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Episodic dependencies in Central and Eastern Europe stock markets
Alexandru Todeaa; Adrian Zoicas-Ienciua
a
Faculty of Economics and Business Administration, Finance Department, Babes-Bolyai University,
Cluj-Napoca, Romania
To cite this Article Todea, Alexandru and Zoicas-Ienciu, Adrian(2008) 'Episodic dependencies in Central and Eastern
Europe stock markets', Applied Economics Letters, 15: 14, 1123 — 1126
To link to this Article: DOI: 10.1080/13504850600993614
URL: http://dx.doi.org/10.1080/13504850600993614
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Applied Economics Letters, 2008, 15, 1123–1126
Episodic dependencies in Central
and Eastern Europe stock markets
Alexandru Todea and Adrian Zoicas-Ienciu*
Downloaded By: [Romanian Ministry Consortium] At: 07:59 7 September 2010
Faculty of Economics and Business Administration, Finance Department,
Babes-Bolyai University, Teodor Mihali 58-60, 400591 Cluj-Napoca,
Romania
This article introduces a modified version of the Hinich and Patterson
(1995) windowed-test procedure and uses it to detect linear and nonlinear
dependencies in the case of six Central and East European stock markets.
Testing the original methodology leads us to the same conclusions as those
found on other emerging markets: relatively long random walk periods are
interrupted by short and intense linear and/or nonlinear correlations.
But, our findings diverge when we run the modified test procedure,
additional windows rejecting the random walk hypothesis (RWH) being
isolated. This divergence, heavily weighing the task of correctly evaluating
the informational efficiency degree (the weak form), is significant for the
Czech, Hungarian and Romanian markets.
I. Introduction
Random walks in stock returns are crucial to the
formulation of rational expectations models and the
testing of weak-form market efficiency. In an efficient
market, stock prices fully incorporate all relevant
information and hence stock returns will display
unpredictable (or random walk) behaviour. The
check of the RWH, being a joint and not a direct
test of the efficient market hypothesis (EMH), leads
us to the question whether the detected dependencies
in stock prices can be used to earn abnormal rates of
returns. In order to get a valid response two
complementary research approaches are needed, one
is identifying/modelling these dependencies and the
other is studying their persistence in time.
Numerous recent studies have used the
Hinich–Patterson windowed-test procedure (1995) to
research the temporal persistence of linear
and especially nonlinear dependencies. Thus,
Ammermann and Patterson (2003), Lim et al. (2003),
Lim and Hinich (2005) or Bonilla et al. (2006) are
emphasizing the existence of different stock price
behaviours, namely long random walk sub periods
alternating with short ones characterized by strong
linear and/or nonlinear correlations. All these studies
suggest that these serial dependencies have an episodic
nature being also the main cause for the low
performance of the forecasting models.
The efficiency studies performed on Central and
East European stock markets confirm, with few
exceptions, the rejection of the RWH but none
of them has checked to what extent the found
dependencies are time persistent. Nivet (1997) finds
evidence of market inefficiency in the early trading
years of the Warsaw Stock Exchange. Studying the
autocorrelation coefficients, he concludes that the
RWH is rejected for those years. Chun (2000) and
Worthington and Higgs (2004) researches also reject
the RWH for the Polish, Czech an Russian stock
markets, the Hungarian market being the only one to
follow a random walk. According to Gilmore and
McManus (2003), the significant autocorrelations
found in some Central European stock markets
are caused by both nonsynchronous trading
and asymmetric response to good and bad news.
By using a model-comparison test they also reject the
RWH for all the stock markets included in
*Corresponding author. E-mail: [email protected]
Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–4291 online ß 2008 Taylor & Francis
http://www.informaworld.com
DOI: 10.1080/13504850600993614
1123
A. Todea and A. Zoicas-Ienciu
1124
the research. Schotman and Zalewska (2005) confirm
that the predictability of the Central European
emerging markets has decreased over time as the
estimated time-paths of the autocorrelation coefficient
gradually become indistinguishable from zero.
This article contributes to the existing literature by
introducing a methodological innovation, as well as
by highlighting the findings related to the informational efficiency of some Central and East European
emerging stock markets.
