Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

Gadjah Mada International Journal of Business
Vol. 13, No. 3 (September - December 2011): 209 - 226

The Behavior of Indonesian Stock Market:
Structural Breaks and Nonlinearity
Rahmat Heru Setianto
Department of Management Faculty of Economics and Business, Universitas Airlangga, Indonesia

Turkhan Ali Abdul Manap
Department of Economics, Kulliyyah of Economics and Management Sciences, International Islamic University,
Malaysia

Abstract: This study empirically examines the behaviour of Indonesian stock market under the efficient
market hypothesis framework by emphasizing on the random walk behaviour and nonlinearity over the
period of April 1983 - December 2010. In the first step, the standard linear unit root test, namely the
augmented Dickey-Fuller (ADF) test, Phillip-Perron (PP) test and Kwiatkowski-Philllips-Schmidt-Shin
(KPSS) test identify the random walk behaviour in the indices. In order to take account the possible
breaks in the index series Zivot and Adrews (1992) one break and Lumsdaine and Papell (1997) two
breaks unit root test are employed to observe whether the presence of breaks in the data series will
prevent the stocks from randomly pricing or vice versa. In the third step, we employ Harvey et al. (2008)
test to examine the presence of nonlinear behaviour in Indonesian stock indices. The evidence of nonlinear behaviour in the indices, motivate us to use nonlinear unit root test procedure recently developed by
Kapetanios et al. (2003) and Kruse (2010). In general, the results from standard linear unit root test, Zivot
and Adrews (ZA) test and Lumsdaine and Papell (LP) test provide evidence that Jakarta Composite
Index characterized by a unit root. In addition, structural breaks identified by ZA and LP test are corresponded to the events of financial market liberalization and financial crisis. The nonlinear unit root test
procedure fail to rejects the null hypothesis of unit root for all indices, suggesting that Jakarta Composite
Index characterized by random walk process supporting the theory of efficient market hypothesis.
Abstrak: Penelitian ini secara empiris mengamati perilaku pasar saham Indonesia dalam kerangka hipotesis
pasar yang efisien dengan menekankan pada perilaku pergerakan harga acak (random walk) dan nonlinier
selama periode April 1983 - Desember 2010. Pada langkah pertama digunakan uji unit root yang standar
dan linier, yaitu uji augmented Dickey-Fuller (ADF), Phillip-Perron (PP) dan Kwiatkowski-Philllips-SchmidtShin (KPSS), yang mengidentifikasi perilaku random walk pada indeks. Untuk memperhitungkan kemungkinan
adanya patahan (breaks) dalam indeks, digunakan uji Zivot dan Adrews (1992) satu breaks dan Lumsdaine
dan Papell (1997) dua breaks unit root, untuk mengamati apakah kehadiran patahan dalam seri data akan
mempengaruhi perilaku harga saham dari perilaku random atau sebaliknya. Pada langkah ketiga, kami
menggunakan model Harvey et al. (2008) untuk memeriksa adanya perilaku nonlinier dalam indeks saham
Indonesia. Adanya temuan perilaku nonlinier dalam indeks, memotivasi peneliti untuk menggunakan

Corresponding authors. E-mail: rahmat.heru@feb.unair.ac.id, and turkhan@iium.edu.my
ISSN: 1141-1128
http://www.gamaijb.mmugm.ac.id/

209

Setianto and Abd. Manap

prosedur tes nonlinear unit root yang dikembangkan oleh Kapetanios et al. (2003) dan Kruse (2010).
Secara umum, hasil dari uji unit root yang standar dan linier, Zivot dan Adrews (ZA) dan Lumsdaine dan
Papell (LP) menunjukkan bahwa IHSG memiliki perilaku pergerakan harga yang acak. Selain itu, adanya
patahan struktural diidentifikasi oleh uji ZA dan LP yang berhubungan dengan peristiwa liberalisasi pasar
keuangan dan krisis keuangan. Prosedur uji unit root nonlinier gagal untuk menolak nul hipotesis unit root
untuk semua indeks, menunjukkan bahwa IHSG ditandai oleh proses random walk mendukung teori
hipotesis pasar efisien.

Keywords: linearity and non-linearity; smooth transition autoregressive (STAR) models; stock markets; structural breaks

210

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

Introduction
Financial markets such as bond and
stock markets plays important role in promoting economic efficiency and economic growth
by channeling funds from people who do not
have a productive use to those who need
funds for productive investment. Equally
important is the information efficiency of the
financial market. Market efficiency is essential because it helps to explain why asset
prices change in financial markets and how
these changes take place. More precisely, efficient market implies that 1) one investment
is as good as any other because the securities’ prices are correct; 2) a security’s price
reflects all available information about the
intrinsic value of the security; 3) security
prices can be used by managers of both financial and nonfinancial firms to assess their
cost of capital (cost of financing their investments) accurately and hence that security
prices can be used to help them make the
correct decisions about whether a specific
investment is worth making or not (Mishkin
2004). Thus market efficiency is indisputably
desirable for market development and economic growth as a whole.
In an efficient market, changes of stock
prices are influenced by different types of
information. Fama (1970) distinguishes three
versions of market efficiency depending on
the underlying information set that is available to market participants: weak form, semistrong form and strong form. Markets are said
to be weak form efficient if the current stock
prices fully reflect information contained in
the past realizations of the price. In an efficient market, stock prices only response unpredictable news, news are random, thus
stock price changes should be also unpredictable and random and one cannot earn abnormal returns on the basis of historical infor-

