AN EMPIRICAL ANALYSIS OF ASYMMETRIC EFFECTS,
STRUCTURAL BREAKS AND LONG MEMORY: EVIDENCE FROM
THE VOLATILITY OF TURKISH STOCK MARKET
1
MESUT BALIBEY, 2SERPIL TURKYILMAZ
1
Department of Business Administration, Faculty of Economics and Administrative Sciences,Tunceli University, Turkey
2
Department of Mathematics, Faculty of Arts and Sciences, BilecikŞeyhEdebali University, Turkey
E-mail: [email protected], [email protected]
Abstract- In this study, long memory and asymmetry properties in volatility of Turkey Stock Market are examined by using
the FIGARCH, FIEGARCH and FIAPARCH models under different distribution assumptions as Normal and Skewed
Student-t for the period 1990-2015. Furthermore, structural changes in volatility of Turkey Stock Market are investigated.
The findings of the study display long memory property and the presence of asymmetric effects of shocks in volatility of
Turkey Stock Market.
Keywords- Asymmetric Effect, Structural Break, FIAPARCH Model, FIEGARCH Model, FIGARCH Model.
market prices of Turkey for the period of 1988-1994.
The author finds that stock market prices have not
random walk process and Turkey’ stock market is not
efficent market. [5] examine whether Spain Stock
Market has long memory property by using daily data
for the period 1980-1993. They couldn’t obtain
findings about long memory property in stock market.
[6] investigate Greece Stock Market by using weekly
data for the period 1981-1990. They show that
Greece Stock Market is inefficient market in weakform. [7] research the existing of long memory
property in Brazilian Stock Market by using
ARFIMA model. They find that stock market hasn’t
long memory property. [8] estimates ARFIMA model
by using monthly data for the period 1960-1999 for
stock market 16 OECD countries. The author displays
that Denmark, Finland and Ireland Stock Markets
have long memory. [9] analyze S&P500 index by
using daily data for the period 1828-1991, and
indicate that S&P500 index has long memory
property. [10] investigates long memory property of
Turkish Stock Market and he shows that Turkish
Stock Market is not an efficient market. [11] finds
that Athens Stock Market is an efficient market by
using ARFIMA model for the period 1990-2000. [12]
examine property of long memory in return and
volatility of Turkish Stock Market by using
ARFIMA-FIGARCH model. They shows that
Turkish Stock Market isn’t an efficient market. [13]
researchs stock markets of Egypt, Jordan, Morocco
and Turkey by using daily data for the period 19972002. He finds that evidence of long memory in the
returns of stock markets related to these countries.
[14] investigate existing of long memory in the return
and volatility of Istanbul Stock Market. They display
that volatility series has long memory property. [15]
examines the long-term dependency of stock return
volatility for 23 developing markets for the period
2000 – 2007. The author indicates persistence in
return volatility for many markets including
Indonesia. [16] research long memory in S&P500,
I. INTRODUCTION
Hyperbolic decrease tendency of return and volatility
in autocorrelation functions which means the property
as rotating to slow average is defined as long
memory. In case the existance of long term
dependency among price movements, there is
positive autocorrelation among price movements. In
case of having Long Memory property, stock market
prices will have a predictable structure and
retrospective tendency of prices can be used for price
estimations in future[1]. Long Memory dynamics are
important indicators showing the existence of
nonlinear relations in a time series’ mean and
variance. Along with the suggestions of [2] and [3]
about ARCH and GARCH type models, modelling of
stock exchange return volatility became a significant
research area. It was found in these studies that stock
market volatility changed in time and presented a
positive serial correlation referred as volatility
clustering. This situation shows that changes in
volatility are not accidential however these models
cannot assess the long memory property in volatility.
Very slow mean-reverting process with hyperbolic
rate of autocorrelation functions related to return and
volatilities is defined as long memory in return and
volatility. It is very important especially while taking
financial investment decision and about whether
financial market behaviours are linear in terms of
monetary policies. Non linear structure of price
movements in financial markets will cause that
standard statistical analysis lead mistaken result while
taking decision for investment. Therefore, complex
structure of financial markets causes academicians,
policy makers and investors approach to the markets
with a different point of view. Many studies in the
literature focus on analysing dual long memory
property in conditional mean and volatility. In recent
years,
modelling
long
memory
property
becamesattractive research area especially in stock
market return and volatility.[4] investigates stock
Proceedings of ISER 8th International Conference, Istanbul, Turkey, 10th October 2015, ISBN: 978-93-85832-10-9
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An Empırıcal Analysıs Of Asymmetrıc Effects, Structural Breaks And Long Memory: Evıdence From The Volatılıty Of Turkısh Stock Market
FTSE100, DAX, CAC40 ve ISE100 stock markets by
using ARFIMA-FIGARCH models. They find that all
of the stock markets have dual long memory
properties. [17] investigate the existing of dual long
memory in Turkish Stock Market for the period 20102013 by using ARFIMA-FIGARCH model, and test
efficient market hypothesis for Turkish Stock Market.
