Earticle

본 연구에서는 한국주식시장을 대상으로 거래량의 평균회귀성을 실증하고, 거래량의 평균회귀성에 영향을 미치는 변수들에 대해 분석하였다. 먼저, 거래량의 시계열에 평균회귀성의 전제조건인 자기상관관계가 존재함을 보이고, Phillips and Perron 검정과 KPSS 검정을 통해 거래량의 평균회귀성을 실증하였다. 이를 통해 한국주식시장에서 나타나는 거래량의 중요 특성을 밝히는 한편, 자기상관관계에 대한 연구에 머물러 있던 거래량의 시계열에 대한 연구영역을 확장했다는 의의가 있다. 또한, Ornstein-Uhlenbeck 모델을 사용하여 평균회귀성의 주요한 속성인 평균회귀속도를 도출하고, 회귀분석을 통해 규모가 적을수록, 주가변동성이 적을수록, 개인투자자의 거래비중이 적을수록, 애널리스트의 이익추정 수가 많을수록 평균회귀속도가 증가함을 보여, 이 변수들이 거래량의 평균회귀성에 중요한 영향을 미치고 있음을 실증하였다. 이러한 결과는 동적거래모델(dynamic trading model) 상의 정보거래자의 정보은닉성 거래(stealth trading)와 행동경제학적 설명인 개인투자자의 주목기반 매수경향(attention based buying tendency)이 거래량의 평균회귀성을 설명할 수 있는 근거가 될 수 있음을 보이고 있다.

This study analyzes the mean reversion of trading volume, which allows us to predict future trading volumes from time-series data. The results have important implications for various related concerns, including the predictability of returns in relation to trading volumes, liquidity, and the use of practical indicators such as the VWAP (volume-weighted average price) and the CGO (capital gains overhang). We test the trading volumes of the indices, size-portfolios, and individual stocks on the Korean stock market from 1999 to 2017. All of the sample data are obtained from FnDataGuide. First, we test the autocorrelation of the trading volume. The results show that the trading volume has a positive autocorrelation, and that changes in trading volume have negative autocorrelations. Therefore, we confirm that the trading volume process (unlike the return process) does not follow an independent distribution. As mean reversion implies a correlated time-series, the autocorrelation of trading volumes serves as the premise for the mean reversion of trading volumes. Next, we use the Phillips-Perron test (Phillips and Perron, 1988) and the KPSS test (Kwiatkowski, Phillips, Schmidt, and Shin, 1992) to verify the mean reversion property of the trading volume. The results show that the trading volume of the indices, size-portfolios, and 96% of the individual stocks, all have a mean reversion property on the Korean stock market. In addition, we calculate the mean-reverting speed for each stock by applying the Ornstein–Uhlenbeck model (Uhlenbeck and Ornstein, 1930) to identify the variables that affect the mean reversion property of the trading volume. We regard the mean-reverting speed as a proxy variable that indicates the relative strength of the mean reversion property across sample stocks. This analysis of the mean-reverting speed enables us to confirm which variables affect the mean reversion of the trading volume. Before the regression analysis, we compare the actual mean-reverting duration of the trading volume with the duration calculated by using the Ornstein-Uhlenbeck model, which is our model for estimating the mean-reverting duration of the trading volume. As the implied error of the model has an acceptable scale, we confirm that our Ornstein-Uhlenbeck model can serve as a reasonable model for trading volume. The regression results on the mean-reverting speed of each stock shows that the smaller the size, the smaller the stock price volatility. In addition, we find that the smaller the ratio of the individual investors’ trading activity and the higher the number of analysts’ reports, the higher the mean-reverting speed. This set of findings suggests that the mean reversion of the trading volume can be explained by the presence of stealth trading (Kyle, 1985; Admati and Pfleiderer, 1988; Foster and Viswanathan, 1990; Wang, 1994) and by individual investors' attention-based trading (Barber and Odean, 2008). Heterogeneity between investors generates trading volume. This heterogeneity is resolved by opinion-sharing with trades. However, stealth trading by informed investors delays the incorporation of information, and attention-based trading by individual investors gives the trading volume a positive feedback. Thus, the mean-reverting speed of a stock is slower in trading environments where it is easier to hide information, and where individual investors trade more actively. Additionally, we show that the future trading volume can be estimated from its mean-reversion property. If we know the mean-reverting speed, the mean value, and the standard deviation of the trading volume, we can obtain the expected trading volume by applying the Ornstein-Uhlenbeck model. This study contributes to the literature in the following four ways. First, and most importantly, it expands research on trading volumes by demonstrating that the volume has a mean reversion property on the Korean stock market. Understanding this property takes us one step beyond making predictions based on the autocorrelation of the trading volume. Second, we find that the future trading volume can be predicted by its mean reversion property. This novel finding helps to expand the knowledge of market dynamics among academics, and it can help practitioners who want to build their positions without causing a serious market impact. Third, we show that the trading volume has a positive autocorrelation in the Korean stock market. Although such autocorrelation of trading volume has been previously studied in the U.S. stock market, it has not been investigated in the Korean stock market. As the scope for applying autocorrelation is wide, we believe that the verification of autocorrelation is also important. Last, we shed light on why the trading volume shows mean-reversion properties. We assess trade sizes, price volatility, the trading activity of individual investors, and the number of analysts’ earnings estimates, all of which influence the mean reversion of the trading volume. All of these factors can be partly explained by stealth trading and the attention-based trading of individual investors.