mation on prices and trading volumes. Stock
prices are characterized by a unit root if stock
prices follow a random walk. Thus, testing
for a unit root in stock prices is one way to
validate the weak form efficiency hypothesis.
Over the years, there has been a large
body of empirical research concerning the
validity of the efficient market hypothesis
with respect to stock markets in both developed and developing countries. Empirical
research on testing the random walk hypothesis has produced mixed results. For instance,
Fama and French (1988), Lo and MacKinlay
(1988); Poterba and Summers (1988); Urrutia
(1995); Grieb and Reyes (1999); Chaudhuri
and Wu (2003); Shively (2003); Narayan
(2008) have found that stock indexes are not
characterized by a unit root. In contrast, others studies have found stock prices are characterized by a unit root process. For instance,
Hubber (1997); Lee (1992); Ozdemir (2008);
Narayan (2005); Narayan and Smyth (2005);
Qiant et al. (2008).
As far as the emerging markets are concerned, it is widely believed that the majority
of emerging markets are less efficient than
developed markets due to certain market
imperfections such as transaction costs, poor
quality of information disclosures, thin trading, and inadequate financial and accounting
regulations. For this reason, recent studies on
emerging markets have mainly stressed the
weak form efficiency whereas the literature
on developed markets is concerned by all
three forms of efficiency. The empirical evidence is also inclusive for the developing
countries. These studies on emerging stock
markets can be divided into two groups depending on findings. Researches who finds the
evidence to support the weak-form efficiency
[e.g., (Urrutia 1995); (Ojah and Karemera
1999); (Abrosimova et al. 2005); (Moustafa
2004)], and others shows the evidence of pre211

Setianto and Abd. Manap

dictability or rejection of the random walk
hypothesis in stock returns [e.g., (Huang
1995); (Poshakwale 1996); (Mobarek and
Keasey 2002); (Khaled and Islam 2005)].
Considering the theoretical and practical significance, the testable implications and
conflicting empirical evidence of the random
walk hypothesis motivates us to have a fresh
look at this issue of weak-form efficiency in
the context of an emerging market, namely
Indonesian stock market. This study is potentially interesting case study for a developing capital market, which shares most of the
characteristics of a typical emerging market.
Secondly, the liberation of financial market
and advance on technology, these markets
become more integrated with global equity
markets, which attracting more international
investors in the hope to benefit from higher
abnormal returns and portfolio diversification, where market efficiency has important
implications for those investors. Thirdly, the
majority of previous studies apply the traditional unit root test in testing the null hypothesis of a unit root in stock prices. It is well
known that the tradition test may bias in not
rejecting the null hypothesis in the presence
of structure breaks (Perron 1989). Chauduri
and Wu (2003), Narayan and Smyth, (2004),
Narayan (2005), Lean and Smyth (2007),
Narayan (2008); Lee et al. (2010) investigate
the stationarity properties using the new unit
test with structure breaks for other markets.
Furthermore, economic theory suggests
that the behavior of stock prices may exhibit
nonlinear pattern in the series due to transaction costs and market frictions, heterogeneity of agent’s investment objectives, and
diversity in agent beliefs (Hasavov 2009).1
1

Therefore the reliability of the finding from
existing studies assuming linearity in the time
series is questionable. To this end, some researcher then adopt to Narayan (2005); Munir
and Mansur (2009) investigate the random
walk hypothesis in the stock market by adopting nonlinear threshold autoregressive (TAR)
model of Caner and Hansen (2001). Furthermore, Hasanove and Omay (2007) and
Hasanov (2009) are among the studies that
examine the random walk hypothesis by
adopting nonlinear unit root test procedure
proposed by Kapetanios et al. (2003).
As far as Indonesian stock is concerned,
limited empirical studies are available yet the
results are mixed. While Huang (1995), Huang
and Yang (1995), Groenwold and Ariff (1998)
Karemera et al. (1999) find the Indonesian
stock weak-form efficient, Magnusson and
Hig gs (2005), Fuss (2005), Kim and
Shamsuddin (2006), Hoque et al. (2006) and
Zulfadin (2008) find that the market is weakform inefficiency. Given Indonesian has gone
through financial liberation, and financial crisis that may cause structural breaks. Previous studies did not take structure breaks into
consideration. Furthermore, previous studies
are based on the assumption of linear data
generating process. Therefore the reliability
of the finding from existing studies is questionable.
Thus, this paper attempts to overcome
the above mentioned problems and contributes to the existing literature on the Indonesian stock market efficiency by taking both
structural breaks and the nonlinearity into
consideration. More specifically, this paper
contributes to exiting literature on random
walk hypothesis for Indonesian stock market

See, Brock and Lebaron (1996), Brock and Hommes (1998), Peters (1994), Guillaume et al. (1995), Dumas
(1992); Shleifer (2000), Hong and Stein (1999), among others

212

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

in four novel ways. Firstly, in addition to the
conventional unit root test, the Zivot and
Andrew (1992) one break and the Lumsdaine
and Papell (1997) two-break unit root tests
are used. Secondly, we employ the powerful linearity test proposed by Harvey et al. (2008)
which is applicable when the order of integration of the time series under investigation
is uncertain. It reveals that the Indonesian
Stock index is nonlinear process in which allow us to question the validity of linear unit
root test. Thirdly, we use nonlinear STAR unit
root test developed by Kapetanios et al.
(2003) and Kruse (2010) which allows for
testing unit root behavior in a more general
nonlinear framework where the transition
between regimes occurs in a smooth manner,
rather than instantaneously. Finally, we also
estimate the speed of transition parameter.
The estimated ESTAR model indicates that
the Indonesian stock market is not mean reversion process.
The rest of the study is organized as
follows: Section two briefly describe about
the methodology employed in the study. Data
on which analysis is based is then presented
in Section 3. Section 4 in turns discusses the
empirical results and some implications of
the study. Finally, Section 5 concludes the
study.

