.000 *	0.000 *
	ANN	-	-	0.000 *
Gwangjin-gu (n = 64)	GA	-	0.012 *	0.010 *
	ANN	-	-	0.983
Guro-gu (n = 127)	GA	-	0.000 *	0.195
	ANN	-	-	0.000 *
Geumcheon-gu (n = 52)	GA	-	0.000 *	0.319
	ANN	-	-	0.000 *
Nowon-gu (n = 304)	GA	-	0.000 *	0.000 *
	ANN	-	-	0.001 *
Dobong-gu (n = 370)	GA	-	0.431	0.005 *
	ANN	-	-	0.448
Dongdaemun-gu (n = 96)	GA	-	0.002 *	0.527
	ANN	-	-	0.002 *
Dongjak-gu (n = 86)	GA	-	0.144	0.457
	ANN	-	-	0.207
Mapo-gu (n = 103)	GA	-	0.087	0.204
	ANN	-	-	0.259
Seodaemun-gu (n = 69)	GA	-	0.472	0.109
	ANN	-	-	0.286
Seocho-gu (n = 130)	GA	-	0.792	0.894
	ANN	-	-	0.680
Seongdong-gu (n = 78)	GA	-	0.000 *	0.029 *
	ANN	-	-	1.000
Seongbuk-gu (n = 116)	GA	-	0.000 *	0.757
	ANN	-	-	0.000 *
Songpa-gu (n = 188)	GA	-	0.000 *	0.686
	ANN	-	-	0.000 *
Yangcheon-gu (n = 186)	GA	-	0.179	0.151
	ANN	-	-	0.564
Yeongdeungpo-gu (n = 121)	GA	-	0.544	0.052
	ANN	-	-	0.086
Yongsan-gu (n = 85)	GA	-	0.014 *	0.020 *
	ANN	-	-	0.628
Eunpyeong-gu (n = 124)	GA	-	0.184	0.326
	ANN	-	-	0.402
Jongno-gu (n = 18)	GA	-	0.000 *	0.034 *
	ANN	-	-	0.000 *
Jung-gu (n = 30)	GA	-	0.038 *	0.874
	ANN	-	-	0.017 *
Jungnang-gu (n = 95)	GA	-	0.000 *	0.000 *
	ANN	-	-	0.001 *

* refers to the significance at the 5% level.

, the performance of models is not observed to be significantly different in some boroughs, whereas, significant differences are observed in other boroughs. Although the average performance of the GA model appears to be the best in Table 8, the grouping process based on 25 boroughs does not seem to improve the performance of the GA model in some groups.

As shown by our experimental results, the grouping process based on the auction appraisal price improves performance of forecasting models. In particular, classification into six zones shows the best performance. To verify the improvement of model performance by grouping based on auction appraisal price, we perform the paired t-test for the GA model with grouping data based on auction appraisal price and five zones of the 2020 Seoul Basic City Plan.

Table 14. p-values of the paired t-test for a GA model with five zones and auction appraisal price grouping.

Segmentation	Area	p-Value
Auction Appraisal Price	Zone 1	0.973
	Zone 2
	Zone 3
	Zone 1	0.000 *
	Zone 2
	Zone 3
	Zone 4
	Zone 1	0.014 *
	Zone 2
	Zone 3
	Zone 4
	Zone 5
	Zone 1	0.000 *
	Zone 2
	Zone 3
	Zone 4
	Zone 5
	Zone 6

* refers to the significance at the 5% level.

reports the results of this paired t-test. The p-values in Table 14 show that the forecasting ability of the GA models with grouping into 4, 5 and 6 zones based on auction appraisal price is significantly different from that with grouping based on five zones of the 2020 Seoul Basic City Plan. These results imply that the price-based variable is a more significant factor in improving the GA model performance than are variables related to administrative and living areas.

5. Conclusions

In this paper, we present three forecasting models for real estate auction sale price using artificial intelligence and statistical methodologies: A regression model and ANN and GA models. Our empirical study shows that the GA model has the best performance. In addition, three grouping processes are applied to improve the performance of the GA models. The GA model with grouping based on auction appraisal price is more efficient than all other forecasting models constructed in this paper. These empirical results imply that appropriate criteria for the grouping process play a key role in increasing the predictive accuracy of a forecasting model. They also offer valuable implications to forward looking investors at real estate auction markets, as well as managers of real estate funds.

Real estate industry has become an essential part of today’s financial markets. Nowadays, a number of researchers and practitioners have explored the real estate field using statistical and artificial intelligence techniques. To offer a comprehensive view of the auction markets, which is an influential sector of real estate industry, this study develops forecasting models to predict future prices of individual real estate auction items. To our best knowledge, this is the first study on using data of individual apartment auction prices to develop forecasting models for real estate auction prices. Real estate fund managers are able to make more efficient investment strategies by using our GA model. It contributes to the investment efficiency of the real estate auction markets and helps to achieve efficient financial markets. In addition, it helps to achieve sustained economic benefits to the related stakeholder of real estate auction markets. In this sense, the model developed in this paper plays a role in sustaining economic growth.

This study has potential limitations. The model developed in this study is based on the data of apartment auction markets in Seoul during the sample period. As such, the empirical results are limited to apartment auction markets in Seoul traded in a specific time period. Based on the idea of our model, future research can be enriched by developing a model that can be utilized for other real estate sectors. More improvement of forecasting ability and wider use of the models are expected with more diverse data. The study could also be extended by researching the key factors of the grouping process to improve model performance.