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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

Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests

Gozbasi, Onur, Kucukkaplan, Ilhan, Nazlioglu, Saban

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Economic Modelling

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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.
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