The authors find that Turkish Stock Market is not an
efficient stock market. [1] examines that whether
Istanbul Stock Exchange is weak form efficient
market. The author indicates that Turkish Stock
Market has long memory.
The study includes testing of structural breaks and the
analysis of long memory properties in volatility of
Turkey stock exchange through FIGARCH,
FIEGARCH and FIAPARCH models under different
distribution assumptions as Normal and Skewed
Student-t distributions for the period of (1990-2015).
[20] indicate in their studies that when 0  d<1, the
effect of a shock on conditional variances of
FIGARCH (p,d,q) processes decreases with
hyperbolic rates.
In this respect, while short term dynamics of
volatility are modelled with traditional GARCH
model parameters, long term dynamics of volatility
can be assessed with fractional integration parameter
as d.
Asymmetric effects of shocks can not be evaluated by
FIGARCH model. For this purpose, [21] propose
FIEGARCH model. FIEGARCH (p, d, q) model can
be expressed as follows;
II. METHODOLOGY
[18]and[19] suggested ARFIMA model in order to
test long memory properties in returns. The purpose
of this model is to assess fractional integrated process
I(d) in conditional mean. The ARFIMA (p, , d)
model is expressed as (1).
=
Where,
,
In (8), first term
FIEGARCH (p, d, q) model;
if d=0, then the process of FIEGARCH becomes an
EGARCH model.
if d=1, then the process of FIEGARCH becomes an
IEGARCH model [21].
Furthermore, FIAPARCH model which evaluates
asymmetric effect of shocks on volatility is proposed
by Tse(1998). FIAPARCH model is as follows;
 t2 are squared errors of GARCH process.
process of vt  is integrated for conditional
zero mean.
variance
 t2
Where, d is long memory parameter. According to
[22], asymmetry parameter is 1<<1. If >0, then
negative shocks (bad-news) cause more volatility
than positive shocks (good-news).
as variations. It is assumed that all roots
of  ( L) and [1   ( L)] stayed out of unit circle.
If d=0, then the process of FIGARCH (p,d,q) is
reduced to the process of GARCH (p,q).
If d=1, then the process of FIGARCH becomes an
integrated process of GARCH (IGARCH). Shocks
have an infinite effect on prospective volatility in this
process.
As it is also indicated above, the model of FIGARCH
(p,d,q) imposes an ARFIMA structure on
Model (2) can be rearranged as follows.
Conditional variance of
 t2
sign effect, second
term  [ z t  E z t ] shows magnitude effect. For
~ (0,1) and
FIGARCH model has been suggested by [20] for
theextended version of squared errors in ARFIMA
model. FIGARCH (p,d,q) model is expressed as (2).
 ( L)(1  L) d  t2    [1   ( L)]vt (2)
v t   2t  2t are serially uncorrelated errors having
The
 ( zt ) shows
 t2 .
III. EMPIRICAL RESULTS
Data used in the study consists of daily stock index
data for the period of 01.02. 1990 - 24.03.2015
including the periods of economic crisis. Daily
logarithmic returns in t-time related to the stock
markets of Turkey (Stock Exchange İstanbulBIST100) are;
The
Where Rt indicates index return in t-time, Pt is the
closure price of index in t-time, Pt-1 is the closure
price of index in (t-1) time. BIST100 data was
obtained from the web site of Stock Exchange
Istanbul.Descriptive statistics related to stock index
is given with;
Proceedings of ISER 8th International Conference, Istanbul, Turkey, 10th October 2015, ISBN: 978-93-85832-10-9
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An Empırıcal Analysıs Of Asymmetrıc Effects, Structural Breaks And Long Memory: Evıdence From The Volatılıty Of Turkısh Stock Market
returns of Turkey (RBIST) is given in Table1.
