Economic Modelling Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
Economic Modelling
2014 / 02 Vol. 38
Contents
- 1
Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
- 1.0.1 Image quality versus outcomes
- 1.0.2 [IEEE 2003 IEEE International Symposium on Electromagnetic Compatibility, 2003. EMC ’03. – Istanbul, Turkey (2003.05.16-2003.05.16)] 2003 IEEE International Symposium on Electromagnetic Compatibility, 2003. EMC ’03. – Prediction of the field radiated at one meter from PCB’s and microprocessors from near EM field cartography
- 1.0.3 Share this:
- 1.0.4 Like this:
- 1.0.5 Related
Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
Gozbasi, Onur, Kucukkaplan, Ilhan, Nazlioglu, Saban
آپ کو یہ کتاب کتنی پسند ہے؟
فائل کی کوالٹی کیا ہے؟
کوالٹی کا جائزہ لینے کے لیے کتاب ڈاؤن لوڈ کریں
فائل کی کوالٹی کیا ہے؟
جلد:
38
زبان:
english
رسالہ:
Economic Modelling
DOI:
10.1016/j.econmod.2014.01.021
فائل:
PDF, 219 KB
ڈاؤن لوڈ کریں (pdf, 219 KB)
پیش نظارہ
مسئلے کے بارے میں بتائیے
File opens
جی ہاں
نہیں
This is a book
جی ہاں
نہیں
Content is appropriate
جی ہاں
نہیں
Description matches
جی ہاں
نہیں
Check Yes if
Check Yes if
Check Yes if
Check Yes if
you were able to open the file
the file contains a book (comics are also acceptable)
the content of the book is acceptable
Title, Author and Language of the file match the book description. Ignore other fields as they are secondary!
Check No if
Check No if
Check No if
Check No if
-
the file is damaged
-
the file is DRM protected
-
the file is not a book (e.g. executable, xls, html, xml)
-
the file is an article
-
the file is a book excerpt
-
the file is a magazine
-
the file is a test blank
-
the file is a spam
you believe the content of the book is unacceptable and should be blocked
Title, Author or Language of the file do not match the book description. Ignore other fields.
This book has a different problem? Report it to us
Change your answer
فائل آپ کے ای میل ایڈریس پر بھیجی جائگی۔ اسے موصول ہونے میں 5 منٹ تک کا وقت لگ سکتا ہے۔.
فائل آپ کے Kindle اکاؤنٹ پر بھیجی جائگی۔ اسے موصول ہونے میں 5 منٹ تک کا وقت لگ سکتا ہے۔.
نوٹ کریں : آپ کو ہر کتاب کی تصدیق کرنی ہوگی جسے آپ اپنے Kindle میں بھیجنا چاہیں۔ Amazon Kindle سے تصدیقی ای میل کے لیے اپنا میل باکس چیک کریں۔
1
Image quality versus outcomes
Jhaveri, Kartik
سال:
2015
زبان:
english
فائل:
PDF, 53 KB
2
[IEEE 2003 IEEE International Symposium on Electromagnetic Compatibility, 2003. EMC ’03. – Istanbul, Turkey (2003.05.16-2003.05.16)] 2003 IEEE International Symposium on Electromagnetic Compatibility, 2003. EMC ’03. – Prediction of the field radiated at one meter from PCB’s and microprocessors from near EM field cartography
de Daran, F., Chollet-Ricard, J., Lafon, F., Maurice, O.
