Are the Global REIT Markets Efficient by a New Approach?

Abstract

This study uses a panel KSS test by Nuri Ucar and Tolga Omay (2009), with a Fourier function based on the sequential panel selection method (SPSM) procedure proposed by Georgios Chortareas and George Kapetanios (2009) to test the efficiency of REIT markets in 16 countries from 28 March 2008 to 27 June 2011. A Fourier approximation often captures the behavior of an unknown break, and testing for a unit root increases its power to do so. Moreover, SPSM can determine the mix of I(0) and I(1) series in a panel setting to clarify how many and which are random walk processes. Our empirical results demonstrate that REIT markets are efficient in all sampled countries except the UK. Our results imply that investors in countries with efficient REIT markets can adopt more passive portfolio strategies. [PUBLICATION ABSTRACT]

Headnote

Summary: This study uses a panel KSS test by Nuri Ucar and Tolga Omay (2009), with a Fourier function based on the sequential panel selection method (SPSM) procedure proposed by Georgios Chortareas and George Kapetanios (2009) to test the efficiency of REIT markets in 16 countries from 28 March 2008 to 27 June 2011. A Fourier approximation often captures the behavior of an unknown break, and testing for a unit root increases its power to do so. Moreover, SPSM can determine the mix of I(0) and I(1) series in a panel setting to clarify how many and which are random walk processes. Our empirical results demonstrate that REIT markets are efficient in all sampled countries except the UK. Our results imply that investors in countries with efficient REIT markets can adopt more passive portfolio strategies.

Keywords: REIT, Efficiency, Sequential panel selection method, Panel KSS test with a Fourier function, Portfolio strategy.

JEL: C23, C52, D53, G11, G14, L85.

(ProQuest: ... denotes formulae omitted.)

Eugene F. Faina (1991) proposed that securities markets generally are efficient be- cause prices instantaneously reflect new information, eliminating opportunities for arbitrage. Real estate investment trust (REIT) markets are recent developments among securities markets. However, compared with the analysis of efficiency for other securities markets, fewer studies have investigated whether price changes for REITs follow a unit root process, and their findings are inconclusive (Yuming Li and Ko Wang 1995; Vinod Chandrashekaran 1999; Michael Cooper, David H. Downs, and Gary A. Patterson 2000; Simon Stevenson 2002; Benjamas Jirasakuldech, Robert D. Campbell, and John R. Knight 2006). The market efficiency of REITs has become an important issue, given their growth in recent years. Besides the extended line of successful products in the United States and Australia, REITs have become important investment vehicles in Europe and Asia (European Public Real Estate Association 2004). Collectively, these markets almost equal the total of all REITs worldwide (Table 1). This paper analyzes whether changes in REIT prices follow a random walk or mean reversion. We are the first to employ a panel KSS test with a Fourier func- tion by the SPSM procedure to document efficiency among REIT indices. Our study fills several gaps in the literature.

1. Literature Review

Some studies have reported inefficiencies in REIT markets, implying mean rever- sion. Chandrashekaran (1999) and Stevenson (2002) documented short-term per- formalice persistence in REIT returns. Cooper, Downs, and Patterson (2000) found that REIT returns are more predictable than returns of small stocks, large stocks, and bonds. Edward Nelling and Joseph Gyourko (1998) and James L. Kuhle and Jaime R. Alvayay (2000) verified that REIT returns are predictable, suggesting evidence of a rational bubble model, and other evidence suggests speculative bubbles in real estate markets (Jim Clayton 1997; Kicki Bjorklund and Bo Soderberg 1999; Maurice J. Roche and Kieran McQuinn 2001). Yuming Fu and Lilian K. Ng (2001) showed ob- vious, prolonged price adjustment to news in real estate markets, suggesting evidence of long memory and slow reversion to the mean. Other studies demonstrate that REIT markets are efficient. Li and Wang (1995) found that REIT returns are no more predictable than returns of other stocks. Jirasakuldech, Campbell, and Knight (2006) showed that REIT markets are not prone to rational bubbles. Jarl Kallberg, Crocker H. Liu, and Paolo Pasquariello (2008) indicate that market prices adjust to reflect the underlying real market behavior and that abnormal REIT returns eventually disap- pear.