Table2:Unit Root Tests for Return Series
Table1:Descriptive Statistics of Return Series
According to the results in Table 2, while high
negative results of ADF and PP tests indicates the
refusal of unit root null hypothesis for all return series
at the significance level of 5%, KPSS test statistics do
not refuse null hypothesis showing I(0) process for all
return series at the significance level of 5%. The
results of unit root tests are supported stationary for
return series RBIST. Long memory property in
volatility will be also analysedby using FIGARCH.
The results of FIGARCH Model for long memory in
volatility of RBISTare shown in Table3.
Table 3: The Results of FIGARCH(1,d,1) Model
According to the results in Table 1, we may assert
that skewness parameter of RBIST return series is
negative and the value of leptokurtosis is high.
According to relevant statistics, it indicates that
RBIST return series shows symmetric properties and
more leptocurtic and fat tail compared to the normal.
Moreover, the statistic of Jarque-Bera having a
relatively high value is also statistically significant as
an indication related to return series non-normal
distribution. For independency test of return error and
squared return error series, Ljung-Box statistics (Q
and Q2) in various delays are estimated. According to
statistics, i.i.d. (property of independent and
identically distributed) process is not observed since
RBIST return errors and squared return errors highly
correlated up to 50th delay. In high degrees especially
showing extensive effect of volatility clusters in stock
exchange returns, statistical value in 50th delay is also
significant. Findings of ARCH-LM test also indicate
the existence of significant ARCH effects in
standardised errors. Q and Q2 statistics present an
evidence of “Long Memory” property in squared
return series considered as the most popular Proxy for
volatilities in financial markets.
Three different unit root test results as ADF
(Augmented Dickey Fuller), PP (Phillips-Perron) and
KPSS (Kwiatkowski, Phillips, Schmidt ve Shin) are
given in Table 2 in order to determine whether the
series is stationary I(0) before long memory test for
stock exchange return series (RBIST) in thestudy.
Proceedings of ISER 8th International Conference, Istanbul, Turkey, 10th October 2015, ISBN: 978-93-85832-10-9
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An Empırıcal Analysıs Of Asymmetrıc Effects, Structural Breaks And Long Memory: Evıdence From The Volatılıty Of Turkısh Stock Market
From Table 3, long memory d parameter for
FIGARCH model under normal and skewed student-t
distributions is significantly different from zero for
RBIST return series and the volatility demonstrates
long memory process. Moreover, we can say that
return series demonstratesi.i.d. property according to
Ljung-Box test statistics. The results of Pearson
Goodness of Fit Test indicate that different
distributions are also appropriate for RBIST.
Similarly, the results of FIEGARCH and FIAPARCH
model which evaluate asymmetric effects are
presented Table 4 and Table 5.
Test indicate that skewed student-t distribution also
appropriate for RBIST.
Moreover, the asymmetry term 1 is statistically
significant. Negative coefficient implies that negative
shocks cause higher volatility in returns than positive
shocks.
Table 5: The Results of FIAPARCH(1,d,1) Model
Table 4: The Results of FIEGARCH(1,d,1) Model
From Table 4, long memory d parameter for
FIEGARCH model under normal and skewed
student-t distributions is significantly different from
zero for RBIST return series and the volatility
demonstrates long memory process. Furthermore,
return error series hasnot i.i.d. property according to
Ljung-Box Q and Q2test statistics except Q2(20)
andQ2(50) . The results of Pearson Goodness of Fit
AccordingtoTable5, long memory parameter in
volatility d is statistically significant, and the power
term  is statistically significant at 5% level.
Estimated asymmetry coefficient  is significant and
positive implying that negative shocks result in
higher volatility than positive shocks. In other words,
the positive sign of  suggests that “bad news”
decrease is more destabilizing than “good news”, i.e.
Proceedings of ISER 8th International Conference, Istanbul, Turkey, 10th October 2015, ISBN: 978-93-85832-10-9
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An Empırıcal Analysıs Of Asymmetrıc Effects, Structural Breaks And Long Memory: Evıdence From The Volatılıty Of Turkısh Stock Market
an unanticipated increase.