سال:
2003
زبان:
english
فائل:
PDF, 494 KB
Economic Modelling 38 (2014) 381–384 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests Onur Gozbasi a,⁎, Ilhan Kucukkaplan b, Saban Nazlioglu c a b c Department of Business Administration, Nuh Naci Yazgan University, Kayseri, Turkey Department of International Trade and Finance, Pamukkale University, Denizli, Turkey Department of Econometrics, Pamukkale University, Denizli, Turkey a r t i c l e i n f o Article history: Accepted 17 January 2014 Available online 15 February 2014 JEL classification: G14 C22 a b s t r a c t This paper re-examines the efficient market hypothesis (EMH) in the Turkish stock market by utilizing the recent developments in nonlinear unit root tests. To this end, we first employ the linearity test developed by Harvey et al. (2008) and then carry out the nonlinear ESTAR unit root test recently developed by Kruse (2011). The results show that Borsa Istanbul stock price index series have nonlinear behavior and follow the random walk (non-stationary) process, supporting the EMH in Turkish stock market which has weak-form efficiency. © 2014 Elsevier B.V. All rights reserved. Keywords: Efficient market hypothesis Turkish stock market Nonlinearity Emerging markets 1. Introduction The efficiency of stock markets is an old question and its importance continues since there is a lack of consensus in empirical studies. In the international literature on different countries, while a number of studies report a lack of evidence to support the EMH (see inter alia, Lo and MacKinlay, 1988; Poterba and Summers, 1988; Kavussanos and Dockery, 1996; Al-Loughani and Chappell, 1997; Grieb and Reyes, 1999; Chaudhuri and Wu, 2003; Narayan, 2006; Narayan, 2008; Hasanov, 2009), some other studies conclude that the behavior of stock prices is consistent with the EMH (Alexeev and Tapon, 2011; Buguk and Brorsen, 2003; Cheung and Coutts, 2001; Munir and Mansur, 2009;; Narayan, 2005; Narayan and Smyth, 2004, 2005; Qian et al., 2008). The controversy in the international literature is also available for the Turkish stock market. Table 1 summarizes the EMH literature on Turkey by focusing on data description, empirical tool(s), and results for the EMH hypothesis. Balaban (1995), by using parametric and nonparametric tests, found that the Istanbul Stock Exchange (ISE) is neither weak-form nor semi-strong-form efficient. Balaban and Kunter (1997) reported significant deviations from the EMH. Demirer and Karan (2002) focused on the existence of the “daily effect” in the ISE and indicated the evidence on market anomalies which is inconsistent with EMH. Buguk and Brorsen (2003) tested the random-walk hypothesis ⁎ Corresponding author. Tel.: +90 352 3240000; fax: +90 352 3240004. E-mail address: onurgozbasi@gmail.com (O. Gozbasi). 0264-9993/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econmod.2014.01.021 for the ISE using its composite, industrial and financial indexes by employing a batter of unit root tests which provided conflicting results. By taking into structural shifts, Ozdemir (2008) found out that the ISE100 composite index is characterized by a unit root, implying the validity of the EMH. Karan and Kapusuzoglu (2010) examined the random walk and overreaction hypothesis and indicated that the Turkish stock market is a weak efficient market. By employing nonlinearity and chaos theories, Ozer and Ertokatli (2010) examined the behavior of the ISE all share equity indices and they supported the existence of nonlinear structure and chaos in the ISE market. The reason why a consensus has not been achieved may be attributed to either the employment of different periods for different markets which have varying development levels, or to the application of different methods that have various levels of restrictive assumptions. Recent studies have also shown that nonlinearity1 in stock prices plays a crucial role in determining the behavior of stock markets. One of the recent tendencies in the EMH literature is the focus on accounting for the nonlinear process of financial series (Hsieh, 1991; Kim et al., 2008; McMillan, 2005; Shively, 2003). Therefore, the potential nonlinearities in financial time series should be taken into consideration to avoid misleading results (Hasanov, 2009). It is understood that the possible nonlinearities in the stock markets of developing countries have not been sufficiently 1 The transaction costs, market frictions, noise traders, short sales, the existence of bidask spreads, and corporate restrictive applications can cause nonlinearity (Hasanov and Omay, 2008; McMillan, 2003). 