Therefore, Perron (1989) then developed
three alternative models, which accommodate a break in the trend function, namely: a)
The crash model, which allows for a one time
structural break in the intercept of the trend
function; b) The changing growth model,
which allows for a structural break in the
slope; c) The crash-cum-growth model, which
allows for a structural break in the intercept
and slope.
However, Zivot and Andrews (1992)
have argued that selecting the break point a
priori based on ex post examination or knowledge of the data, as developed by Perron
(1989) could lead to an over rejection of the
unit root hypothesis. Hence, to avoid spurious results the break date is also treated as
being endogenous. To this end, Zivot and
Andrews (1992) developed two versions of
the sequential trend break model to investigate the unit root hypothesis, as follows:
Model A:
Y t= 0 + Yt-1 + t + DUt +
k

d Yt-j + t.................(1)

j=1 j


Model C:
Y t= 0 + Yt-1 + t + DUt + DTt +
k

Methodology
Unit Root Test With One
Structural Break
According to Perron (1989), if structural break exist, the power to reject a unit
root decreases when the stationary alternative is true and the structural break is ignored.


d Yt-j + t.........................(2)
j=1 j
The null hypothesis for model 1 and 2
is that  = 0, which implies there is a unit
root in Yt, against the alternative hypothesis
 < 0, which implies that Yt is breakpoint
stationary. Where DUt is an indicator dummy
variable for a mean shifting occurring at time
TB, while DT is the corresponding trend shift
variable, where:

213

Setianto and Abd. Manap

DUt={

1 if t > TB

0 otherwise

Y t= 0 + Yt-1 + t + DUt + DTt +
k

d Yt-j + t
DU2t + DT2t 
j=1 j

and
DUt={

t - TB if t > TB

0 otherwise
Furthermore, to implement the sequential trend break model, some region must be
chosen such that the end points of the sample
are not included. This is because in the presence of the end points the asymptotic distribution of the statistics diverges to infinity.
Zivot and Andrews (1992) suggest the trimming region be specified as (0.15T, 0.85T),
which is followed here. Thus, the break points
are selected by choosing the value of TB for
which the ADF t-statistic is maximized.

Unit Root Test
with Two Structural Breaks
A possible problem with the Zivot and
Andrews (1992) test is the loss of power if
there are two structural breaks in the series.
In response to this condition, Lumsdaine and
Papell (1997) proposed the extension of
Zivot and Andrews (1992) model A and C to
allow for two structural breaks. Lumsdaine
and Papell (1997) then call these models AA
and CC respectively. Model AA allows for
two breaks in the intercept of the trend and
model CC allows for two breaks in the intercept and slope of the trend. Model AA can
be represented as follows:
Y t= 0 + Yt-1 + t + DUt + DUt +
k

d Yt-j + t.................(3)

j=1 j


Model CC takes the following form:

214

.............................................(4)
The null and alternative hypotheses are
the same as in the one break case. DU1t and
DU2t are indicator dummy variables for a
mean shift occurring at TB1 and TB2 respectively, where TB2 > TB1 + 2 and DT1t and
DT22 are the corresponding trend shift variables:
DU1t {
DU2t {

1

if t > TB1

0

otherwise

1

if t > TB2

0

otherwise

and
DU1t={
DU2t={

t - TB1 if t > TB1

0

otherwise

t - TB1 if t > TB1

0

otherwise

The same trimming region is used as in
the case of model A and C. The critical values
are calculated using the same methodology
as in the case of model A and C.

Nonlinear Unit Root Test of
Kapetanios et al. (2003)
Consider a univariate smooth transition
autoregressive (STAR) model of order one:
y t =yt-1 + yt-1F(;yt-d) + t
t= 1, ... T

........................(5)

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

where yt is a mean zero stochastic process
and eti.i.d. (0, 2), and  and  are unknown
parameters. The transition function is assumed to be of the exponential form:
F(;yt-d)= 1 - exp(-y2t-d).................(6)
Where it is assumed that  and d 1is
the delay parameter. The exponential function is bounded between zero and one, i.e.
F:R[0,1] has the properties F(0)= 0;
limxF(x)= 1and is symmetrically U-shaped
around zero. The parameter  is slope coefficient and determines the speed of transaction between to regimes that correspond to
extreme values of the transition function.
Substituting (6) into (5) one obtains the following exponential STAR (ESTAR) model:
yt= yt-1 + yt-1 [1 - exp(-y2t-d)] + t ......(7)
Subtract yt-1 from both side of (3), we
have:
yt= yt-1 + yt-1 [1 - exp(-y2t-d)] + t ......(8)
where . The ESTAR model has a nice
property that it allows modeling different
dynamics of series depending on the size of
the deviations from the fundamental equilibrium (Teräsvirta 1994; Michael et al. 1997).
The theory suggests that arbitrageurs
shall not engage in reversion strategies if deviations from the equilibrium are small in size
(arbitrage is not profitable). If the deviations
from equilibrium are large enough, however,
arbitrageurs shall engage in profitable reversion trading strategies, and thus bring the
prices to their equilibrium levels. In the context of ESTAR model, this would imply that
while  is possible, one must have  < 0
and  for the process to be globally