A unit root test measures the efficiency of the security price series, and many scholars have employed it to examine whether security market prices are a random walk (Kausik Chaudhuri and Yangru Wu 2003; Julia Junttila 2003). Jirasakuldech, Campbell, and Knight (2006) used it and found no evidence of rational bubbles in the REIT market. However, some studies propose that conventional unit root tests have less power than near-unit root but stationary alternatives and also fail to consider cross-regional information, resulting in less efficient estimations (Mark P. Taylor and Lucio Samo 1998; Gangadharrao S. Maddala and Shaowen Wu 1999; Andrew Levin, Chien-Fu Lin, and Chia-Shang J. Chu 2002; Kyung S. Im, Hashem M. Pesaran, and Yongcheol Shin 2003). John H. Cochrane (1988) showed that the test power of conventional unit root tests is insufficient for small samples. Ronald Balvers, Yangru Wu, and Erik Gilliland (2000) proposed that empirical results for data with a brief time series usually cannot reject the random walk hypothesis, as a lengthy progression is needed for documenting mean reversion.

To overcome this difficulty, researchers have used panel data to increase power in testing for a unit root (Balvers, Wu, and Gilliland 2000; Jeffrey Gropp 2004; Ranjpour Reza and Karimi T. Zalira 2008). Levin, Lin, and Chu (2002) and Im, Pesaran, and Shin (2003) used panel data with the asymptotic finite-sample prop- erties of ADF tests, which significantly improved power even in small panels. How- ever, the all-or-nothing nature of the Levin, Lin, and Chu (2002) tests has not been refined (Taylor and Samo 1998; Janice B. Breuer, Robert McNown, and Myles Wallace 2001). Tests by Taylor and Samo (1998), Maddala and Wu (1999) and Im, Pesaran, and Shin (2003) permitted autoregressive parameters to differ across panel members under the stationary alternative when the null hypothesis is rejected. Reza and Zalira (2008) using different panel unit root tests, examined whether economic convergence and catching-up have been characteristics of economic growth in ten new members of the European Union. However, these panel tests do not delineate which series are stationary, as they are not joint tests of the null hypothesis. Sune Karlsson and Mickael Lothgren (2000) and Breuer, McNown, and Wallace (2001) insisted that researchers do not conclude each series in the panel to be stationary when the null hypothesis is rejected. The sequential panel selection method (SPSM) proposed by Chortareas and Kapetanios (2009) can determine the mix of 1(0) and 1(1) series in a panel setting so as to group a whole panel into stationary and nonsta- tionary series. Moreover, Guochen Pan, Sen-Sung Chen, and Tsangyao Chang (2012) applied the SPSM to examine whether the growth rate of total insurance premium is independent from their size for 35 insurance companies in China. Pierre Perron (1989) proposed that when the stationary alternative is true and the structural break is ignored, the power to reject a unit root decreases if a structural break occurs, making it easier to accept the null hypothesis of a unit root. When using dummy variables to approximate breaks, some limitations arise. Among these limits, the exact number and location of the breaks must be known, the tests account only for one to two breaks, and use of dummies means sharp and sudden changes in the trend or level term. Stephen Leyboume, Paul Newbold, and Dimitrios Vougas (1998) deemed that breaks should be approximated as smooth and gradual processes. Philip H. Franses and Timothy J. Vogelsang (1998) and Charles Harvey (2001) use the HEGY sea- sonal unit root testing with an unknown breakpoint to be estimated from the data, and Ozlem Tasseven (2008) extends the HEGY testing procedure by allowing for sea- sonal mean shifts with double exogenous break points. Furthermore, Bong-Soo Lee (1998), Ralf Becker, Walter Enders, and Stan Hum (2004) and Razvan Pascalau (2010) indicated that a Fourier approximation often captures the behavior of an un- known break, even if it is not periodic. Their testing framework requires only the specification of the proper frequency in the estimating equations, and the tests are confirmed to have good size and power regardless of the time or shape of the break since the number of estimated parameters is reduced. Moreover, although many stud- ies have shown nonlinear adjustment of REIT indexes empirically (John Okunev, Patrick Wilson, and Ralf Zurbruegg 2000; Kim H. Liow and Haishan Yang 2005; Yen-Hsien Lee and Chien-Liang Chiu 2010; Kuang-Liang Chang 2011), evidence of nonlinear adjustment need not imply a nonlinear random walk (nonstationarity). Perron (1989) proposed that conventional unit root tests, such as the augmented Dickey-Fuller (ADF) test, tend not to reject the null hypothesis of the unit root when examining nonlinear data. Hence, efficiency tests on a nonlinear framework with the panel unit root must be applied. Ucar and Omay (2009) combine the nonlinear framework in Kapetanios, Shin, and Andy Snell (2003) with the panel unit root test- ing procedure of Im, Pesaran, and Shin (2003) to produce a nonlinear panel unit root test.