To obtain reliable estimates of model parameters,
structural breaks in volatility have been investigated
by using algorithms of ICSS [23], ICSS(Kappa-1)
and ICSS(Kappa-2) developed by [24]. The algorithm
of ICSS InclanTiao (IT) shows 46 structural break. In
addion, the algorithms of ICSS(Kappa-1) and
ICSS(Kappa-2) display 21 and 6 structural breaks in
variance respectively. the dates of breaks in
conditional variance according to ICSS (K-1) and
ICSS (K-2) are displayed in Table61.
dummy variable of FIGARCH model are presented
Table 7.
Table 7: The Results of FIGARCH Model With
Dummy Variable
Table 6: Structural Breaks in Volatility of RBIST
According to Table 7, dummy parameter (D) for
structural breaks is statistically significant.
Furthermore, the values of long memory parameter d
of FIGARCH model with dummy are not very
different from model parameters in Table3.
Consequently, it can be said that structural changes
don’t affect long memory property in conditional
variance of returns. In other words, long memory
property in Turkey Stock Market returns don’t be
affected by structural breaks in conditional variance
of returns.
According to Table 6, dummy variable for structural
breaks in conditional variance are used to estimate
FIGARCH model. The results of estimation with
1
[25] display that in case of serial correlation in residuals, ICSS
test misrepresents the size of structural break in unconditional
variances. Therefore, a new method is necessary to account for
serial dependence of residuals. Furthermore, [25] and [24] indicate
upward bias in estimation of ICSS statistic whenever returns follow
GARCH process. Moreover, the assumption of t~iidN(0, 2) is
inappropriate since residuals have leptocurtic distribution. [26]
report that these assumptions cause over estimation of the number
of breaks using the ICSS test. Our results show a non-normal
distributions of returns, serial correlation, heteroskedasticity and
“fat-tailed” Leptokurtic distribution. Therefore, ICSS test alone
may not be appropriate for this study. WeuseInclan-Tiao, Kappa-1
(K-1) and Kappa-2 (K-2) tests of [24]. Therefore, the results of
estimation with dummy variable for structural breaks in variance
through Kappa-1(K-1) and Kappa-2 (K-2).
CONCLUSIONS
The study evaluates long memory property,
asymmetric effects and structural changes in volatility
of Turkey Stock Market for the period of 01.02.199024.03.2015.
For this purpose,
FIGARCH,
FIEGARCH and FIAPARCH models for long
memory in volatility of returns are estimated.
Proceedings of ISER 8th International Conference, Istanbul, Turkey, 10th October 2015, ISBN: 978-93-85832-10-9
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An Empırıcal Analysıs Of Asymmetrıc Effects, Structural Breaks And Long Memory: Evıdence From The Volatılıty Of Turkısh Stock Market
[11] Vougas, D. V., “Analysing Long memory and volatility of
returns in the Athens stock exchange”, Applied Financial
Economics, 14, 2004, pp. 457-460.
[12] Kasman, A. and Torun, E., “Long memory in the Turkish
stock market return and volatility”, Central Bank Review,
ISSN 1303-0701 print / 1305-8800 online 2, 2007, pp. 1327.
[13] Assaf, A., “Fractional integration in the equity markets of
MENA region”, Applied Financial Economics, 17, 2007,
pp. 709-723.
[14] Korkmaz, T., Çevik, E.İ., veÖzataç, N., “Testing for long
memory in ISE using ARFIMA-FIGARCH Model and
structural break test”, International Research Journal of
Finance and Economics, 26, 2009, pp. 186-191.
[15] Jayasuriya, S.A.. A Sub Period Analysis of Long Memory
in Stock Return Volatility for Emerging Markets, 9th
Global Conference on Business and Economics
Proceedings, Cambridge University, U.K., 2009, pp. 1-31.
[16] Ural, C., Küçüközmen, C., “Analyzing the Dual Long
Memory in Stock Market Returns”, Ege Academic
Review, 10, 2011, pp. 19-28. (ErişimTarihi: 13. 04. 2013)
http://www.onlinedergi.com/makaledosyalari/
51/pdf2011_5_3.pdf.
[17] Türkyılmaz,
S.
and
Balıbey,
M.,
“
TürkiyeHisseSenediPiyasasıGetiriveOynaklığındakiUzun
DönemBağımlılıkİçinAmpirikBirAnaliz”,
DokuzEylülÜniversitesiSosyalBilimlerEnstitüsüDergisi,
16(2), 2014, pp:281-302.
[18] Granger, C.W.J. and Joyeux, R., “An introduction to longmemory time series models and fractional differencing”,
Journal of Time Series Analysis, 1, 1980, pp:15-39.