382 O. Gozbasi et al. / Economic Modelling 38 (2014) 381–384 Table 1 Summary of the EMH literature on Turkey. Study Data Methodology Series EMH Balaban (1995) January 04, 1988 August 05, 1994 January 1989 July 1995 January 04, 1988 March 29, 1996 Weekly data 1992-1999 Runs test OLS regression Granger causality ISE composite index Reject ISE composite index Reject Kruskal Wallis Test Three way ANOVA ADF unit root Fractional integration Variance ratio tests Structural breaks unit root test ADF unit root Runs test Variance ratio test Nonlinear programming model ADF unit root test BDS nonlinearity test Hinich bispectral test NEGM test ISE composite index Reject ISE composite, industrial, and financial indexes Accept ISE-100 index Accept 21 firms' stocks in ISE-30 index ISE-100 index Accept Reject Balaban and Kunter (1997) Demirer and Karan (2002) Buguk and Brorsen (2003) Ozdemir (2008) January 1990 June 2005 Karan and Kapusuzoglu (2010) Ozer and Ertokatli (2010) 2003–2007 February 02, 1997 March 16, 2009 studied so far (Hasanov and Omay, 2007; Lim and Brooks, 2011; Lim and Liew, 2007). This empirical paper re-examines the EMH for the Turkish stock market by means of recently developed time series methods within the context of a nonlinear framework. In this respect, we first question whether or not the Turkish stock market is characterized by linear or nonlinear behavior by employing the nonlinearity test developed by Harvey et al. (2008). After we found evidence on nonlinearity, we then proceed to testing the EMH by utilizing the nonlinear unit root tests recently proposed by Kruse (2011). This study shows evidence that the EMH is supported by the Turkish stock market. Although Turkey has experienced rapid growth during the last decade, there are still limited studies investigating the behavior of Turkish stock market in the international literature. To the best of our knowledge, there is no study which applies nonlinear unit root methods for testing the EMH in the case of Turkish stock market. where the null hypothesis of linearity (H0,I(1) : λ2 = λ3 = 0) is tested against the alternative hypothesis of nonlinearity (H1,I(0) : λ2 ≠ 0 and/ or λ3 ≠ 0) by the Wald statistics defined as W1 = T(RSSr1/RSSu1 − 1) where RSSu1 and RSSr1 are the residual sum of squares from the unrestricted and restricted form of the model (2). If the unit root characteristics of the series are unknown, it also becomes unclear which statistic (W0 or W1) will be used. The approach by Harvey et al. (2008) asymptotically chooses W0 if the series is stationary and W1 if the series is non-stationary. If the integration of the series is unknown, the weighted statistic – Wλ = {1 − λ}W0 + λW1 – is applicable to test the null of linearity against the alternative of nonlinearity, where λ is some function that converges in probability to zero when the series is stationary and to one if the series is non-stationary. This simply implies that under the null of either I(0) or I(1) linearity, Wλ selects the efficient test in the limit, and is asymptotically distributed as chi-square with two degrees of freedom. 2. Econometric methods 2.2. Nonlinear unit root test 2.1. Linearity test Harvey et al. (2008) proposed a linearity test that can be applied in cases that the unit root properties of data are unclear. If the time series is stationary (I(0)), the following model is estimated: 2 3 yt ¼ β0 þ β1 yt−1 þ β2 yt−2 þ β3 yt−3 þ p X β4; j Δyt− j þ εt ð1Þ j¼1 where p is the number of lags,2 and Δ is the first difference operator. To test for the null hypothesis of linearity; (H0,I(0) : β2 = β3 = 0) is tested against the alternative hypothesis of nonlinearity (H1,I(0) : β2 ≠ 0 and/or β3 ≠ 0) by the use of Wald statistic defined as W0 = T(RSSr0/RSSu0 − 1), where T is the number of observations, RSSu0 and RSSr0 are, respectively, the residual sum of squares from the unrestricted and restricted forms of the model (1). On the other hand, in cases when the series are nonstationary (I(1)), the regression model is: 2 3 Δyt ¼ λ1 Δyt−1 þ λ2 ðΔyt−1 Þ þ λ3 ðΔyt−1 Þ þ p X λ4; j Δyt− j þ εt ð2Þ j¼1 2 Harvey et al. (2008) recommend that it can be determined by means of the sequential testing method using a 10% significance level, after the suitable number of lags (p) is determined to be the maximum number of lags pmax = int[8(T/100)1/4]. The developments in the unit root literature show that time series are generated by nonlinear characteristics, and