Because Fourier approximation often captures the unknown break, this study uses a panel KSS test with a Fourier function by the SPSM procedure to search for random walks among REIT indices in 16 countries. In addition, previous studies as- sume that countries' REIT indexes are cross-sectionally independent, whereas our study recognizes that they may be contemporaneously correlated and that independ- ence cannot be assumed. We approximate the bootstrap distribution of the tests to control for cross-sectional dependence among REIT indices. If changes in a coun- try's REIT index are a random walk, investors cannot use historical price movements to predict future returns, so they can adopt more passive portfolio strategies such as diversifying investment among a few efficient REIT markets. However, if prices re- vert to the mean, investors potentially can predict future returns of the index, and they can adopt more active portfolio strategies.

Section 2 presents data used in our study. Section 3 describes the SPSM test proposed by Chortareas and Kapetanios (2009). Section 4 presents our empirical re- sults. Section 5 discusses economic and policy implications of our empirical find- ings. Section 6 concludes.

2. Data Scope

Our empirical data cover 16 countries: the U.S., Canada, Australia, New Zealand, Belgium, Bulgaria, France, the Netherlands, Turkey, the United Kingdom, Taiwan, Hong Kong, Japan, Singapore, South Korea, and China. Data exclude countries in Africa with the least REIT capitalization. Among these, the U.S. market has the larg- est capitalization, and Australian is second largest (Table 2). France has Europe's largest REIT market and is in order contrast to the remaining countries, including the United Kingdom, the Netherlands, Belgium, Turkey, and Bulgaria. REITs in Ger- many, Greece, and Italy were established after mid-2007. Because changes in REIT indices in Germany, Greece, and Italy are small because of short establishing times or less liquidity, we omit data for these three countries. Japan and Singapore have Asia's largest REIT markets and are in order contrast to the remaining countries, in- cluding Hong Kong, Taiwan, South Korea, and China. We also delete data for India, Malaysia, Thailand, and the Philippines because of infrequent changes in REIT indi- ces or their brief existence.

This study uses daily data from 28 March 2008 to 27 June 2011. All REIT in- dices are taken from Datastream, and each was transformed into a natural logarithm before analysis. Table 5 provides summary statistics. Our empirical results show that the average return of Australian REITs is significantly higher than those among other nations, perhaps because of its capitalization and because Australia has the highest ratio of securitized real estate among sampled countries. Turkish REITs are the most volatile in our sample (standard deviation = 0.162), and New Zealand REITs are the least volatile (standard deviation = 0.096). Average return and standard deviation for New Zealand REITs are the lowest, suggesting that investors in New Zealand face a trade-off between REITs' risk and average return. Results of our Jarque-Bera test indicate that, except for South Korea, the REIT return datasets are approximately non-normal for all other 15 sample countries.