본 연구의 목적은 전력소비량 및 주식시장 활동 상호 간의 예측력을 실증적인 방법으로 확인하 는 것이다. 지금까지 수행된 전력소비량 예측 연구는 예측변수로서 국내총생산, 국민총생산 등과 같은 경제성장률 지표에 초점을 맞추었으나, 경제상황과 밀접한 관련성을 가진 국내 주식시장 활동을 고려 하지 않았다. 뿐만 아니라, 경기순환의 대리변수 중 하나인 전력소비량이 주식시장 활동에 미치는 영 향력을 확인하는 연구 또한 수행되지 않았다. 따라서 본 연구는 전력소비량 및 주식시장 활동 상호 간 의 예측 가능성을 검토한다. 본 연구는 우리나라 산업용 전력소비량 중 많은 비중을 차지하는 제조업 및 서비스업 전력소비량에 초점을 맞추었다. 또한 주식시장 활동을 나타내는 지표로서 국내 주식시장 전체의 주가 움직임을 나타내는 종합주가지수(KOSPI)를 고려하였다. 본 연구는 실증분석을 위하여, 1982년 1월부터 2014년 12월까지 발생된 우리나라 제조업 및 서비스업 전력소비량, 종합주가지수의 월간 데이터를 수집하였고, 이를 기반으로 시계열 분석을 수행하였다. 가장 먼저, 단위근 및 공적분 검 정, 적정시차 분석을 통해 벡터오차수정모형을 수립하였고, 이를 기반으로 제조업 및 서비스업 전력소 비량과 종합주가지수 상호 간의 예측력을 확인하였다. 벡터오차수정모형 분석결과, 서비스업 전력소 비량과 제조업 전력소비량은 상호 간에 대한 예측력을 가지는 것으로 나타났으며, 서비스업 전력소비 량은 종합주가지수(KOSPI)에 대한 예측력을 가지고 있는 것으로 나타났다. 본 연구는 에너지 관리 및 재무경영학 문헌에 학술적인 시사점을 제공하며, 전력수요 관리 및 주식시장 활동 측면의 실무적 시사점을 제공한다.

The purpose of this study is investigate that relationship between electricity consumption and KOSPI. Prior many studies in financial literature suggest that variables correlated with business cycle can predict stock market activities. We considered industrial electricity consumption to be a good proxy of a business cycle as higher electricity consumption reflects more intensive capital utilization and implies more maintenance investment. Many researchers in energy fields suggest that energy consumption leads to economic growth. KOSPI is defined as the macroeconomic variable that is a series of indexes that track the overall Korean Stock Exchanges. This index represents a barometer of the overall macroscopic economic situation in Korea. Thus, we empirically showed that predictive power of electricity consumption on KOSPI, and predictive power of KOSPI on electricity consumption. For the empirically analysis, we collected data of measured electricity consumption and KOSPI from 1982 January to 2014 December. We first performed unit root test and cointegration test. Based on the results, we employed Vector Error Correction Model(VECM) to estimate the predictive power between electricity consumption and KOSPI. In VECM analysis results, we found that electricity consumption in service industry negatively correlated with electricity consumption in manufacturing industry. Contrary, electricity consumption of manufacturing industry has positively correlated with electricity consumption of service industry. On the other hand, electricity consumption of service industry has negatively correlated with KOSPI. The results of this study contribute to energy management and finance literature. We provide implication of academics and practice for energy management and financial management.

