1 Introduction

The housing market in Korea was unstable for a period of 5 years from 2003 to 2007, during which time the government took measures on several occasions to manage the rising prices in the housing market. There are three types of housing (apartments, single houses, and row houses) in Seoul, Korea. Housing prices in Seoul have had boom and bust cycles for the past two decades in the apartment sector [1]. During the period of instability from 2003 to 2007, housing prices rose 23.9 %, showing a 64.6 % increase over the prices of the previous 10 years. Skyrocketing apartment prices have led to problems in the geographically limited area of Gangnam (Gangnam-gu, Seocho-gu, and Songpa-gu), as well as in some suburban cities such as Bundang and Ilsan [2].

The housing market is very unstable. Unstable housing prices reflect a collective anxiety about unexpected events, such as changes in economic circumstances or the anticipation of future uncertainties. Housing prices are also related to macroeconomic variables, spatial differences (density of housing), characteristics of community structure, and environmental amenities [3–7]. Housing prices may also be influenced by interventional policies on the part of the government [8, 9].

Many studies have attempted to identify the relationship between government housing stabilization policies and housing prices [10–14]. The Korean government has traditionally relied on a package of regulation, taxation, and finance to stabilize the housing market. Approximately three dozen packages involving taxation and regulations on housing transactions and mortgage financing were introduced between 2003 and 2007 [7, 15]. These policies were aimed at removing the instability surrounding the housing market as quickly as possible. Despite the concern that strong measures could impede economic recovery in the short term, the government continued to apply stronger and more comprehensive anti-speculation measures to address the rapidly increasing prices in the housing market at the time.

Housing is both a consumer good and an investment good. The modern view of housing emphasizes its role as an asset in household portfolios [16]. Buyers need long-term financing, and the decision to purchase is subject to the difference between the expected profits from purchasing and the cost of capital–interest rates. Under these market conditions, buyers and sellers come together to exchange housing at an agreed price. Housing prices are determined by interest rates and expected profit changes in terms of the asset. An interest rate, determined by a financial agency, is applied to housing transactions in any given city. However, housing policies, such as development planning or regulations, affect local areas to such an extent that expected profits differ locally. Therefore, expected changes of profit according to housing policy changes at the local level is the key factor in housing price dynamics, thus raising the need to quantify spatial patterns of housing prices [17].

Typical spatial patterns of housing prices are random, and include hotspots (areas in which prices are more expensive) and cold spots (areas in which prices are cheaper). The random pattern is the result of housing market equilibrium, and the hotspots and cold spots are the outcome of an imbalance between demand and supply in a housing market. Hotspots occur in local areas where housing prices are much higher than elsewhere, and the phenomenon has a high spatial association with neighborhoods. Spatial association has been modeled to analyze spatial dependency using several statistical measures. For global measures, Moran’s I and G statistics are used, both of which assume that the magnitude of a spatial autocorrelation is reasonably stable across a region of study [18–20]. In addition, the variability of spatial autocorrelation is relatively constant over space. We can detect the presence of hotspots or cold spots over an entire area of study using general G statistics. In reality, however, the variability of spatial autocorrelation may not be stable over a region. Therefore, it is necessary to use local measures to depict the spatial variability of spatial autocorrelation [21, 22]. Indeed, local measures of spatial association can reveal where high clusters (hotspots) and low clusters (cold spots) are located [23]. While the concept of spatial patterns is static insofar as a pattern only shows how geographic objects are distributed at one given time, the concept of spatial processes is dynamic, because spatial processes depict and explain how the distribution of geographic objects comes to exist and how it may change over time [24]. Not only location, but also time, plays an important role in explaining the dynamics of housing prices. It is well recognized that housing prices depend not only on recent market events, but also on lagged prices [25, 26]. Without considering the temporal dependency of housing prices, it is possible to misread a spatial pattern at any given time because the pattern is not able to adjust to the transient fluctuation of housing price dynamics.

However, little attention has been paid to the use of local spatial autocorrelation for the detection of hotspots in spatiotemporal dimensions [27]. A thorough examination of such spatiotemporal effects may require an approach that incorporates both spatiality and temporality [28–30]. Spatial local G statistics only show hotspots at one given time. With spatial local G statistics, therefore, we are unable to compare hotspots at one given time with hotspots at other times, because the hotspots have different means and variance in terms of housing prices. This study analyzes spatial processes of housing price dynamics using spatiotemporal local G statistics in Seoul, South Korea, thereby providing decision makers with useful information for the enactment of housing policies.