3. Methodology: Sequential Panel Selection Method and Panel KSS Unit Root Test with a Fourier Function

Numerous studies have shown empirical evidence for nonlinear adjustment of REIT indexes, but their findings need not imply a nonlinear random walk (nonstationarity). Therefore, efficiency (nonstationarity) tests based on a nonlinear framework must be applied. The KSS test proposed by Kapetanios, Yongcheol, and Snell (2003) seeks to detect the appearance of nonstationarity against a nonlinear but stationary exponen- tial smooth transition autoregressive (ESTAR) process. The model is expressed as follows:

... (1)

where Xt is the data series of interest, vt is an i.i.d. error with zero mean and con- stant variance, and 0 >0 is the transition parameter of the ESTAR model and gov- erns the speed of transition. In the null hypothesis, Xt follows a linear unit root process, whereas Xt follows a nonlinear stationary ESTAR process in the alterna- tive hypothesis. Given that y cannot be identified in the null hypothesis, Ritva Luukkonen, Pentti Saikkonen, and Timo Teräsvirta (1988) and Kapetanios, Yongcheol, and Snell (2003) used a first-order Taylor series to estimate i1 - exp(-6lY;! )} approximately. In regard to the null hypothesis 0 = 0, Equa- tion (1) can be rewritten as the auxiliary regression:

... (2)

In this framework, the null and alternative hypotheses are expressed as 8 = 0 (non- stationarity) against A < 0 (nonlinear ESTAR stationarity). Ucar and Ornay (2009) expanded a nonlinear panel data unit root test based on Regression (3). The regres- sion is as follows:

... (3)

They also applied first-order Taylor series approximation to the PESTAR (1) model around 0. = 0 for all i and obtained the auxiliary regression:

... (4)

where 8i = 6iyi. Their hypotheses for unit root testing based on Regression (4) are as follows:

...

Recalling that a Fourier approximation often captures unknown breaks, the system of a nonlinear panel data with a Fourier function that we estimate here is as follows:

... (5)

The rationale for selecting [sin(2^/ / / ), cos(27lkt / / )] is that a Fourier expression can approximate absolutely integrable functions to any accuracy, where k represents the frequency selected for the approximation and [a;,b -]' measures the amplitude and displacement of the frequency component. If there is a structural break, at least one frequency component must be present. Since their Monte Carlo experiments, Enders and Junsoo Lee (2009) suggest that no more than one or two frequencies should be used because the loss of power associated with a larger num- ber of frequencies occurs. Because there is no information about the shape of breaks in the data, we first perform a grid search to find the fitted frequency. Finally, based on the SPSM procedure, we can separate the entire panel into groups evidencing a random walk and groups displaying mean reversion. The SPSM procedure is detailed in Chortareas and Kapetanios (2009).

4. Empirical Results

First, we used several univariate unit root tests to test the null of a unit root in REIT indices for the 16 sampled countries. Then, we employed first- and second- generation panel unit root tests. Three univariate unit root tests - Augmented David A. Dickey and Wayne A. Fuller (1981), Peter C. B. Phillips and Perron (1988), and Denis Kwiatkowski et al. (1992) - in Table 6 consistently concluded that all exam- ined indices follow unit roots. This result shows that the power of these univariate unit root tests is low when a few indices may follow mean reversion, implying that REIT indices in all 16 countries were efficient during the period. Other explanations for the poor power of these tests might be that REIT index processes are nonlinear or researchers used a finite sample. Moreover, panel-based unit tests are found to in- crease the power of the order of the integration analysis by allowing combinations of cross-sectional and temporal dimensions.