This research aims to examine the predictive power of multiple online stock message boards, namely, NAVER Finance and PAXNET, which are the most popular stock message boards in South Korea, in stock market activities. If predictive power exists, we then compare the predictive power of multiple online stock message boards. To accomplish the research purpose, we constructed a panel data set with close price, volatility, Spell out acronyms at first mention.PER, and number of posts in 40 companies in three months, and conducted a panel vector auto-regression analysis. The analysis results showed that the number of posts could predict stock market activities. In NAVER Finance, previous number of posts positively influenced volatility on the day. In PAXNET, previous number of posts positively influenced close price, volatility, and PER on the day. Second, we confirmed a difference in the prediction power for stock market activities between multiple online stock message boards. This research is limited by the fact that it only considered 40 companies and three stock market activities. Nevertheless, we found correlation between online stock message board and stock market activities and provided practical implications. We suggest that investors need to focus on specific online message boards to find interesting stock market activities.

본 논문은 기업가비율이 실업률, 소득수준과 어떠한 장기적 관계에 있는지, 그리고 어떠한 설명변수들이 기업가비율에 영향을 미치는지 분석한다. 이를 위해 1980년부터 2008년까지 OECD 23개 국가를 패널 분석한다. 잘못된 추정과 편의의 위험을 피하기 위해 분석대상 변수들의 단위근 검정을 통해 수준변수들이 비정상적인지를 검정하고, 비정상적 변수들 간에 공적분관계가 존재하는지를 검정한다. 소득수준, 개방도, 규제정도, 실업률, 금융접근성, 노조 조직률 그리고 제조업비율이 기업가비율과 장기균형관계에 있음을 확인하였다. 기업가비율의 추세는 국가별로 큰 편차를 보이기 때문에, 비슷한 패턴을 보이는 국가그룹으로 분류하여 DOLS추정하였다. 증가추세의 국가그룹에서 소득수준, 개방도, 실업률, 제조업비율, 금융접근성이 유의한 양의 영향을, 인적자본수준과 노조 조직률은 유의한 음의 영향을 주고 있다. 이러한 추정결과는 기업가비율이 감소패턴을 보이는 국가그룹과 상이하다. 감소패턴의 국가그룹에서는 노조 조직률을 제외한 나머지 모든 변수에서 상반된 추정 계수값을 보인다. 즉, 어떤 그룹에 속하는지에 따라 기업가비율에 영향을 미치는 요소의 영향의 방향이 달라진다. 기업가비율이 다른 설명변수들과 반대의 인과관계를 갖는지를 테스트하기 위해 오차수정모형(error correction model)을 추정하였다. 기업가비율은 소득수준 및 실업율과의 관계에서 양방향 인과관계가 성립하며, (기업가비율 ⇄ 소득수준), (기업가비율 ⇄ 실업률)의 충격반응모형을 통해, 충격에도 불구하고 장기균형수준에 수렴함을 보인다.