stationary. Under these conditions, the process might display unit root for small values
of y2t-d, but for larger values of, it has stable
dynamics, and as a result, is geometrically
ergodic. Furthermore, the speed of mean reversion increases with the size of deviation
from the fundamental equilibrium.
Following the practice in the literature
(Balke and Fomby 1997 in the context of
TAR models and Michael et al 1997 in the
context of ESTAR models), Kapetanios et
al. (2003) further impose, implying that follows a unit root in the middle regime. The
reason is that, in some economic contexts it
is reasonable to assume that the variable displays a mean reverting behavior towards an
attractor when it is sufficiently far away from
it, but a random walk representation in the
neighborhood of the attractor. In this case,
the ESTAR model can be written as:
yt= yt-1 [1 - exp(-y2t-d)] + t .............(9)
The global stationarity of the process
can be established by testing the null hypothesis H0 : = 0 against the alternative H0 : >
1. However, testing the null hypothesis directly is not feasible since the parameter is
not identified under the null. To overcome
this problem, Kapetanios et al. (2003) follow suggestion of Luukkonen et al. (1988)
to replace the transition function by its appropriate Taylor approximation to derive a ttype test statistic. Replacing the transition
function with its first order Taylor approximation yields the following auxiliary regression:
yt= y3t-1 + t .....................(10)
where et comprises original shocks t as well
as the error term resulting from Taylor ap-

215

Setianto and Abd. Manap

proximation. The test statistic for  = 0
against < 0 is obtained as follows:
v

v

tNL= /s.e.()...........................(11)
where,
v

=

the OLS estimate, and

v

v

s.e.()= the standard error of .
The asymptotic distribution of this test tNL is
non-standard and KSS (2003) derive it and
provide asymptotic critical values.
To accommodate stochastic processes
with nonzero means and/or linear deterministic trends, the following modifications are
needed. In the case where the data has nonzero mean, i.e., xt =  + yt, one must replace
the raw data with de-meaned data yt = xt - x
where x is the sample mean. In the case where
the data has a nonzero mean and a nonzero
linear trend, i.e., xt =  + t + yt, one must
instead use the de-meaned and de-trended
data yt = xt t where and  are ordinary least square (OLS) estimators of  and
. If errors in (10) are serially correlated, one
may augment (9) and (10) into following:
v

However, Kapetanios et al. (2003) test
assumes that the location parameter c in the
smooth transition function is equal to zero.
According to Kruse (2010) when relaxing this
assumption, we are faced with a nonstandard testing problem. Since standard inference
c techniques are not appropriate in this situation, Kruse (2010) then proposed new approach to allow for a non-zero location parameter c in the exponential transition function. Following Kapetanios et al. (2003),
Kruse (2010) applies a first order Taylor approximation to G[yt;,c=(1-exp{-(yt-1 - c]2})
around  = 0 and proceed with the test regression:
yt = 1y3t-1 + 2y2t-1 + 3yt-1 + ut ...(14)

v

v

v

p

yt =  jyt-1 + yt-1[1 - exp(-y2t-d)] + t
j=1

.....................................................(12)
p

yt =   jyt-j + y3t-d + t ...............(13)
j=1

In practice, the number of augmentations p and the delay parameter d must be
selected prior to the test. Kapetanios et al.
(2003) propose that standard model selection
criteria or significance testing procedure be
used for selecting the number of augmentations p. They also suggest that the delay pa216

rameter d be chosen to maximize goodness
of fit over d - {1,2,...dmax}. However, in practice, d is set to be one, see for example,
Kapetanios et al. (2003) and Daiki (2005,
2006).

Following Kapetanios et al. (2003) he
impose 3= 0 to improve the power of the
test, hence we proceed with:
Dyt = b1y3t-1 + b2y2t-1 + ut .......(15)
where 1=  and 2= 2c. Kruse (2010)
interested in the pair of hypotheses given by
H0:  = 0 against H1:  > 0. In the regression
(15), this pair of hypothesis is equivalent to
H0: 1 = 1 = 0 against H1: 1 < 0, 2  0.
Note that the two-sidedness of 2 under H1
stems from the fact that c is allowed to take
real values. This testing problem is nonstandard in the sense that one parameter is one
sided under H1 while the other is two-sided.
A standard Wald test would be inappropriate
and he therefore applies the methods of
Abadir and Distaso (2007) to derive a suit-

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

able test. In a nutshell, the one-sided parameter is orthogonalized with respect to the two
sided one. The modified Wald test builds upon
the one-sided parameter (1) and the trans1 that are
formed two-sided parameter, say ,
2
stochastically independent by definition.
Let the parameter vector of the regression model (15) be = [1 2]’. Following the
notation of Abadir and Distaso (2007), the
null hypothesis of a unit root is written as:
H0: h()h1() h2()]’ [b1 b2]’ - [0 0]’ ...................(16)
The alternative hypothesis of a globally
stationary ESTAR model is given by:
H1 : h1 ()<0 or h2 ()
which includes the subset hypothesis
H1:h1()< 0 and h2 ()  Theorem 6 in
Abadir and Distaso (2007) states that the
modified Wald test is consistent against H1
as well as H1.
Kruse (2010) then modified the standard Wald test statistic based on the Hessian
matrix. Hence, now we have the new test statistic for the unit root hypothesis against globally stationary ESTAR. A simpler and more
intuitive way to formulate the statistic is:


= t2 1 = 0 + 1(1 < 0)t2
2

1=0

The two summands appearing in the test
statistic can be interpreted as follows: the
first term is a squared t-statistic for the hy1
pothesis  2  1 - 1v21/v11with 1 being or2
thogonal to 1. Additionally, the second term
is a squared t-statistic for the hypothesis 1=

0, the one-sidedness under H1 is achieved by
the multiplied indicator function.