Tables 7 and 8 present the results for the first- and second-generation panel- based unit root tests. Three first-generation panel-based unit root tests of Maddala and Wu (1999), Levin, Lin, and Chu (2002) and Kapetanios, Shin, and Snell (2003) show similar results, indicating that REIT indices are stationary in our sampled coun- tries. The first-generation panel-based unit root tests do not combine possible cross- sectional dependencies with the panel-based unit root test procedure, and failure to consider contemporaneous correlations among data will bias the panel-based unit root test toward rejecting the joint unit root hypothesis (Paul G. J. O'Connell 1998). The four second-generation panel-based unit root tests of In Choi (2001), Jushan Bai and Serena Ng (2004), Hyungsik R. Moon and Benoit Perron (2004) and Pesaran (2007) consider cross-sectional dependencies to offer a superior test of the indices' efficiency. Table 8 presents the results. The Bai and Ng (2004) and Kapetanios, Shin, and Snell (2003) tests show that REIT indices follow a random walk, but results from the other two tests indicate mean reversion in all sampled countries. Second- generation panel-based unit root tests cannot confirm that REIT indices in our sam- pled countries are efficient.

Panel-based unit root tests also cannot determine the mix of 1(0) and 1(1) se- ries in a panel setting and offer limited usefulness detecting a random walk among REIT indices because they do not incorporate structural breaks in the model. How- ever, the SPSM procedure can clarify how many and which series in the panel are stationary or nonstationary processes. Table 9 shows the results of panel KSS unit root test with a Fourier function on the indices where the panel KSS statistics are produced with the bootstrap p-values, individual minimum KSS statistics, and sta- tionary series identified each time. The residual sum of squares (RSS) indicates that the best frequency is 2 for most of the series. Except for sequence 1, 3, 4, 8, 11, 13, and 15, we found that the best frequency is 4, 3, and 1. When we first used the panel KSS unit root test on the whole panel in Table 9, the null hypothesis of a unit root for the REIT index was rejected, producing a value of -1.871 with a p-value of 0.075. Following the SPSM procedure, our results show that only the UK is stationary with the minimum KSS value of -3.608. We removed UK data and reimplemented the panel KSS unit root test on the remaining sets of series. We found that the procedure stopped just at sequence 1, after the UK REIT index was removed from the panel while continuing the procedure until the panel KSS unit root test failed to reject the unit root null hypothesis at the 10% significance level. Therefore, by using the panel KSS unit root test with a Fourier function, the SPSM procedure provides strong evi- dence of a random walk among REIT indices in our sampled countries. We conclude that REIT markets are efficient in surveyed countries outside the UK.

Regulative limits may create the UK REIT market's inefficiency. UK REITs must raise funds through listings on recognized stock exchanges and reside for tax purposes in the UK, which impairs their growth and liquidity. Nonresident investors should be subject to UK income tax withholding on REIT payments, which is prob- lematic in the context of the UK's double tax, as distributions of property income will be treated as dividends for treaty purposes. Also, companies that have held REIT status fewer than 10 years are subject to corporation tax during that accounting pe- riod. Although REITs in the UK may hold foreign real estate, the 10% portfolio limit is enforced, and they pay tax in the country where the real estate is located. The limi- tation on gearing will restrict the scope for sheltering this with interest expense, a drawback compared with other REITs with established cross-border investment structures. Finally, each UK resident member of a group must distribute 95% of the profits of its tax-exempt business, which should give greater flexibility in apportion- ing tax-exempt investment business and taxable development business. However, our overall results insist that REIT markets in our sampled countries are efficient and display nonlinear random walks.

5. Economic and Investing Implications

Past studies are inconclusive about whether REIT markets are efficient. Scholars like Sanjoy Basu (1977) have proposed that capital markets are inefficient because of trading costs and taxes; trading costs of REITs in most countries are low, and many avoid double taxation. Although previous studies have found inefficiencies in REIT markets (Cooper, Downs, and Patterson 2000; Kuhle and Alvayay 2000; Roche and McQuinn 2001; Stevenson 2002), the efficiency hypothesis holds up rather well in the real markets (see Faina 1998). Faina (1991) indicated that the deviations from the extreme version of the efficiency hypothesis are within trading cost and information. Also, Faina (1998) asserted that the probabilities of investors' underreaction and overreaction are each 50%, the entire market is still efficient when they are placed together. Therefore, we expect the REIT markets to be efficient in our sampled coun- tries, and our results confirm that expectation. Our results reinforce those of Brent W. Ambrose, Esther Ancel, and Mark D. Griffiths (1992), Crocker H. Liu and Jianping Mei (1992) and Jirasakuldech, Campbell, and Knight (2006) which support the effi- ciency of REIT markets for most countries.