therefore it is important to take into account this information (nonlinear properties) for modeling and forecasting. In developing nonlinear unit root tests, the exponential smooth transition autoregressive (ESTAR) models are widely utilized to better understand the nonlinear properties of macro variables as well as a variety of financial series. Within the context of ESTAR specification in unit root testing, the Dickey–Fuller type test proposed by Kapetanios et al. (2003) is widely utilized. Their approach assumes that the location parameter in the smooth transition function is zero, which is difficult to hold in empirical analysis on financial series (see, for instance, Taylor et al., 2001; Rapach and Wohar, 2006). Table 2 Linearity test. Index Wλ statistic BIST-100 composite Industry Financial Services 34.01⁎⁎⁎ 55.88⁎⁎⁎ 27.95⁎⁎⁎ 25.77⁎⁎⁎ The critical values for χ22 distributions: 9.21 (1%), 4.60 (10%), and 5.99 (5%). ⁎⁎⁎ Denotes 1% significance level. O. Gozbasi et al. / Economic Modelling 38 (2014) 381–384 383 Table 3 Unit root test. Index Lag(s)a BIST-100 composite 1 2 3 1 2 3 1 2 3 1 2 3 Industry Financial Services Critical values 1% 5% 10% Log-level series 7.63 7.72 7.74 7.45 7.25 7.17 7.23 7.53 7.58 9.12⁎ 9.17⁎ 9.45⁎ 13.15 9.53 7.85 Demeaned series Demeaned + detrended series 5.29 5.55 5.47 6.80 6.67 6.42 4.25 4.74 4.67 7.69 7.54 7.70 7.18 7.44 7.24 3.98 4.10 3.82 6.48 6.88 6.67 11.40⁎ 10.99 10.72 13.75 10.17 8.60 17.10 12.82 11.10 ⁎ denotes 10% level of significance, respectively. Asymptotic critical values are based on 20,000 replications. a Since the lag structure may affect test statistics, we conducted the unit root analysis up to three lags in order to deal with any serial correlation problem. In order to allow for a nonzero location parameter in the exponential transition function, Kruse (2011) considers the following nonlinear model: n o 2 þ εt Δyt ¼ ϕyt−1 1− exp −γðyt−1 −cÞ ð3Þ where γ is the smoothness and c is the location parameter. By applying a first-order Taylor approximation to G(yt − 1; γ, c) = (1 − exp {− γ(yt − 1 − c}2) around γ = 0, the regression model for the testing procedure is written as follows: 3 2 Δyt ¼ β1 yt−1 þ β2 yt−1 þ β3 yt−1 þ ut : ð4Þ In order to improve the power of the test statistic, the zero restriction on β3 is imposed and hence the model estimated is: 3 2 Δyt ¼ β1 yt−1 þ β2 yt−1 þ ut ð5Þ where β1 = γϕ and β2 = −2cγϕ. In this specification, we are interested in testing the null hypothesis of the unit root (H0 : γ = 0) against the alternative hypothesis of the global stationary ESTAR process. For the test regression in Eq. (5), this pair of hypothesis is equivalent to H0 : β1 = β2 = 0 against H0 : β1 b 0, β2 ≠ 0. It is important to note here that under the alternative hypothesis while β1 is one-sided, β2 is two-sided, this is due to allowing the location parameter to be different from zero (c ≠ 0). In this sense, since the standard Wald test would be inappropriate, by following Abadir and Distaso (2007), Kruse (2011) developed a modified Wald-type test for the unit root hypothesis against globally stationary ESTAR. The new test is simply formulated by 2 ^ b0 t 2 τ ¼ t β⊥ ¼0 þ 1 β β1 ¼0 1 2 ð6Þ where two-summands in this statistic can be interpreted as: the first term is the squared t-ratio for the hypothesis β⊥ ¼ 0 that β⊥ is orthog2 2 onal to β1 and the second term is the squared t-ratio for the hypothesis β1 = 0. The test statistic in Eq. (6) has a non-standard asymptotic distribution and the asymptotic critical values are derived under the standard assumptions for the error term. It is also worthwhile to note that in order to solve a potential serial correlation in Eq. (5), the critical values are not affected by the lagged values of Δyt (see, Kruse, 2011, p.77). 3. Data and findings We employ daily data for the Borsa Istanbul composite index (BIST 100) and three sector (industry, financial, and services) indexes for the period of 1 July 2002–7 July 2012. We also employ sub-sectors – BIST 100 industrial, financial, and services sector indexes – in order to determine whether the results for the EMH hypothesis differ among main sector indexes. The data is obtained from FINNET's database (www.finnet. com.tr) and the natural logarithm of the series is used in the empirical analysis. To investigate whether the series are characterized by a linear or nonlinear pattern, we carried out the Wλ statistic by Harvey et al. (2008). The results in Table 2 shows that the null hypothesis of linearity is rejected for all the series at a 