Downloaded By: [Romanian Ministry Consortium] At: 07:59 7 September 2010
II. Methodology
The return sample, {R(t)}, is considered by the
Hinich–Paterson methodology to be the realization
of a stochastic process, where t (integer) is the time
unit. The procedure implies the division of the N
returns sample in NW nonoverlapped subsamples of
volume n, named windows, NW being the largest
integer satisfying NW (N21)/(n21).
In each window, the null hypothesis is that R(t)
is the realizations of a white noise process
with null correlations and bi-correlations, described by CEE(r) ¼ E[R(t)R(t þ r)] and CEEE(r, s) ¼
E[R(t)R(t þ r)R(t þ s)], where r and s are integers
satisfying 0 < r < s < L with L being the number of
lags. Correlations identification is made using the
portmanteau test (C) for linear correlations and the
bicorrelation test (H) for the nonlinear ones. In order
to compute them, a standardized series (Zt) is used:
ZðtÞ ¼
RðtÞ mR
R
ð1Þ
where t takes values from 1 to n and mk, k are the
mean and SD within each window. The correlations
and bicorrelations are then given by:
CRR ðrÞ ¼ ðn rÞ1=2
ns
X
CRRR ðr, sÞ ¼ ðn sÞ1
nr
X
ZðtÞZðt þ rÞ
ð2Þ
t¼1
ZðtÞZðt þ rÞZðt þ sÞ
t¼1
0rs
ð3Þ
The C and H statistics are distributed according to
a 2 law of probability with L respectively (L21) * (L/
2) degrees of freedom, having the following formulas:
C¼
H¼
L
X
½CRR ðrÞ2
r¼1
L X
s1
X
G2 ðr, sÞ
ð4Þ
The number of lags (L) is specified as L ¼ nb, with
0 < b < 0.5. Hinich and Patterson recommends the
usage of b ¼ 0.4 in order to maximize the power of the
test assuring in the same time a good asymptotical
approximation. The window length must be long
enough to offer a robust statistical power and yet
short enough for the test to be able to identify the
arrival and disappearance of transient dependencies,
as changes in the variables behaviour (35 observations recommended). The rejection of the null
hypothesis by the C and H tests is done with a
determined risk level, generally 1 and 5%.
The Hinich–Patterson methodology does not allow
an accurate identification of sub-periods exhibiting
linear/nonlinear dependencies, because the test results
depend on how the first day of the sample is chosen.
The following example shows how the RWH can be
accepted in the first window just because dependencies exist in a small time fraction of the windowed
sub-period, while, if we considered the first day of the
sample the last fraction of the first window, RWH is
rejected.
RW
RW
NRW
RW
NRW
A correct identification of the windows rejecting
the RWH is essential for gaining a more accurate
overview on the market efficiency degree (the weak
form) and improves the significance of the efficiency
evolution tests.
Thus, the ‘first day effect’ can be eliminated by
running the Hinich–Patterson methodology in a
successive way, considering the first day of the
sample each of the first n1 days from the first
window. Due to the translation, each succesive
application eliminates a return from the last
window making it insignificant. Theoretically, with
the exception of the last return, each return from the
first window can be considered with the same
probability the starting point of the sample. Thus,
for each sample, the percentage of significant
windows (rejecting RWH) is given by:
!
n1
X
1
x1
xi
þ
100
pð%Þ ¼
n 1 NW i¼2 NW 1
where xi denotes the number of significant windows
found on step i.
ð5Þ
III. The Data
ð6Þ
The data consists of daily closing prices for six
Central-East European stock market indices, the
s¼2 r¼1
Gðr, sÞ ¼ ðn sÞ1=2 CRRR ðr, sÞ
Episodic dependencies in Central and Eastern Europe stock markets
starting day being given in brackets: Hungary
(BUX, from 1 August 1991), Czech Republic
(PX50, 14 September 1993), Slovakia (SAX, 4 July
1995), Poland (WIG, 7 January 1994), Romania
(BET, 19 September 1997) and Russia (RTS,
4 September 1995). The last closing price for each
index is 31 May 2006, the samples length varying
between 2135 and 3850 observations. The data is
transformed into a series of continuously compounded returns, rt ¼ ln (Pt/Pt 1), where Pt and
Pt 1 denote two consecutive trading days.