A major implication of our study is that investors generally cannot use price changes in the REIT indexes of our sampled countries to predict future returns. For 15 of 16 sampled countries, price movements do not determine whether a REIT in- dex is overvalued or undervalued. Hence, REIT investors in efficient markets can adopt more passive portfolio strategies, such as diversifying investment, among these efficient REIT markets. Inefficiency arises in the UK, where price movements of the REIT index can be used to predict future returns. Investors there can consider fre- quent-adjusting portfolio strategies. Knowing the market's efficiency enables inves- tors to select a type of portfolio strategy in the REIT markets.

6. Conclusions

In recent years, many investors have gravitated to REITs; however, previous studies offer inconsistent conclusions about the efficiency of REIT markets. This paper used the SPSM approach proposed by Chortareas and Kapetanios (2009), capable of de- termining the mix of 1(0) and 1(1) series in a panel setting, to examine the efficiency of REIT markets in 16 countries from 28 March 2008 to 27 June 2011. The panel KSS test with a Fourier function based on the SPSM procedure presents a clear pic- ture about the random walk of country-specific REIT markets.

Our results signify that REIT markets in 15 of 16 global countries are effi- cient, the exception being the UK, where regulative limits may impose inefficiency. This study implies that price changes in the world's REIT indices generally cannot be used to predict their future returns. Hence, investors in efficient REIT markets can adopt more passive portfolio strategies such as diversifying investment.

References

References

Ambrose, Brent W., Esther Ancel, and MarkD. Griffiths. 1992. "The Fractal Structure of Real Estate Investment Trust Returns: The Search for Evidence of Market Segmentation and Nonlinear Dependency." American Real Estate and Urban Economics Association Journal, 20(1): 25-54.

Bai, Jushan, and Serena Ng. 2004. "A Panic Attack on Unit Roots and Cointegration." Econometrica, 72(4): 1127-1177.

Balvers, Ronald, Yangru Wu, and Erik Gilliland. 2000. "Mean Reversion across National Stock Markets and Parametric Contrarian Investment Strategies." Journal of Finance, 55(2): 745-772.

Basu, Sanjoy. 1977. "Investment Performance of Common Stocks in Relation to their Price- Earnings Ratio: A Test of the Efficient Market Flypothesis." Journal of Finance, 32(3): 663-682.

Becker, Ralf, Walter Enders, and Stan Hum. 2004. "A General Test for Time Dependence in Parameters." Journal of Applied Econometrics, 19(7): 899-906.

Bjorklund, Kicki, and Bo Soderberg. 1999. "Property Cycles, Speculative Bubbles and the Gross Income Multiplier." Journal of Real Estate Research, 18(1): 151-174.

Breuer, Janice B., Robert McNown, and Myles Wallace. 2001. "Misleading Inferences from Panel Unit-Root Tests with an Illustration from Purchasing Power Parity." Review of International Economics, 9(3): 482-493.

Chandrashekaran, Vinod. 1999. "Time-Series Properties and Diversification Benefits of REIT Returns." Journal of Real Estate Research, 17(1-2): 91-112.

Chang, Kuang-Liang. 2011. "The Nonlinear Effects of Expected and Unexpected Components of Monetary Policy on the Dynamics of REIT Returns." Economic Modelling, 28(3): 911-920.

Chaudhuri, Kausik, and Yangru Wu. 2003. "Random Walk versus Breaking Trend in Stock Prices: Evidence from Emerging Markets." Journal of Banking and Finance, 27(4): 575-592.

Choi, In. 2001. "Unit Root Tests for Panel Data." Journal of International Money and Finance, 20(2): 249-272.

Chortareas, Georgios, and George Kapetanios. 2009. "Getting PPP Right: Identifying Mean-Reverting Real Exchange Rates in Panels." Journal of Banking and Finance, 33(2): 390-404.