1% level of significance, indicating strong evidence on that the Turkish stock market indexes have nonlinear patterns. The evidence on nonlinearity may imply the validity of asymmetric information in Turkish stock market indexes. Therefore, testing the EMH with the conventional unit root tests which are not able to account for the information on nonlinearity may be misleading and this provides us with the opportunity to apply nonlinear methods. The results from the nonlinear unit root test in Table 3 indicate that, for log-level series, the null hypothesis of the unit root cannot be rejected at each lag length for the BIST-100, industry, and financial indexes. For the services index the null of unit root is rejected only at the 10% level of significance. Stock prices may contain time trend (Beechey et al., 2000), and if a stock market is efficient, fluctuations from trend should be unpredictable (Hasanov, 2009). Hence, in addition to testing for unit root for log-level data, we also use demeaned and detrended series.3 For demeaned and detrended series the null of unit root is not rejected at each lag for all the indexes with the exception of services where we can reject the null hypothesis at lag one at the 10% level of significance. Thereby, the results overall show that the Turkish stock market indexes appear to have a unit root (non-stationary structure) and we can conclude that the Turkish stock market is a weakform efficient market. The findings imply that the series do not have a mean reverting process and thereby any shock to the stock market seems to be permanent. Accordingly, any deviation from equilibrium may not be corrected by market forces. 3 The demeaned series were obtained by subtracting the sample mean from the loglevel of the index series. The demeaned and de-trended series were constructed by regressing the series on a constant and a linear time trend. 384 O. Gozbasi et al. / Economic Modelling 38 (2014) 381–384 4. Conclusion As with the international markets, the efficiency for Turkish stock market indexes has been tested by researches for a long time; however, conflicting results provided us with the opportunity to test the EMH for Turkey. To this end, we first examined the data generating process of the series by the use of the linearity test and this provided evidence of nonlinear behavior. Then we tested the EMH by means of a recently developed nonlinear unit root test and found out that the Turkish stock market index series follow a non-stationary process. Thereby, the main result suggests that the Turkish stock market supports the validity of the EMH and it is weak-form efficient. The findings imply that Turkish stock market is characterized by asymmetric price information and thereby global investors are not able to establish profitable investment strategy using the price data. It is therefore important to control other financial variables as well as international stock markets' dynamics in making investment decision for Turkish financial markets. Our findings also suggest that future research can concentrate on nonlinearities in stock markets of other emerging countries to better understand to what extend asymmetric information plays a role in portfolio strategies. References Abadir, K.M., Distaso, W., 2007. Testing joint hypotheses when one of the alternatives is one-sided. J. Econ. 140, 695–718. Alexeev, V., Tapon, F., 2011. Testing weak form efficiency on the Toronto Stock Exchange. J. Empir. Financ. 18, 661–691. Al-Loughani, N., Chappell, D., 1997. On the validity of the weak-form efficient markets hypothesis applied to the London Stock Exchange. Appl. Financ. Econ. 7, 173–176. Balaban, E., 1995. Informational efficiency of the Istanbul Securities Exchange and Some Rationale for Public Regulation. Discussion Paper No: 9502. The Central Bank of the Republic of Turkey (Available At http://tcmb.gov.tr/yeni/evds/teblig/95/9502.pdf). Balaban, E., Kunter, K., 1997. A note on the efficiency of financial markets in a developing country. Appl. Econ. Lett. 4, 109–112. Beechey, M., Gruen, D., Vickery, J., 2000. The Efficient Market Hypothesis: A Survey. Research Discussion Paper No. 2000-01. Reserve Bank of Australia (Available at http://www.rba. gov.au/publications/rdp/2000/pdf/rdp2000-01.pdf). Buguk, C., Brorsen, B.W., 2003. Testing weak-form market efficiency: evidence from the Istanbul Stock Exchange. Int. Rev. Financ. Anal. 12, 579–590. Chaudhuri, K., Wu, Y., 2003. Random walk versus breaking trend in stock prices: evidence from emerging markets. J. Bank. Financ. 