Data Description
This study employs monthly Jakarta
Composite index (JCI) over the period April
1983 to December 2010. The index is taken
from Bloomberg database through a subscription by the Kulliyyah of Economics and
Management Sciences, International Islamic
University Malaysia. Specifically we retrieve
the closing prices of the last trading days of
all months and transformed into natural logarithm.

Empirical Results and
Discussion
Standard Linear Unit Root Test
Results
As preliminary step, the traditional unit
root test such as ADF (Dickey and Fuller
1981), Phillip Perron and Kwiatkowski et al.
(KPSS 1992) tests are employed, (see Table
1) indicates that the traditional unit-root tests
provide no evidence of trend stationary, failing to reject the unit-root null at conventional
significance levels. However, we find evidence that this variable is stationary when
expressed in the first difference. Accordingly,
JCI series seem to be integrated of order 1,
or I (1). Hence, we can conclude that Jakarta
Composite Index series behave according to
random stochastic process.

217

Setianto and Abd. Manap

Figure 1. Plot of Monthly Closing Price of the Jakarta Composite Index and Its
Transformation (April 1983-December 2010)
(a)
4000
JCI
3000

2000

1000

0
84 86 88 90 92 94 96 98 00 02 04 06 08

10

(b)
9
LJCI
8

7

6

5

4
84 86 88 90 92 94 96 98 00 02 04 06 08

218

10

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

Table 1. Linear Unit Root Test on Jakarta Composite Index
Series

ADF

PP

KPSS

No Trend

Trend

No Trend

Trend

No Trend

Trend

lnJCI

-0.3485

-2.1430

-0.2529

-2.0568

1.7791*

0.1744**

lnJCI

-14.8831*

-14.8809*

-14.8975*

-14.8809*

0.0929

0.0687

Note: *, and ** denote significance at 1% and 5% level respectively

Table 2. Unit Root Test with One Structural Break on Jakarta Composite Index
Model A

Model C

TB


10/1988
-0.1083
[-3.0265]

10/1988
-0.1064
[-2.9393]




0.0567**
[2.4670]
-

k

8

0.0482***
[1.5045]
-0.0003
[-0.3779]
8

Critical values
for t
1%
5%
10%

-5.34
-4.80
-4.58

-5.57
-5.08
-4.82

Notes: The optimum lag length k is selected according
to Schwarz Information Criteria (SIC). Model A
refers to structural break in the intercept only
k

Yt= k + Yt-1 + t + DUt + j =
1djYt-1 + t, and model C refers to structural
breaks both in the intercept and slope of the
trend function Yt= k + Yt-1 + t + DTt
k

+ DU2 t + DT2t + DT2t j 
1djYt-j + t. Number in parentheses are t-statistics. *,** and *** denote significance at 1 percent, 5 percent and 10percent level respectively.

Zivot and Andrews (1992) One
Structural Break Test
Table 2 reports the Zivot and Andrews
(ZA) test results for Jakarta Composite Index. Table 2 clearly reveals that the null of
unit root hypothesis still cannot be rejected
for series of Jakarta Composite Index even
after the structural breaks is allowed. It can
be identified from the estimated test statistics of  (-3.0265) which is greater than ZA
critical value for all significance level. While
for model C also indicating the same results,
where the test statistics of coefficient  (2.9393) is greater than ZA critical value, fail
to reject null hypothesis of non-stationary.
Furthermore, from the estimated coefficient of  in model A the break in the intercept is found to be statistically significant at
the 5 percent level (based on critical value
from the standard normal distribution). While
for model C it is found that estimated coefficient of  is statistically significant at 10 percent level, implying the Jakarta Composite
Index series exist at least one structural break
in the intercept. The break date provided by
model A and C is during October 1988. Period of 1987-1988 is corresponds to the issuance of PAKDES (December Package) 87
to give ways for companies to go public and
foreign investors to invest their money in Indonesia. Furthermore, in December 1988, the
government issued PAKDES 88 to encour-

219

Setianto and Abd. Manap

age companies go public and some other regulations that brought positive impacts on the
capital market growth.

Lumsdaine and Papell (1997) Two
Structural Breaks Test
We now consider the case in which the
series assumed to contain two structural
breaks, with the break point determined endogenously. We estimate model AA and CC
and compute the t-statistic for testing the
level of significant for each parameter. Table
3 presents the test results, with t-ratios exhibited in parentheses. Several observations
can be drawn from Table 3.
Model AA in the Table 3 provides
strong evidence that by allowing for two
structural breaks it is still not possible to reject the unit root null hypothesis, indicated
from the statistical value of the estimated
coefficient  (-4.0574) which is greater than
LP critical value at all significant level. While,
the results obtained from model CC indicate
that Jakarta Composite Index is characterized
by unit root process, it can be seen from the
statistical value of  (-5.1812) which is
greater than critical value of LP test for all
significant level. These results support the existence of random walk process in the Jakarta
Composite Index.
In addition, according to model AA the
estimated coefficient of  and  are statistically significant at 1 percent level (based on
critical value from the standard normal distribution), implying that in the stock price
series there exist at least two structural breaks
in trend. While according to model CC, we
found that first break in the slope is statistically significant at 1 percent, this results indicated from the statistical value of 
(4.9237). For the second break, we have significant break in the slope at 5 percent sig-

220

nificant level and break in the intercept at 1
percent level of significant, as indicated from
the statistical value of  (2.5550) for break
in the slope and statistical value  (4.6856)
for break in the intercept.
Table 3. Unit Root Test with Two Structural Break on Jakarta Composite Index
Model A