Clayton, Jim. 1997. "Are Flousing Price Cycles Driven by Irrational Expectations?" Journal of Real Estate Finance and Economics, 14(3): 341-363.

Cochrane, John H. 1988. "Flow Big Is the Random Walk in GNP?" Journal of Political Economy, 96(5): 893-920.

Cooper, Michael, David H. Downs, and Gary A. Patterson. 2000. "Asymmetric Information and the Predictability of Real Estate Returns." Journal of Real Estate Finance and Economics, 20(2) : 225-244.

Dickey, David A., and Wayne A. Fuller. 1979. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Econometrica, 74(366): 427-431.

Enders, Walter, and Junsoo Lee. 2009. "The Flexible Fourier Form and Testing for Unit Roots: An Example of the Term Structure of Interest Rates." Department of Economics, Finance & Legal Studies, University of Alabama Working Paper.

Fama, Eugene F. 1991. "Efficient Capital Markets: II." Journal of Finance, 46(5): 1575- 1617.

Fama, Eugene F. 1998. "Market Efficiency, Long-Term Returns, and Behavioral Finance." Journal of Financial Economics, 49(3) : 283-306.

Franses, Philip H., and Timothy J. Vogelsang. 1998. "On Seasonal Cycles, Unit Roots, And Mean Shifts." The Review of Economics and Statistics, 80(2): 231-240.

Fu, Yuming, and Lilian K. Ng. 2001. "Market Efficiency and Return Statistics: Evidence from Real Estate and Stock Markets Using a Present-Value Approach." Real Estate Economics, 29(2) : 227-250.

Gropp, Jeffrey. 2004. "Mean Reversion of Industry Stock Returns in the U.S., 1926-1998." Journal of Empirical Finance, 11(4): 537-551.

Harvey, Charles. 2001. "Possible Causes of Eligh Arsenic Concentrations in the Well Water of Bangladesh." Eiivironmental Sciences, 8(5): 491-504.

Im, Kyung S., Hashem M. Pesaran, and Yongcheol Shin. 2003. "Testing for Unit Roots in Eleterogeneous Panels." Journal of Econometrics, 115(1): 53-74.

Jirasakuldech, Benjamas, Robert D. Campbell, and John R. Knight. 2006. "Are There Rational Speculative Bubbles in REIT s?" Journal of Real Estate Finance and Economics, 32(2): 105-127.

Junttila, Juha. 2003. "Detecting Speculative Bubbles in an IT-Intensive Stock Market." Journal of Economics and Finance, 27(2): 166-189.

Kallberg, Jarl, Crocker H. Liu, and Paolo Pasquariello. 2008. "Updating Expectations: An Analysis of Post-9/11 Returns." Journal ofFinancial Markets, 11(4): 400-432.

Kapetanios, George, Yongcheol Shin, and Andy Snell. 2003. "Testing for a Unit Root in the Nonlinear STAR Framework." Journal of Econometrics, 112(2): 359-379.

Karlsson, Sune, and Mickael Lothgren. 2000. "On the Power and Interpretation of Panel Unit Root Tests." Economics Letters, 66(3): 249-255.

Kuhle, James L., and Jaime R. Alvayay. 2000. "The Efficiency of Equity REIT Prices." Journal of Real Estate Portfolio Management, 6(4) : 349-354.

Kwiatkowski, Denis, Peter C. B. Phillips, Peter Schmidt, and Yongcheol Shin. 1992. "Testing the Null Elypothesis of Stationary against the Alternative of a Unit Root: Flow Sure Are We that Economic Time Series Llave a Unit Root?" Journal of Econometrics, 54: 159-178.

Lee, Bong-Soo. 1998. "Permanent, Temporary, and Non-Fundamental Components of Stock Prices." Journal of Financial and Quantitative Analysis, 33(1): 1-32.

Lee, Yen-Hsien, and Chien-Liang Chiu. 2010. "Nonlinear Adjustment of Short-Term Deviations Impacts on the US Real Estate Market." Applied Economics Letters, 17(6): 597-603.