2 Methods

2.1 Study area

The study area is Seoul, the capital city of South Korea, which is located at the center of the Korean peninsula with a population of approximately 10.6 million people as of 2011. The area of Seoul is 605.77 km2, and the Han River bisects the city into two parts, northern (Gangbuk) and southern (Gangnam) Seoul (Fig. 1). Seoul has 25 local governments (gu) with 525 districts (dongs).

Fig. 1
figure 1

Study area

Full size image

We selected 420 apartment locations in Seoul according to monthly housing prices from January 2004 to December 2007, limiting our selection to one per dong, using apartment market prices that are serviced online by Kookmin Bank. We used monthly average change rates of apartment prices between current and previous months. Among the 525 dongs, 105 dongs were not selected because Kookmin Bank did not service housing prices due to too few apartments in a dong (such as Gangbuk City Core) or because there was insufficient apartment information due to apartment reconstruction projects. One apartment per dong, meeting our criteria of being located in the biggist apartment complex, with an approximate area of 105 m2, was selected as a representative apartment for each dong.

2.2 Spatiotemporal local G statistics

To detect the phenomenon of pricing hotspots in a geographic context, this study used spatiotemporal local G statistics, which modify local G statistics into a space–time version [27]. The weighting schemes for spatiotemporal proximity were built by combining the concepts of distance decay and time decay. There are two weighting regimes that can be used, including fixed kernel and adaptive kernel regimes. For the fixed kernel weighting regime, distance is constant, but the number of nearest neighbors varies. The most commonly used kernels are Gaussian distance decay-based functions [31]:

$$ {{\upomega }}_{\text{ij}} \left( {\text{d}} \right) = { \exp }\left( { - \frac{{{\text{d}}_{\text{ij}}^{2} }}{{{\text{h}}^{2} }}} \right) $$

where dij is the measure of distance between location i and j, and; h is a non-negative parameter known as bandwidth, which produces a decay of influence with distance.

When the distance d increases, the weight of that location will decrease according to the Gaussian curve. If Gaussian distance decay-based functions are used to construct a spatial–temporal weight matrix, then we will have a spatiotemporal weighting matrix [25], as follows:

$$ {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right) = { \exp }\left( { - \frac{{\left( {{\text{d}}_{\text{ij}}^{\text{s}} } \right)^{2} }}{{\left( {{\text{h}}^{\text{s}} } \right)^{2} }}} \right) \times { \exp }\left( { - \frac{{\left( {{\text{d}}_{\text{ij}}^{\text{t}} } \right)^{2} }}{{\left( {{\text{h}}^{\text{t}} } \right)^{2} }}} \right) $$

where \( {\text{d}}_{\text{ij}}^{\text{s}} \) is the measure of spatial distance between location i and j, hs is a non-negative parameter known as bandwidth, which produces a decay of influence with spatial distance, \( {\text{d}}_{\text{ij}}^{\text{t}} \) is the measure of temporal distance between location i and j, and ht is a non-negative parameter known as bandwidth, which produces a decay of influence with temporal distance.

Accordingly, we can build a spatiotemporal weight matrix \( {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right) \) by combining the spatially weighted matrix \( {{\upomega }}_{\text{ij}} \left( {\text{d}} \right) \) and the temporally weighted matrix \( {{\upomega }}_{\text{ij}} \left( {\text{t}} \right) \).

$$ {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right) = {{\upomega }}_{\text{ij}} \left( {\text{d}} \right) \times {{\upomega }}_{\text{ij}} \left( {\text{t}} \right) $$

Local G statistic, \( {\text{G}}_{\text{i}}^{ *} \)(d), indicates the degree of spatial autocorrelation as to whether a location i is surrounded by a cluster of high or low values within a given distance d in comparison to the mean of the whole space at a given time, including the value of i [22].