Model C



10/1988
08/2004
-0.1908
[-4.0574]
0.2814*
[3.6508]
0.1664**
[2.6690]
-



-

K

8

08/1988
01/2000
-0.0958
[-5.1812]
0.1524*
[4.9237]
-0.0602**
[-2.5550]
-0.0003
[-1.2857]
0.0017*
[4.6856]
8

TB1
TB2
A



Critical values for t
1%
-6.94
5%
-6.24
10%
-5.96

-7.34
-6.82
-6.49

Notes: The optimum lag length k is selected according
to Schwarz Information Criteria (SIC). Model A refers
to structural break in the intercept only Yt= k + Ytk

1

+ t + DUt + DUt +  j = 1djYt-1 + t and

model CC refers to structural breaks both in the intercept and slope of the trend function Yt= k + Yt-1
k

+ t +DUt + DTt + DU2t + DT2tj 
1djYt-j + t. Number in parentheses are t-statistics.
*,** and *** denote significance at 1 percent, 5 percent
and 10 percent level respectively.

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

Furthermore, the statistically significant
structural break in the model AA is happened
during October 1988 and August 2004, while
for model CC is happened during August 1988
and January 2000. As discussed in the Zivot
and Andrews (1992) model, the first structural break for model AA and CC for JCI series is October 1988 and August 1988, corresponds to some important policies made by
Indonesian stock market authorities. PAKTO
(October Package) 88 designed for the banking sector, but having an impact on the development of capital markets. PAKTO 88
contains provisions on 3 L (Legal, Lending,
Limit), and the imposition of tax on deposit
interest. The imposition of this tax had a
positive impact on the development of capital markets. Because with the release of this
policy means the government gives equal
treatment between the banking sector and
capital market sectors. Followed by the issuance of PAKDES 88, this package basically
gives further impetus to the capital market
by opening opportunities for the private sector to hold the stock. Prior to these two policies, on June 1988 Indonesia Pararel Bourse
started to operate and managed by the securities and money trading organization, it consisted of brokers and dealers. Because these
three policies Indonesian stock market became active capital markets for the period
1988 to the present. On the other hands,
during October 1987 stock market around the
world crashed, shedding a huge value in a very
short time. Major indexes of market valuation in the United States dropped 30 percent

2

or more. This was the greatest loss Wall Street
had ever suffered on a single day.2
The second break for model CC is January 2000, where during 2000 Indonesian stock
market experienced a negative trend, due to
the political and economic instability after
general election on the late of 1999. The
negative trend was ended after 2003-2004
period as indicated from the second break of
model AA which is happened on August
2004. As we can see from the plot graph in
the Appendix, starting from this period
Jakarta composite index went up continued
until the end of 2007 where the global financial crisis started to attack Indonesian capital market.

Linearity Test
Before we perform the nonlinear unit
test, we investigate whether we can reject the
linear autoregressive model in favor of nonlinear model. The existing tests of the null
of linearity against a nonlinearity alternative
in the literature such proposed by Luukkonen
et al. (1998), Granger and Teräsvirta (1993)
and Teräsvirta (1994), however, rely on an
assumption of I(0) behavior in the underlying series. In this study, we employ linearity
test newly developed by Harvey et al. (2008).
This test, the W test, does not require an a
priori assumption as to the order of integration of the process. Using this test, we obtain W0.7.24 which is significant at the 5
percent level suggesting that the linearity is
rejected.

http://hnn.us/articles/895.html

221

Setianto and Abd. Manap

Table 4. Nonlinear Unit Root Test on Jakarta Composite Index

tNL /

SE of 

Demeaned Series

De-trended Series

KSS

T

KSS



-0.11020
0.00658
0.00509

1.269

-2.01698
0.00432
0.00323

4.172

13.75
10.17
8.60

-3.93
-3.40
-3.13

17.10
12.82
11.10

Critical values of the tNL and  statistic
1%
-3.48
5%
-2.93
10%
-2.66

Notes: Asymptotic critical values of the tNL statistic are taken from Table 1, Kapetanios et al. (2003). Asymptotic critical
values of the  statistic are taken from Table 1, Kruse (2010).

Nonlinear unit root test of
Kapetanios et al. (2003)
Having established the evidence of
nonlinearity based on the Harvey et al. (2008)
test, we use the test of Kapetanios et al.
(2003) as well as Kruse (2010) where the null
of a linear unit root process is tested against
the alternative of a globally stationary nonlinear ESTAR model. The estimated results
of nonlinear unit root test base on equation
(13) and (18) for Jakarta Composite Index are
presented in Table 4. Table 4 reveals, the null
hypothesis of unit root could not be rejected
for both demeaned and de-trended series, indicated from the value of tNL which is greater
than tNL critical value for all significance level.
In line with the results form KSS test, the
Kruse (2010) test also cannot reject the null
hypothesis of unit root giving the value of 
test which is less than their critical value. In
addition, the estimates of transition parameters  for both series are also insignificant,
indicating that no mean reversion for the series under consideration. This is an expected

222

result since under the null hypothesis that  =
0, the series follow a unit root.