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IV. Empirical Results
We ran both the original Hinich–Patterson
methodology and the modified one in the case of
six major Central and East European stock markets
using 35 observations for the window length, 0.4
for the b parameter and considering a risk level of
1% (we also developed a Pascal-based software
solution to do the necessary data processing).
Using the original methodology we reached the
same conclusions found on the Asian markets
(Lim and Hinich, 2005) and those from Latin
America (Bonilla et al., 2006), namely that the
RWH is rejected by maximum 10% from the total
1125
number of windows. Moreover, we found significant
differences between the markets, some indices like
SAX and WIG having just one window rejecting the
RWH while for the BET index we found nine such
windows. It is also interesting to notice that we could
not find any windows exhibiting nonlinear dependencies in the case of the Slovakian and Polish indices
(The results are reported in Table 1).
Using the modified methodology, we found a
significant increase of the proportion of windows
rejecting the RWH in the case of the BET, BUX and
PX50 indices and some originally inexistent nonlinear
correlations for the SAX and WIG indices. The most
radical change of behaviour is noticed in the case of
PX50 where the RWH is rejected in 30% of its
windows. As an exception, we could not find
significant changes for the Russian index which
means that the modified methodology does not
necessary leads to a decrease of the market efficiency
degree (The results are reported in Table 2).
V. Conclusions
This article uses the Hinich and Patterson windowedtest procedure and a modified methodology in
order to isolate linear and/or nonlinear correlation
Table 1. The original methodology-results.
Original methodology
Index
Total number
of windows
Windows – C
significant
Windows – H
significant
Windows – C
or H significant
BET
BUX
PX 50
RTS
SAX
WIG
61
110
86
76
75
89
3
2
6
1
1
1
6
6
4
5
0
0
9 – (14.75%)
7 – (6.36%)
8 – (9.3%)
6 – (7.89%)
1 – (1.33%)
1 – (1.12%)
–
–
–
–
–
–
(4.92%)
(1.82%)
(6.98%)
(1.32%)
(1.33%)
(1.12%)
–
–
–
–
–
–
(9.84%)
(5.45%)
(4.65%)
(6.58%)
(0%)
(0%)
Table 2. The modified methodology-results
Modified methodology
Index
Total number
of windows
Windows – C
significant
Windows – H
significant
Windows – C
or H significant
BET
BUX
PX 50
RTS
SAX
WIG
2114
3826
2996
2648
2611
3097
145
275
700
80
88
154
251
624
500
163
13
167
384
804
916
234
98
286
–
–
–
–
–
–
(6.85%)
(7.19%)
(23.36%)
(3.02%)
(3.37%)
(4.97%)
–
–
–
–
–
–
(11.87%)
(16.3%)
(16.69%)
(6.15%)
(0.49%)
(5.39%)
–
–
–
–
–
–
(18.16%)
(21.01%)
(30.57%)
(8.84%)
(3.75%)
(9.23%)
A. Todea and A. Zoicas-Ienciu
Downloaded By: [Romanian Ministry Consortium] At: 07:59 7 September 2010
1126
sub-periods from those accepting the RWH in the
case of six indices from Central and Eastern Europe
stock markets. In its original form, the methodology
leads to the same conclusions reached on other
emerging markets, namely that long sub periods of
random walk are interrupted by short and intense sub
periods with linear and/or nonlinear correlations, the
intensity of these dependencies being different from
market to market.
When the Hinich–Patterson methodology is used in
a successive way, the proportion of windows rejecting
the RWH substantially increases although this result
is not a necessary consequence of the modified
methodology, as we proved it. We found that by
considering the ‘first day of the sample effect’ the
results are different compared with the previous
studies, additional sub periods rejecting the RWH
being revealed.
Acknowledgements
The authors acknowledge Professors Timo Teräsvirta
and Wladyslaw Milo for useful comments and
suggestions on an earlier draft on this article. We
are also benefited from conversations with Professor
Joseph Plasmans and other participants at the 5th
Annual International Conference Forecasting
Financial Markets and Economic Decision-Making’
in Lodz (Poland, 11–13 May 2006).
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