What kind of explanatory variables affect business ownership rate? How is the business ownership rate related to income per capita and what are the direction of causality between them?This paper examines the long-term relationship between business ownership rate and a number of variables for a panel of 23 OECD developed countries over the period from 1980 to 2008. To do this we first investigate the stationarity of variables concerned, then test cointegration among the variables by employing the Westerlund’s (2007) error correction panel method. Commonly used econometrics methods are the so-called first generation panel unit root tests, such as Hadri and Levin A, Lin CF, Chu(=LLC). Because these first-generation tests assume cross-sectional independence, exhibit severe size distortions in the presence of cross-sectional dependence, we also use second-generation panel unit root tests such as CIPS(=cross-sectionally augmented IPS) to allow for cross-sectional dependence. For all level variables, both Hadri and LLC test do not reject the null hypothesis of a unit root at from the 1 % to 5% level. With regard to the first differences of the series, the test statistics are greater than the 1% or 5% critical absolute value and thus the null hypothesis is rejected. The CIPS test results also offer identical conclusions,To test if the null hypothesis of no cointegration can be rejected, Westerlund (2007) has developed two group-mean tests and two analogous panel tests. In the two group-mean based tests, the alternative hypothesis is there is cointegration at least in one cross section unit, which is the same in many traditional panel cointegration tests. Results using two pairs (no intercept, no time trend), (intercept, time trend) and one-period lead and lag values indicate that all four tests reject the null of no cointegration at the 1% or 5% level. Finally we bootstrapped robust critical values for the test statistics. Overall, those results show that there exists a long run cointegrating relationship among the variables in equation. Having confirmed the stationarity of variables and the existence of a long run relationship between the variables in equation, DOLS(Dynamic OLS) were utilized to estimate the respective parameters. Empirical results show that the sign of estimated parameter coefficients are different between country groups. While income per capita, economic openness, level of human capital, and credit accessibility significantly positive affect business ownership rate in riser country group, the signs of those coefficients in faller group are almost negative. This implies that the parameters of determinants are heterogenous between two groups of countries even though all of these countries are the OECD members. The above interpretation of the estimation results is based on the assumption that long-run causality runs from explanatory variables to business ownership rate. However, while cointegration implies causality in at least one direction, it says nothing about the direction of the causal relationship between the variables, as discussed above. Causality may run in either direction, from income per capita to business ownership rate or from business ownership rate to income per capita, or in both directions. To test the direction of long-run causality, we follow common practice in the applied panel cointegration methods and employ two-step procedure. And same procedure applies to causal relationship between unemployment rate and business ownership rate. In the first step, we use the DOLS estimate of the long-run relationship to derive the disequilibrium term. In the second step, we estimate the error correction model. From this we conclude that long-run causality is bidirectional, implying that increasing business ownership rate is both a consequence and cause of increasing level of income per capital or decreasing unemployment rate. To check the robustness of this conclusion, we perform a panel Granger causality test based on a levels VAR regression with fixed effects. the null hypothesis of no Granger causality from business ownership rate to income per capita or unemployment rate is not rejected. This confirms our result that increasing business ownership rate leads to increasing income level or decreasing unemployment rate. We employ generalized impulse response functions based on a one or two-lag panel vector error correction model over a 28-year horizon. A one-standard-deviation shock in business ownership rate results in a gradual and permanent decrease in income level or unemployment rate and reaches its full impact after 15 years. And we also shows that income or unemployment rate gradually and permanently decreases in response to a one-standard-deviation shock in business ownership rate and that the full impact is reached after 15 years. The impulse response functions are thus consistent with the Granger causality tests. The main contribution of this paper is that it is the first attempt to apply panel cointegration technique to examine the long-run relationship between business ownership rate and number of concerned variables such as income per capita, unemployment rate, economic openness, human capital level, union membership rate, credit accessibility and manufacturing sector ratio. And also we shed light on the direction of causality between income level, unemployment rate and business ownership rate. While structural breaks in OECD countries such as collapse of Berlin wall, formation of Euro-zone, political regime shifts, financial or trade liberalization, financial or fiscal crisis and so on may affect the above panel test statistics, we do not take into account structural breaks, which may limit our conclusions and implications.

본 연구에서는 군산의료원 재정의 추이를 살펴보고 재정의 지속가능성을 분석한 선행연구들을 검토한 후, 지방의료원 재정의 지속가능성을 검증하기 위한 모형과 방법을 정식화하고, 2003년부터 2010년까지의 군산의료원 재정수입과 재정지출에 대하여 단위근검정과 공적분검정을 수행하였다. 분석결과 군산의료원의 재정수입이 불안정적인 데 비해 재정지출은 안정적으로 나타났다. 또한 군산의료원의 재정수입과 재정지출 간에 공적분관계가 존재하지 않아서 재정적자가 지속가능하지 않은 것으로 나타났다. 따라서 군산의료원의 재정수입과 재정지출 간에 장기적인 균형관계가 존재하지 않으므로 향후 군산의료원은 재정건전화에 역점을 두어야 할 것이다.

This study reviewed previous literature analyzing fiscal sustainability, had an overview of fiscal trends of Gunsan medical center, formulated a model and methods for testing the fiscal sustainability of public medical centers, and then performed both unit root and cointegration tests for financial revenues and expenditures of Gunsan medical center in Jeonbuk Province from 2003 through 2010. Analytical results indicate that financial revenues show to be nonstationary, while financial expenditures reveal to be stationary. In addition, since a cointegrating relationship between revenues and expenditures does not exist, financial deficits turn out to be nonsustainable. Since there are no long-run equilibrium relationship between revenues and expenditures, Gunsan medical center should attach importance to financial consolidations ahead from now.