27, 575–592. Cheung, K.-C., Coutts, J.A., 2001. A note on weak form market efficiency in security prices: evidence from the Hong Kong Stock Exchange. Appl. Econ. Lett. 8, 407–410. Demirer, R., Karan, M.B., 2002. An investigation of the day-of-the-week effect on stock returns in Turkey. Emerging Markets Finance & Trade 38Turkey in the financial liberalization process (II) 47–77. Grieb, T., Reyes, M.G., 1999. Random walk tests for Latin American equity indexes and individual firms. J. Financ. Res. 22, 371–383. Harvey, D.I., Leybourne, S.J., Xiao, B., 2008. A Powerful Test for Linearity When the Order of Integration is Unknown. Studies in Nonlinear Dynamics & Econometrics, 12. Berkeley Electronic Press 1–24. Hasanov, M., 2009. Is South Korea's stock market efficient? Evidence from a nonlinear unit root test. Appl. Econ. Lett. 16, 163–167. Hasanov, M., Omay, T., 2007. Are the transition stock markets efficient? Evidence from nonlinear unit root tests. (Online) Cent. Bank Rev. (ISSN: 1305-8800) 7, 1–12. Hasanov, M., Omay, T., 2008. Nonlinearities in emerging stock markets: evidence from Europe's two largest emerging markets. Appl. Econ. 40, 2645–2658. Hsieh, D.A., 1991. Chaos and nonlinear dynamics: application to financial markets. J. Financ. 46, 1839–1877. Kapetanios, G., Shin, Y., Snell, A., 2003. Testing for a unit root in the nonlinear STAR framework. J. Econ. 112, 359–379. Karan, M.B., Kapusuzoglu, A., 2010. An Analysis of the random walk and overreaction hypotheses through optimum portfolios constructed by the nonlinear programming model. Aust. J. Basic Appl. Sci. 4, 1215–1220. Kavussanos, M.G., Dockery, E., 1996. Testing the efficient market hypothesis using panel data, with application to the Athens stock market. Appl. Econ. Lett. 3, 121–123. Kim, S.-W., Mollick, A.V., Nam, K., 2008. Common nonlinearities in long-horizon stock returns: evidence from the G-7 stock markets. Glob. Financ. J. 19, 19–31. Kruse, R., 2011. A new unit root test against ESTAR based on a class of modified statistics. Stat. Pap. 52, 71–85. Lim, K.P., Brooks, R., 2011. The evolution of stock market efficiency over time: a survey of the empirical literature. J. Econ. Surv. 25, 69–108. Lim, K.P., Liew, V.K.S., 2007. Nonlinear mean reversion in stock prices: evidence from Asian markets. Appl. Financ. Econ. Lett. 3, 25–29. Lo, A.W., Mackinlay, C.A., 1988. Stock market prices do not follow random walks: evidence from a simple specification test. Rev. Financ. Stud. 1, 41–66. McMillan, D.G., 2003. Non-linear predictability of UK stock market returns. Oxf. Bull. Econ. Stat. 65, 557–573. McMillan, D.G., 2005. Non-linear dynamics in international stock market returns. Rev. Financ. Econ. 14, 81–91. Munir, Q., Mansur, K., 2009. Is Malaysian stock market efficient? Evidence from threshold unit root tests. Econ. Bull. 29, 1359–1370. Narayan, P.K., 2005. Are the Australian and New Zealand stock prices nonlinear with a unit root? Appl. Econ. 37, 2161–2166. Narayan, P.K., 2006. The behaviour of US stock prices: evidence from a threshold autoregressive model. Math. Comput. Simul. 71, 103–108. Narayan, P.K., 2008. Do shocks to G7 stock prices have a permanent effect? Evidence from panel unit root tests with structural change. Math. Comput. Simul. 77, 369–373. Narayan, P.K., Smyth, R., 2004. Is South Korea's stock market efficient? Appl. Econ. Lett. 11, 707–710. Narayan, P.K., Smyth, R., 2005. Are OECD stock prices characterized by a random walk? Evidence from sequential trend break and panel data models. Appl. Financ. Econ. 15, 547–556. Ozdemir, Z.A., 2008. Efficient market hypothesis: evidence from a small open-economy. Appl. Econ. 40, 633–641. Ozer, G., Ertokatli, C., 2010. Chaotic processes of common stock index returns: an empirical examination on Istanbul Stock Exchange (ISE) market. Afr. J. Bus. Manag. 4, 1140–1148. Poterba, J.M., Summers, L.H., 1988. Mean reversion in stock prices: evidence and implications. J. Financ. Econ. 22, 27–59. Qian, X.-Y., Song, F.-T., Zhou, W.-X., 2008. Nonlinear behaviour of the Chinese SSEC index with a unit root: evidence from threshold unit root tests. Phys. A 387, 503–510. Rapach, D.E., Wohar, M.E., 2006. The out-of-sample forecasting performance of nonlinear models of real exchange rate behavior. Int. J. Forecast. 22, 341–361. Shively, P.A., 2003. The nonlinear dynamics of stock prices. Q. Rev. Econ. Financ. 43, 505–517. Taylor, M.P., Peel, D.A., Sarno, L., 2001. Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles. Int. Econ. Rev. 42, 1015–1042.