Conclusions
This study investigates the behavior of
Indonesian stock market using various statistical tools. The results from the conventional unit root test with and without structural breaks indicate that the stock market is
characterized by a unit root process. Further
nonlinear test revealed that the Indonesian
stock market prices follow nonlinear dynamic
process. An application of the recent nonlinear unit test of KSS (2003) and Kruse (2010)
both indicate that Indonesian stock market
prices are consistently characterized by random walk behavior in line with the efficient
market hypothesis. Furthermore, we also find
that Indonesian stock market exhibit significant structural breaks.
Our finding has important implications
to both academician and investment practitioners. Given the evidence that Indonesian

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

stock market are characterized by nonlinear
dynamic process and experienced significant
structural breaks, any results from previous
or future without taking structure breaks or
nonlinearity may lead to an inappropriate

conclusions. For investors, our findings indicates that both foreign and domestic investors could, when making their investment
decisions, consider an asset price to reflect
its true fundamental value at all times.

References
Abadir, K. M., and W. Distaso. 2007. Testing joint hypotheses when one of the alternatives is one-sided.
Journal of Economic 140: 695–718.
Abrosimova, N., G. Dissanaike, and D. Linowski. 2005. Testing the weak-form efficiency of the Russian
Stock Market. Social Science Research Network (SSRN) Working Paper. http://papers.ssrn.com/ sol3/
papers.cfm?abstract_id=302287.
Balke, N. S., and T. B. Fomby. 1997. Threshold Cointegration. International Economic Review 38 (3): 627-45.
Brock, W. A., and B. D. LeBaron. 1996. A dynamic structural model for stock return volatility and trading
volume. The Review of Economics and Statistics 78 (1) (February): 94-110. MIT Press.
Brock, W. A., and C. H. Hommes. 1998. Heterogeneous beliefs and routes to chaos in a simple asset
pricing model. Journal of Economic Dynamics and Control 22: 1235–74.
Caner, M., and B. E. Hansen. 2001. Threshold Auto regression with a Unit Root. Econometrica, Econometric
Society 69 (6) (November): 1555-1596.
Chaudhuri, K., and Y. Wu. 2003. Random walk versus breaking trend in stock prices: evidence from
emerging markets. Journal of Banking and Finance 27: 575–92.
Daiki, M. 2005. The term structure of interest rates with nonlinear adjustment: Evidence from a unit root
test in the nonlinear STAR framework. Economics bulletin 5: 1-7.
Daiki, M. 2006. Non-linear adjustment in the term structure of interest rates: a cointegration analysis in the
non-linear STAR framework. Applied Financial Economics 11: 1301-1307.
Dickey, D., and W. Fuller. 1979. Distribution of the estimators for autoregressive time series with a unit
root. Journal of the American Statistical Association 74: 427–431.
Dumas, B. 1992. Dynamic equilibrium and the real exchange rate in a spatially separated world. Review of
Financial Studies 5: 153–180.
Fama, E. F. 1970. Efficient capital markets: a review of theory and empirical work. Journal of Finance 25:
383–417.
Fama, E. F. 1995. Random walks in stock market prices. Finance Analyste Journal 21: 55-59. http://
www.jstor.org/stable/4469865.
Fama, E. F., and K. R. French. 1988. Permanent and temporary components of stock prices. Journal of
Political Economy 96 (2) (April): 246-273.
Fuss, R. 2005. Financial liberalization and stock price behaviour in Asian emerging market. Economic Change
and Restructuring 38: 37-62.

223

Setianto and Abd. Manap

Grieb, T. A., and M. G. Reyes. 1999. Random walk tests for Latin American equity indexes and individual
firms. Journal of Financial Research 22: 371–83.
Groenewold, N., and M. Ariff. 1998. The Effects of de-regulation on share market efficiency in the Asia
Pacific. International Economic Journal 12 (4): 23-47.
Harvey, D. I., S. J. Leybourne, and B. Xiao. 2008. A powerful test for linearity when the order of integration is unknown. Studies in Nonlinear Dynamics and Econometrics 12 (2).
Hasanov, M. 2009. Is South Korea’s Stock Market efficient? Evidence from a nonlinear unit root test.
Applied Economics Letters 16: 163-167.
Hasanov, M., and T. Omay. 2007. Are the Transition Stock Markets Efficient? Evidence from NonLinear Unit Root Tests. Central Bank Review. Central Bank of the Republic of Turkey.
Hong, H., and J. C. Stein. 1999. A unified theory of under reaction, momentum trading, and overreaction
in asset markets. Journal of Finance 54: 2143–84.
Hoque, H. A. A. B., J. H. Kim, and C. S. Pyun. 2006. A Comparison of variance ratio tets of random
walk: A case of Asian emerging markets. International Review of Economics and Finance.
Huang, B-N. 1995. Do Asian stock market prices follow random walks? Evidence from the variance
ratio test. Applied Financial Economics 5: 251-6.
Huang, B. N., and C. W. Yang. 1995. The Fractal Structure in Multinational Stock Returns. Applied Economics
Letters 2: 67-71.
Huber, P. 1997. Stock market returns in thin markets: evidence from the Vienna stock Exchange. Applied
Financial Economics 7: 493-498.
Islam, A., and M. Khaled. 2005. Tests of weak-form efficiency of the Dhaka Stock Exchange. Journal of
Business Finance and Accounting 32: 1613-1624.
Kapetanios, G., Y. Shin, and A. Snell. 2003. Testing for a unit root in the nonlinear STAR framework.
Journal of Econometrics 112: 359–79.
Karamera, D., K. Ojah, and J. A. Cole. 1999. Random walks and market efficiency tests: Evidence from
emerging equity market. Review of Quantitative Finance and Accounting 13: 171-188.
Kim, J. H., and A. Shamsuddin. 2007. Are Asian Stock Markets efficient? Evidence from new multiple
variance ratio tests. Journal of Empirical Finance 15: 518 – 532.
Kruse, R., 2010. A new unit root test against ESTAR based on a class of modified statistics. Statistical
Papers. DOI: 10.1007/s00362-009-0204-1.
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin. 1992. Testing the null hypothesis of stationarity
against the alternative of a unit root: How sure are we that economic time series have a unit root?
Journal of Econometrics 54: 159 -178.
Lean, H. H., and R. Smyth. 2007. Do Asian Stock Markets follow a random walk? Evidence from LM
unit root tests with one and two structural breaks. Review of Pacific Basin Financial Markets and Policies
10: 15-31.
Lee, C. C., J. D Lee, and C. C. Lee. 2010. Stock prices and the efficient market hypothesis: Evidence from
a panel stationary test with structural breaks. Japan and the World Economy 22 (1) (January): 49-58.
Lee, U. 1992. Do stock prices follow random walk? Some international evidence. International Review of
Economics and Finance 1 (4): 315-27.