$$ {\text{G}}_{\text{i}}^{ *} \left( {\text{d}} \right) = \frac{{\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}} \left( {\text{d}} \right){\text{x}}_{\text{j}} - {\bar{\text{x}}}\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{i}} \left( {\text{d}} \right)}}{{{\text{S}}\sqrt {\frac{{{\text{N}}\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}}^{2} \left( {\text{d}} \right) - \left( {\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}} \left( {\text{d}} \right)} \right)^{2} }}{{{\text{N}} - 1}}} }} $$

where n is the number of spatial neighbors of location i, xj is the value of jth spatial neighbors of location i, and \( {{\upomega }}_{\text{ij}} \left( {\text{d}} \right) \) is the spatial weight matrix within distance d of location i.

$$ {\bar{\text{x}}} = \frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{n}} {\text{x}}_{\text{i}} }}{\text{N}} $$
$$ {\text{S}} = \sqrt {\frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{n}} {\text{x}}_{\text{i}}^{2} }}{\text{n}} - \left( {{\bar{\text{x}}}} \right)^{2} } $$

The spatiotemporal local G statistic, \( {\text{G}}_{\text{i}}^{\text{st*}} \)(d), indicates the degree of spatiotemporal autocorrelation as to whether a location i is surrounded by a cluster of high or low values within a given distance d and a given time t in comparison to the mean of the whole space within a given time period [27].

$$ {\text{G}}_{\text{i}}^{\text{st*}} \left( {{\text{d}},{\text{t}}} \right) = \frac{{\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right){\text{x}}_{\text{j}} - {\bar{\text{x}}}\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right)}}{{{\text{S}}\sqrt {\frac{{{\text{n}}\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}}^{2} \left( {{\text{d}},{\text{t}}} \right) - \left( {\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right)} \right)^{2} }}{{{\text{n}} - 1}}} }} $$

where n is the number of spatiotemporal neighbor of location i, xj is the value of jth spatiotemporal neighbor of location i, and \( {{\upomega }}_{\text{ij}} \left( {{\text{d}},{\text{t}}} \right) \) is the spatiotemporal weight matrix within distance d and t of location i.

$$ {\bar{\text{x}}} = \frac{{\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {\text{x}}_{\text{j}} }}{\text{n}} $$
$$ {\text{S}} = \sqrt {\frac{{\mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} {\text{x}}_{\text{j}}^{2} }}{\text{n}} - \left( {{\bar{\text{x}}}} \right)^{2} } $$

2.3 Comparing spatial patterns of housing market dynamics

Spatial pattern analysis of a housing market based on mean and standard deviations at a given time is appropriate for investigating spatial relationships at a given time. However, it is difficult to compare the results of different times using local G statistics due to differing bases. As shown in Fig. 2, the maximum point (t3) and the minimum point (t1) of housing prices change in temporal housing markets, and have their own spatial hotspots or cold spots. Therefore, it is difficult to compare the relative importance and range of two spatial hotspots, because a standard base is needed to compare the spatial patterns of housing market dynamics in a certain period. This standard base is the mean and standard deviation of the entire time. Therefore, we developed a standard base for the spatiotemporal local G statistic in order to explore the spatial processes of housing price dynamics.

Fig. 2
figure 2

Temporal trend of monthly change rates of housing prices in the housing market

Full size image

2.4 Temporal dependency of spatial process

The dynamics of a housing market are best understood in their entirety through a simultaneous review of the discrete and continuous temporal status at a certain time, because the previous trend affects the current trend, and the current trend affects the future. Typical types of temporal continuity are convex, flat, and concave patterns (Fig. 3). A convex pattern shows that housing prices are rising continuously and falling at peak, a concave pattern is diametrically opposed to a convex one, and a flat pattern shows a stable trend. Housing market dynamics near convex and concave points are unstable and create anomalous spatial patterns. Given the temporal dependency of housing prices, we can adjust the spatial pattern of housing prices at a given time, and more easily interpret the spatial process of housing prices.