Levin, Andrew, Chien-Fu Lin, and Chia-Shang J. Chu. 2002. "Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties." Journal of Econometrics, 108(1): 1- 24.

Leyboume, Stephen, Paul Newbold, and Dimitrios Vougas. 1998. "Unit Roots and Smooth Transitions." Journal of Time Series Analysis, 19(1): 83-97.

Li, Yuming, and Ko Wang. 1995. "The Predictability of REIT Returns and Market Segmentation." Journal of Real Estate Research, 10(4): 471-482.

Liow, Kim H., and Haishan Yang. 2005. "Long Term Co-Memories and Short-Run Adjustment: Securitized Real Estate and Stock." Journal of Real Estate Finance and Economics, 31(3): 283-300.

Liu, Crocker H., and Jianping Mei. 1992. "The Predictability of Returns on Equity REITs and Their Co-Movement with Other Assets." Journal of Real Estate Finance and Economics, 5(4): 401-418.

Luukkonen, Ritva, Pentti Saikkonen, and Timo Teräsvirta. 1988. "Testing Linearity against Smooth Transition Autoregressive Models." Biometrika, 75(3) : 491-499.

Maddala, Gangadharrao S., and Shaowen Wu. 1999. "A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test." Oxford Bulletin of Economics and Statistics, 61(S1): 631-652.

Moon, HyungsikR., and Benoit Perron. 2004. "Testing for a Unit Root in Panels with Dynamic Factors." Journal of Econometrics, 122(1): 81-126.

Nelling, Edward, and Joseph Gyourko. 1998. "The Predictability of Equity REIT Returns." Journal of Real Estate Research, 16(3): 251-268.

O'Connell, Paul G. J. 1998. "The Overvaluation of Purchasing Power Parity." Journal of International Economics, 44(1): 1-19.

Okunev, John, Patrick Wilson, and Ralf Zurbruegg. 2000. "The Causal Relationship between Real Estate and Stock Markets." Journal of Real Estate Finance and Economics, 21(3): 251-261.

Pan, Guochen, Sen-Sung Chen, and Tsangyao Chang. 2012. "Does Gibrat's Law Elold in the Insurance Industry of China? A Test with Sequential Panel Selection Method." Panoeconomicus, 59(3): 311-324.

Pascalau, Razvan. 2010. "Unit Root Tests with Smooth Breaks: An Application to the Nelson-Plosser Data Set J Applied Economics Letters, 17(4-6): 565-570.

Perron, Pierre. 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Elypothesis." Econometrica, 57(6): 1361-1401.

Pesaran, Hashem M. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-Section Dependence." Journal of Applied Econometrics, 22(2) : 265-312.

Phillips, Peter C. B., and Pierre Perron. 1988. "Testing for a Unit Root in Time Series Regression." Biometrika, 75(2): 335-346.

Reza, Ranjpour, and Karimi T. Zahra. 2008. "Evaluation of the Income Convergence Elypothesis in Ten New Members of the European Union. A Panel Unit Root Approach." Panoeconomicus, 55(2): 157-166.

Roche, Maurice J., and Kieran McQuinn. 2001. "Testing for Speculation in Agricultural Land in Ireland." European Review of Agricultural Economics, 28(2) : 95-115.

Stevenson, Simon. 2002. "Momentum Effects and Mean Reversion in Real Estate Securities." Journal of Real Estate Research, 23(1-2): 47-64.

Taylor, Mark P., and Lucio Samo. 1998. "The Behavior of Real Exchange Rates during the Post-Bretton Woods Period." Journal of International Economics, 46(2): 281-312.

Tasseven, Ozlem. 2008. "Modeling Seasonality: An Extension of the E1EGY Approach in the Presence of Two Structural Breaks." Panoeconomicus, 55(4): 465-484.

Ucar, Nuri, and Tolga Omay. 2009. "Testing for Unit Root in Nonlinear Eleterogeneous Panels." Economics Letters, 104(1): 5-8.