224

Gadjah Mada International Journal of Business - September -December, Vol. 13, No. 3, 2011

Lo, A. W., and A. C. MacKinlay. 1988. Stock market prices do not follow random walks: Evidence from
a simple specification test. The Review of Financial Studies 1 (1): 41-66.
Luukkonen, R., P. Saikkonen, and T. Terasvirta. 1988. Testing linearity against smooth transition
autoregressive models. Biometrika 75: 491–9.
Lumsdaine, R., and D. Papell. 1997. Multiple trend breaks and the unit-root hypothesis. Review of Economics
and Statistics 79: 212–218.
MacKinnon, J. 1991. Critical values for cointegration tests. In: Engle R,Granger C. (eds) Long-Run Economic
Relationships: Readings in Cointegration. Oxford University Press, Oxford: 267–276.
Michael, P., R. A. Nobay, and D. A. Peel. 1997. Transaction costs and nonlinear adjustment in real exchange rates: an empirical investigation. Journal of Political Economy 105: 862–79.
Mishkin, F. S. 2004. The Economics of Money, Banking, and Financial Market (7th ed.). USA: The AddisonWesley series in economics.
Mobarek, A., and K. Keasey. 2002. Weak-form market efficiency of and emerging market: Evidence
from Dhaka Stock Market of Bangladesh. E-document. Retrieved October 26, from: http://
www.bath.ac.uk/centers/ CDS/Enbs-papers/Mobarek_new.htm.
Moustafa, M. A. 2004. Testing the weak-form efûciency of the United Arab Emirates Stock Market.
International Journal of Business 9 (3).
Munir, Q., and K. Mansur. 2009. Is Malaysian Stock Market efficient? Evidence from threshold unit root
tests. Economics Bulletin 29 (2): 1359-1370.
Narayan, P. K. 2005. Are the Australian and New Zealand stock prices nonlinear with a unit root? Applied
Economics 37: 2161-2166.
Narayan, P. K. 2008. Do shocks to G7 stock prices have a permanent effect? Evidence from panel unit
root tests with structural change. Mathematics and Computers in Simulation 77: 369-373.
Narayan, P. K., and R. Smyth. 2004. Is South Korea’s stock market efficient? Applied Economics Letters 11:
707-710.
Narayan, P. K., and R. Smyth. 2005. Exchange rates and stock prices in South Asia: Evidence from
Granger causality tests. ICFAI Journal of Applied Finance 11: 31-37.
Nelmida., N., M. Annuar, and T. Hassan. 2009. The impact of new information regime on the Jakarta
Stock Exchange. International Research Journal of Finance and Economics (3). ISSN 1450-2887.
Ojah, K., and D. Karemera. 1999. Random walk and market efficiency tests of Latin American emerging
equity markets: A revisit. The Financial Review (34) (2): 57-72.
Ozdemir, Z. A. 2008. Efficient market hypothesis: evidence from a small open-economy. Applied Economics 40: 633–641.
Perron, P. 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica 57: 1361–
401.
Peters, E. E. 1994. Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. John Wiley and
Sons.
Phillips, P. C.B., and P. Perron. 1988. Testing for a unit root in time series regression. Biometrika 75: 335346.
Poshakwale, S. 1996. Evidence on weak form efficiency and day of the week effect in the Indian Stock
Market. Finance India X (3): 605-616.

225

Setianto and Abd. Manap

Poterba, J. M., and L. H. Summers. 1988. Mean reversion in stock prices: Evidence and implications.
Journal of Financial Economics 22 (1): 27-59.
Qian, X. Y., F. T. Song, and W. X. Zhou. 2008. Nonlinear behaviour of the Chinese SSEC index with a
unit root: Evidence from threshold unit root tests. Physica A (387): 503-510.
Shively, P. A. 2003. The nonlinear dynamics of stock prices. The Quarterly Review of Economics and Finance 43:
505–517.
Shleifer, A. 2000. Inefficient Markets. An Introduction to Behavioural Finance, Clarendon Lectures in Economics.
Oxford: Oxford University Press.
TerSasvirta, T. 1994. Specifcation, estimation and evaluation of smooth transition autoregressive models.
Journal of the American Statistical Association 89: 208–218.
Urrutia, J. L. 1995. Test of random walk and market efficiency for Latin American emerging equity
markets. Journal of Financial Research 18: 299-309.
Zivot, E., and D.W. K. Andrews. 1992. Further evidence on the great crash, the oil-price shock and the
unit root hypothesis. Journal of Business and Economic Statistics 10: 251-70.
Zulfadin, R. 2008. Random walk hypothesis test: An aplication of linear and non-linear test on Indonesia
Stock Market indices. Jurnal Keuangan dan Moneter 11 (1).

226