Fig. 3
figure 3

Temporal pattern of the monthly change rates of housing prices within a temporal distance

Full size image

3 Results and discussion

3.1 Trends in housing prices and housing policies

The monthly average rate of change of housing prices from January 2004 to December 2007 in Seoul was 0.75 %, while housing prices in the Gangnam area (Gangnam-gu, Seocho-gu, Songpa-gu) increased nearly 0.91 % in the same time period. In June 2005, the monthly rate of change of housing prices in the Gangnam area went up to 6.03 %, against an average monthly rate of change of 1.53 % in other parts of Seoul (Fig. 4). There were three peaks in change rate in housing prices in this period, occurring in June 2005, March 2006, and November 2006. The rates of change of housing prices in the Gangnam area in June 2005 and March 2006 were 4–5 times higher than the average change rate of housing prices in Seoul, but both indexes were high in November 2006. There were four relatively flat periods and two one-year periods of stability among the periods before and after the three peaks in change rates for housing prices in Seoul (including the Gangnam area).

Fig. 4
figure 4

Monthly change rates of housing prices from February 2004 to December 2007

Full size image

This temporal pattern is related to government housing policies at the time. During this period, the government took action with several measures to control housing prices, which had been increasing drastically since January 2005. The first government intervention was the measure of “housing market stabilization in the metropolitan area,” enacted on February 17, 2005 (known as the 2.17 measure). Next, the government enacted the “housing prices stabilization” measure on May 4, 2005 (the 5.4 measure), because the situation remained unstable regardless of the 2.17 measure. As the 5.4 measure proved to have no stabilizing impact on the rising housing prices, the government enacted “housing policy reform for stabilizing ordinary people’s housing and controlling housing speculation” on August 31, 2005 (the 8.31 measure). This shows that housing prices were increasing, reaching the first peak in June of 2005 regardless of the 2.17 and 5.4 measures, but that prices began to decrease following the 8.31 measure due to the announcement of powerful regulation on the part of the government. The measure for the “enhancement of ordinary people’s welfare and realization of the housing market” on March 30, 2006 (the 3.30 measure), which intended to control housing prices that had again begun to increase in January 2006, stabilized the second peak for a while. Subsequently, two other measures (the 11.15 measure in 2006 and the 1.11 measure in 2007) stabilized the third peak.

Moran’s I Index shows that a higher spatial association happened at the same time as the higher rate of change in housing prices (Fig. 5). This means that a higher rate of change in housing prices makes a spatial cluster over the defined space. Moran’s I value in November 2006 was less than Moran’s I value at the time of the other two peaks because the change rate of housing prices was evenly distributed in Seoul in November of 2006.

Fig. 5
figure 5

Spatial association using Moran’s I Index from February 2004 to December 2007. Significant values (P < 0.05) of Moran’s I are indicated with solid squares

Full size image

3.2 Comparing spatial patterns of housing market dynamics

We compared spatiotemporal local G statistics and local G statistics using the monthly average rates of change in housing prices from the 3 months that represent the maximum (November 2006), mean (April 2005), and minimum (November 2004) housing price values over 4 years. A spatial lag distance to reflect spatial neighborhood effects was 3 km in consideration of the mean size of the gu (local government), which is the planning unit for stabilization policies for housing prices, such as designated districts for speculation or land transactions.

The local G statistics showed a general distribution of hotspots and cold spots with similar proportions at a given time, because each time was based on its own mean and standard deviation. Accordingly, it is difficult to detect temporal changes in the distribution of hotspots and cold spots due to different mean and standard deviations with local G statistics. In contrast, with spatiotemporal local G statistics, the month with the minimum monthly average rate of change in housing prices was classified as comprising mostly cold spots, the month with the maximum change rate was classified as a hotspot, and the mean month was shown to comprise hotspots and cold spots, because the measure used the same mean and standard deviation for the whole period of time (Fig. 6). This result shows that to best understand the dynamics of a housing market, spatial pattern analysis for a temporal comparison should be based not on a given time, but on a period of time in its entirety. Therefore, spatiotemporal local G statistics using the same mean and standard deviation for an entire period of time is a more suitable method for monitoring temporal changes in pricing hotspots and cold spots in a housing market.

Fig. 6
figure 6

Comparison between G statistics and spatiotemporal local G statistics without a time lag

Full size image

3.3 Temporal dependency of spatial processes

We applied spatiotemporal local G statistics without a time lag and with a three-month time lag to the period of temporary stability in July 2006 to observe the temporary and continuous trends in the housing market. We set 3 months as the temporal lag distance to compare temporal neighborhood effects because a temporal lag distance of more than 3 months may lose the detailed temporal dynamics of the housing market due to the temporal smoothing of the prices index.