본 논문에서는 주요국 화폐 및 아시아 태평양 국가 화폐를 이용하여 글로벌 금융위기 이전 (2000년-2006년)과 글로벌 금융위기 이후 (2009 년-2019년)의 환율의 무작위 보행을 연구하였다. 주요국 화폐로는 일본엔, 유로, 영국파운드, 캐나다 달러를 선정하였고, 아시아 태평양 국가 화폐로는 우리나라 원화를 비롯하여 호주달러, 태국바트, 싱가포르 달러, 인도네시아 루피아가 선정되어 모두 9개국의 화폐가 본 연구에 사용 되었다. 또한 환율의 무작위 보행을 검정하기 위한 방법으로는 단위근 검정과 분산비율 검정을 채택하였다. 단위근 검정에서는 글로벌 금융 위기 이전과 이후 모두 대부분의 화폐가 무작위 보행을 하는 것으로 나타나고 있어 글로벌 금융위기 이전과 이후에 따른 환율의 무작위 보행 행태의 차이가 없었다. 등분산 분산비율 검정결과를 보면 글로벌 금융위기 이전에는 9개국 모든 화폐에서 무작위 보행이 기각되었다. 반면에 글로벌 금융위기 이후의 검정에서는 우리나라 원, 싱가포르 달러 태국 바트, 그리고 인도네시아 루피아는 무작위 보행이 기각되었지만 일본 엔, 캐나다 달러, 그리고 호주 달러에서는 무작위 보행의 행태가 나타났다. 유로와 영국 파운드는 글로벌 금융위기 전에 비하여 자기상관이 많 이 약화되었다.

The purpose of this study is to examine the random walk hypothesis on nine currencies before and after global financial crisis. Japanese, Euro, British, Canadian currencies are selected as major currencies and Korean, Australian, Thai, Singapore, Indonesian currencies are selected as thoes of Asian-Pacific region. The empirical analysis is employed on randomwalk in nine daily exchange rates from2000 to 2019 using unit root test and variance ratio test. This study covers two sub-periods, the periods before and after global financial crisis. The results show that random walk is found in most currencies for both sub-periods, using unit root test. When variance ratio test is employed, random walk is not found in all currencies for the first sub-period. However, randomwalk is found in Japanese, Euro, and Australian currencies, while no random walk is found in rest 6 currencies. Autocorrelation of both Euro and pound is weakened after global financial crisis. The most rejections of random walk hypothesis under homoscedasticity are robust to heteroscedasticity. This shows that rejections of random walk is due to autocorrelation of exchange rates rather than heteroscedasticity of exchange rates.

시계열의 구조 변화란, 전체 시계열 자료를 구성하는 기간에서 관측치들의 분포가 상대적으로 안정적이다가, 특정 시점에서 분포 특성의 급격한 변화를 보이는 것을 의미한다. 비정상(non-stationary) 장기 시계열 안에서도, 단기적인 추세의 변화가 일시적인 것인지, 아니면 구조적으로 변한 것인지를 적시에 판단하는 것은 중요하다. 이는 시계열 추세의 변화를 상시 감지하여, 변화에 맞는 적정한 대응을 할 필요가 있기 때문이다. 본 연구에서는 단위근 검정법을 기반으로 한 검정 결과를 시각화함으로써, 의사결정자가 시계열의 구조 변화를 손쉽게 파악할 수 있는 방안을 제시하였다. 특히 시계열을 분할한 후 검정하는 방법을 통해, 장기 시계열일 때에도 단기 구조 변화를 파악할 수 있도록 하였다.

Structural change of time series means that the distribution of observations is relatively stable in the period of constituting the entire time series data, but shows a sudden change of the distribution characteristic at a specific time point. Within a non-stationary long-term time series, it is important to determine in a timely manner whether the change in short-term trends is transient or structurally changed. This is because it is necessary to always detect the change of the time series trend and to take appropriate measures to cope with the change. In this paper, we propose a method for decision makers to easily grasp the structural changes of time series by visualizing the test results based on the unit root test. Particularly, it is possible to grasp the short-term structural changes even in the long-term time series through the method of dividing the time series and testing it.