[19] Hosking, J.R.M., “Fractional Differencing”, Biometrica,
68, 1981, pp. 165-176.
[20] Baillie, R. T., Bollerslev, T. and Mikkelsen, H. O.,
“Fractionally integrated generalized autoregressive
conditional heteroskedasticity”, Journal of Econometrics,
74, 1996, pp. 3-30.
[21] Bollerslev, T. and Mikkelsen, H. “Modeling and Pricing
Long Memory in Stock Market Volatility”, Journal of
Econometrics, 73, 1996, pp. 151–184.
[22] Tse, Y.K., “The conditional heteroscedasticity of the yendollar exchange rate”, Journal of Applied Econometrics ,
13, 1998, pp. 49-55.
[23] Inclan, C. and G. Tiao, Use of the cumulative sums of
squares for retrospective detectionof changes of variance,
Journal of the American Statistical Association, 89, 1994,
pp. 913-923.
[24] Sanso, A., Arago, V., and Carrion, J. L., “Testing For
Changes in the Unconditional 145 Variance of Financial
Time Series”, Revista de EconomíaFinanciera, 2004, pp.
1-24.
[25] Rapach, D. E. and Strauss, J. K., Structural Breaks and
GARCH models. Journal of Applied Econometrics 23,
2008 65-90.
[26] Andreou, E. and Ghysels, E., Detecting Multiple Breaks in
Financial Market Volatility Dynamics, Journal of Applied
Econometrics, 17(5), 2002, pp. 579-600.
Furthermore, structural changes in volatility are
tested by using algorithms of ICSS [23],
ICSS(Kappa-1) and ICSS(Kappa-2) developed by
[24]. Consequently, the findings approve that there is
long memory property in volatility of Turkey Stock
Market. This predictable structure of volatility
indicates that Turkey Stock Market is inefficient
market. Moreover, the effects of shocks on the
volatility are asymmetric. In other words, negative
shocks (bad-news) affect volatility more than positive
shocks (good-news). Finally, structural changes in
volatility for the period of 1990-2015 are not
statistically significant on long memory in volatility
of returns. The results of study present important
findings for investors, policy-makers, financial
analysists and academicians.
REFERENCES
Çevik,
E.İ.,
“İstanbul
menkulkıymetlerborsası’ndaetkinpiyasahipotezininuzunha
fızamodelleriileanalizi:
sektörelbazdabirinceleme”,
YaşarÜniversitesi E-Dergisi, 7(26), 2012, pp. 4437-4454.
[2] Engle,
R.F.,
“Autoregressive
Conditional
Heteroscedasticity with Estimates of the Variance of
United Kingdom Inflation”, Econometrica, 50, 1982, pp.
987-1008.
[3] Bollerslev, T., “Generalized Autoregressive Conditional
Heteroskedasticity”, Journal of Econometrics, 31, 1986,
pp. 307-327.
[4] Balaban, E., “Some Empirics of the Turkish Stock
Market”, Discussion Paper in Central Bank of Republic of
Turkey Research Department, 9508, 1995.
[5] Blasco, N. and Santamaria, R., “Testing Memory Patterns
in the Spanish Stock Market”, Applied Financial
Economics, 6, 1996, pp. 401-411.
[6] Barkoulas, J.T., Baum, C.F., veTravlos, N., “Long
memory in the Greek stock market”, Applied Financial
Economics, 10, 2000, pp. 177-184.
[7] Resende, M. and Teixeira, N., “Permanent Structural
Changes in the Brazilian Economy and Long Memory: A
Stock Market Perspective”, Applied Economics Letter, 9,
2002, pp. 373-375.
[8] Tolvi, J., “Long Memory and Outliers in Stock Market
Returns”, Applied Financial Economics, 13, 7, 2003, pp.
495-502.
[9] Caporale, G.M., ve Gil-Alana, L.A., “Long range
dependence in daily stock returns”, Applied Financial
Economics, 14, 2004, pp. 375-383.
[10] Kılıç, R., “On the Long Memory Properties of Emerging
Capital Markets: Evidence from Istanbul Stock
Exchange”, Applied Financial Economics, 14, 2004, pp.
915-922.
[1]
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Proceedings of ISER 8th International Conference, Istanbul, Turkey, 10th October 2015, ISBN: 978-93-85832-10-9
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