A cold spot in the Gangnam area was temporarily detected in the temporal discrete pattern without a time lag, whereas hotspots in the Yeongdeungpo and Gangseo areas were steady in the temporal continuous pattern with a three-month time lag (Fig. 7). We were able to see that the housing market was stable because a cold spot was found in the temporal discrete pattern analysis. Similarly, we were able to determine that the housing market was continuously unstable because hotspots existed in the same areas in previous and next times according to the temporal continuous pattern analysis. This means that the current price of housing is determined by the pattern of past prices and future expectations.

Fig. 7
figure 7

Comparison of spatiotemporal local G statistics between the temporal discrete pattern without a time lag and the temporal continuous pattern with a three-month time lag

Full size image

3.4 Spatial process for housing market dynamics

The Roh Administration in Korea enacted a great deal of housing policies to stabilize the drastically increasing housing prices of the time (Table 1). What the policies caused, however, was an overly dynamic housing market with periods of temporary stability and high peaks. Spatiotemporal local G statistics without a time lag for temporal discrete pattern analysis (Fig. 8) and with a three-month time lag for temporal continuous pattern analysis (Fig. 9) were used to analyze the relationship between government housing policies and the housing market.

Table 1 Government housing policies
Full size table
Fig. 8
figure 8

Results of spatiotemporal local G statistics without a time lag (bold and underlined text indicates government housing policies)

Full size image
Fig. 9
figure 9

Results of spatiotemporal local G statistics with a three-month time lag (bold and underlined text indicates government housing policies)

Full size image

The temporal discrete pattern analysis and continuous pattern analysis showed spatial patterns before and after the first peak, at which point three housing policies (the 2.17, 5.4 and 8.31 measures) had been enacted. In the temporal discrete pattern analysis, cold spots mainly occurred before March 2005 and hotspots were expanding in the Gangnam-to-Mokdong area. The 2.17 and 5.4 measures could not control the expansion of hotspots, but the hotspots disappeared and cold spots appeared after the 8.31 measure. Both of the pattern analyses showed similar results, with the exception of a hotspot identified in the Mokdong area in the temporal discrete pattern analysis, which was not found in the temporal continuous pattern analysis. This means that the hotspot in the Mokdong area had a temporary status.

The second peak occurred across the entire Gangnam region in March 2006. The 3.30 measure stabilized housing prices for a while in July 2006 according to the temporal discrete pattern analysis. Regardless, hotspots in the Gangseo area occurred again in September 2006, and had begun to expand to all of Seoul by November 2006 at the time of the third peak. After the 11.15 and 1.11 measures were enacted, hotspots disappeared in March of 2007. Likewise in the temporal continuous pattern analysis, the phenomenon of housing price stabilization in July 2006 was temporary and unstable, and in fact, all of Seoul was emerging as a hotspot in September 2006.

4 Conclusions

The spatiotemporal patterns of housing prices in Seoul change dramatically according to space. This study applies spatiotemporal local G statistics to detect spatiotemporal phenomena and to understand these patterns, obtaining reasonable results. A statistical model developed by Yu and Lee [7] finds that the housing price policies of the Roh Administration had no observable impact on the Korean housing market. However, our study shows that the government housing price policies impacted the spatial patterns of housing prices insofar as some policies had no effect, while other policies did have an effect on the patterns. Although conventional macroeconomic variables have a statistically significant association with housing price instability in Korea [7], spatial statistics reflecting time are needed to identify the spatiotemporal patterns of housing prices on space.

This study finds that housing price hotspots were detected spatially and temporally in certain areas, such as Gangnam and the new towns, in terms of spatiotemporal autocorrelation, and that housing policies on the part of the government had an impact on the spatiotemporal patterns of housing prices. These results indicate that we are able to monitor the spatiotemporal patterns of housing prices in a housing market, and use this approach to support the decisions of housing policy makers. Further studies are needed to understand the detailed dynamics of housing prices in Seoul by applying this approach to surrounding areas, because Seoul is the center of a metropolitan area that includes other cities, and because housing prices in Seoul affect the surrounding cities and are affected by the surrounding cities in turn.