비정상(non-stationary) 장기 시계열 안에서도, 단기적으로 추세의 변화가 일시적인 것인지, 아니면 구조적으로 변한 것인지를 적시에 판단하는 것은 중요하다. 이는 시계열 추세의 변화를 상시 감지하여, 변화에 맞는 적정한 수준의 대응을 할 필요가 있기 때문이다. 본 연구에서는 장기 시계열이 주어진 상황에서, 단위근 검정법을 기반으로 단기적으로 구조변화를 감지하여, 이러한 변화가 얼마나 지속될 것인지를 시각적으로 판단할 수 있는 방법을 제시하고자 한다.

비정상(non-stationary) 장기 시계열 안에서도, 단기적으로 추세의 변화가 일시적인 것인지, 아니면 구조적으로 변한 것인지를 적시에 판단하는 것은 중요하다. 이는 시계열 추세의 변화를 상시 감지하여, 변화에 맞는 적정한 수준의 대응을 할 필요가 있기 때문이다. 본 연구에서는 장기 시계열이 주어진 상황에서, 단위근 검정법을 기반으로 단기적으로 구조변화를 감지하여, 이러한 변화가 얼마나 지속될 것인지를 시각적으로 판단할 수 있는 방법을 제시하고자 한다.

Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.

Unit root test for temporally aggregated first order autoregressive process is considered. The temporal aggregate of fist order autoregression is an autoregressive moving average of order (1,1) with moving average parameter being function of the autoregressive parameter. One-step Gauss-Newton estimators are proposed and are shown to have the same limiting distribution as the ordinary least squares estimator for unit root when complete observations are available. A Monte-Carlo simulation shows that the temporal aggregation have no effect on the size. The power of the suggested test are nearly the same as the powers of the test based on complete observations.

We consider nonstationary autoregressive autoregressive process with infinite variance of error. In the case of infinite cariance, the limiting distribution of the estimated coefficient is different from that under the finite cariance assumption. In this paper we show that the bootstrap method can be used to approximate the distribution of ordinary least squares estimator of the coefficient in the first order random walk process with infinite variance through some empirical studies and we suggest a test procedure based on bootstrap method for the unit root test.

Efforts to obtain more power for unit root tests have continued. Pantula at el.(1994) compared empirical powers of several unit root test statistics and addressed that the weighted symmetric estimator(WSE) and the unconditional maximum likelihood estimator(UMLE) are the best among them. One can easily see that the powers of these two statistics are almost the same. In this paper we explain a connection between WSE and UMLE and suggest a unit root test statistic which may explain the connection between them.

In the analysis of time series it is an important issue to determine whether a time series under study is stationary. For the test of the stationary of the time series the Dickey-Fuller (DF) type tests have been mainly used. In this paper, we consider the regular unit root tests and seasonal unit root tests based on the generalized Durbin-Watson (DW) statistics when the errors are independent. The limiting distributions of the proposed DW-type test statistics are the functionals of standard Brownian motions. We also obtain the finite distributions and powers of the DW-type test statistics and compare the performances with the DF-type tests. It is observed that the DW-type test statistics have good behaviors against the DF-type test statistics especially in the nonzero (seasonal) mean model.

This study examines the explosive behaviors of house prices in Seoul and its metropolitan areas during 2008Q1~2023Q1. In order for the relationship between house prices and cash flows to reflect better the Korean housing market, this study adopts price-to-income ratio, real transaction-based house prices and personal income. Based on the generalized supremum ADF (GSADF) test, our empirical findings show that housing bubbles are identified in all three markets. According to the starting period, duration periods, and magnitude and prominent peaks among GSADF statistics, the bubbles in Seoul housing market appear to be most serious and further be transmitted to the housing markets of its metropolitan area, Incheon and Gyeonggi-do. Since the methodology used in this study provides policy-makers and investors with real-time information on bubbles, they could formulate a better early warning system to tackle the bubble problem. Specially, our empirical finding helps policy makers to prioritize Seoul over the other housing markets to cope with ongoing bubbles.

In this paper, we investigate the limiting distribution of the Ljung-Box test statistic in the unit root AR models with ARCH errors. We show that the limiting distribution is approximately chi-square distribution with the degrees of freedom only depending on the number of autocorrelation lags appearing in the test. Some simulation results are provided for illustration.

We consider the asymptotic results of the variance ratio statistic when the underlying processes have moving average(MA) unit roots. This degenerate situation of zero spectral density near the origin cause the limit of the variance ratio to become zero. Its asymptotic behaviors are different from non-degenerating case, where the convergence rate of the variance ratio statistic is formally derived.