Economic Modelling Reexamining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
Reexamining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
Economic Modelling
2014 / 02 Vol. 38
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Reexamining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
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Reexamining the Turkish stock market efficiency: Evidence from nonlinear unit root tests
Gozbasi, Onur, Kucukkaplan, Ilhan, Nazlioglu, Saban
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Economic Modelling 38 (2014) 381–384 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod Reexamining 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 reexamines 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 (nonstationary) process, supporting the EMH in Turkish stock market which has weakform 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; AlLoughani 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 weakform nor semistrongform 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 randomwalk hypothesis ⁎ Corresponding author. Tel.: +90 352 3240000; fax: +90 352 3240004. Email address: onurgozbasi@gmail.com (O. Gozbasi). 02649993/$ – 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 19921999 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 ISE100 index Accept 21 ﬁrms' stocks in ISE30 index ISE100 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 reexamines 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 nonstationary. 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 nonstationary. 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 chisquare 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 BIST100 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 BIST100 composite 1 2 3 1 2 3 1 2 3 1 2 3 Industry Financial Services Critical values 1% 5% 10% Loglevel 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 ﬁrstorder 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 onesided, β2 is twosided, 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 Waldtype 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 twosummands in this statistic can be interpreted as: the ﬁrst term is the squared tratio for the hypothesis β⊥ ¼ 0 that β⊥ is orthog2 2 onal to β1 and the second term is the squared tratio for the hypothesis β1 = 0. The test statistic in Eq. (6) has a nonstandard 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 subsectors – 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 loglevel series, the null hypothesis of the unit root cannot be rejected at each lag length for the BIST100, 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 loglevel 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 (nonstationary 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 detrended 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 nonstationary process. Thereby, the main result suggests that the Turkish stock market supports the validity of the EMH and it is weakform 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 onesided. 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. AlLoughani, N., Chappell, D., 1997. On the validity of the weakform 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. 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