Ranking Efficiency for Twenty-six Emerging Stock Markets

8/11/2019 Ranking Efficiency for Twenty-six Emerging Stock Markets

1/12

ISSN 1750-9653, England, UKInternational Journal of Management Scienceand Engineering Management, 7(1): 53 -63, 2012http://www.ijmsem.org/

Ranking efficiency for twenty-six emerging stock markets

and financial crisis: evidence from the shannon entropy

approach

Walid Mensi

Department of finance, Faculty of Management and Economic Sciences of Tunis, El Manar University, B.P. 248, C.P. 2092, TunisCedex, Tunisia

(Received 5 November 2011, 20 December 2011, Accepted 29 January 2012)

Abstract. In this paper the evolution of a weak-form efficiency for twenty six emerging stock markets is tested. To do this, amodified Shannon entropy and a Symbolic Time Series Analysis are employed over the period September 1997 to November 2007.

A regression is performed for time windows with 100 observations and a rolling sample approach. The empirical results show thatstock market efficiency changes over time and differs from one market to another and across geographic areas. For example, theArgentinian market is a more efficient market whereas the Tunisian stock market is less efficient. The inefficiency in stock marketsis dynamic. Furthermore, a negative relationship was found between the financial crisis and stock market efficiency. The findingsof this evolving market efficiency may be attributed to microstructure variables. These results have several implications for stockportfolio hedgers and policy makers.

Keywords: informational efficiency, emerging stocks markets, rolling sample approach, symbolic time series analysis, Shannonentropy

1 Introduction

The efficiency market hypothesis (EMH hereafter) playsa crucial role in modern financial theory. According to Fama

(1991)[15], a financial market is considered efficient if thecurrent security prices fully reflect available information atany point in time. Jensen (1978)[17]cited another less re-strictive definition saying that a market is supposed efficientwith respect to information set t if saying that a marketis supposed efficient with respect to information set t ifclaimed that markets do not allow investors to earn above-average returns without accepting above-average risks. Ac-cording to these definitions, historical sequence prices donot predict futures prices because they are yet embodiedand consequently there are no accurate patterns. However,as investors may not release excessive returns in this mar-ket, the price changes randomly over time. In addition, in anefficient market, the market price of a security does not nec-essarily equal to its intrinsic value as all bad and good newsaffects security prices. Empirical studies, testing the weakform show mixed results for both developed and emergingmarkets. Previous studies assume that the level of marketefficiency stays unchanged in their regressions1. Recently,several researchers have looked at time-varying weak-formefficiency in financial markets (Lim and Brooks, 2011 [20]).

The main motivation for this study was to test evolv-ing weak-form market efficiency taking an econophysics ap-proach. A Symbolic Time Series Analysis (STSA) and a

modified Shannon entropy metric, a basic tool in informa-tion theory and statistical physics, were used for the firsttime to analyze temporal efficiency in twenty-six emergingmarkets and to examine the relationship between efficiency

levels and the financial crisis using a logit model. Benteset al. (2008) [5]argued that entropy measures have provenuseful in describing financial time series problems. Zuninoet al. (2009) [40] argued that different statistical physicsmethods like entropies were recently introduced to rankstock markets in order to distinguish between emerging anddeveloped economies. This paper extends the work of Risso(2008) [30]to rank stock markets according to their level ofefficiency, which is considered important in strategic assetallocation, and portfolio risk management.

The remainder of the paper is structured as follows. Sec-tion 2 presents the literature review. Section 3 describesthe methodology. Section 4 provides empirical results andinterpretations while conclusions are given in section 5.

2 Literature review

Cajueiro and Tabak (2004) [8] examined long range de-pendence and efficiency in 11 emerging markets, and the USand Japan. Using daily closing prices from January 1992-December 2002 and a rolling sample approach to calculatethe R/S statistics, modified R/S statistics and Hurst ex-ponents, they found that the U.S., and Japan were more

Correspondence to: Tel.: +216-24-514-829. E-mail address : [email protected].

1 See among others, Cajueiro and Tabak (2004, 2005) [8,9], Cajueiro et al. (2009)[7], Lim (2007) [19], Lim et al. (2008) [20], Risso(2008)[30], Yang et al. (2011)[38], Yang et al. (2008) [37].

International Society of Management Science

And Engineering Management

Published by World Academic Press,

World Academic Union
http://www.ijmsem.org/http://www.ijmsem.org/


2/12

54 W. Mensi: Ranking efficiency for twenty-six emerging stock markets and financial crisis

efficient than Asian markets and Latin American markets(with the exception of Chile).

Cajueiro and Tabak (2005) [9]employed the same model(time-varying Hurst exponents) and a sample to test thelong range dependence of the volatility of equity returnsover the period January 1992-January 2004 and suggestedthat the Asian equity markets were more efficient thanthose of Lain America, and that the U.S. and Japan were

the most efficient.Lims (2007) [19] study was inspired by that of Ca-

jueiro and Tabak (2005) [9] for testing the relative effi-ciency of stock markets. Lim (2007) [19] used Portman-teau bi-correlation test statistics and a data rolling samplefor eleven emerging and two developed markets (US andJapan) over the period January 1992 to December 2005(with the exception of the Argentinian Merval index thatthat begins on August 1993). Lims (2007) [19] study em-ployed a percentage of time windows by the markets devi-ation from efficiency instead of the median measure used inCajueiro and Tabak (2005)[9]. This tool detects the chang-ing level of efficiency in a stock market. Lim concluded thatmarket efficiency was not static and showed that the non-linear dependence of stock returns were localized in time.

Risso (2008) [30] examined the relationship betweenweak-form financial efficiency and the financial crashes byusing the Shannon entropy on five Stock market indexes(Japan, Malaysia, Mexico, Russia and US) which showedthat developed markets were more efficient than emergingmarkets confirming Cajueiro and Tabaks (2004, 2005) [8,9]conclusion.

Risso (2008) [30] found an inverse relationship betweenlevel efficiency and crashes, the probability of crashes de-creased with increasing efficiency. Lim et al. (2008) [21]tested the effect of the 1997 financial Asian crisis on theefficiency of eight Asian stock markets via a rolling bi-correlation test statistic which showed a negative relation-ship between market efficiency and the financial crisis andthat the degree of efficiency improved in the post-crisis pe-riod.

Lagorade-Segot and Lucey (2008)[18] tested weak-formefficiency in seven emerging Middle-Eastern North African(MENA) stock exchange markets. A unit root test and avariance ratio test of daily data was applied on data fromJanuary 1998 to November 2004. The null random walkhypothesis (RWH hereafter) was rejected and the marketspresented different levels of efficiency. The scale of effi-ciency in the MENA markets was affected by corporategovernance but economic liberalization appeared insignifi-cant.

In the Gulf countries, Marashdeh and Shrestha (2008)[24] tested the RWH on the Emirates exchange from Au-gust 2003 to April 2008. Using daily stock market data,two approaches were used. The first based on unit roottests (ADF, PP) and the second based on Perron (1997)

[28]tested the unit root hypothesis in the presence of un-known structural breaks. For both the ADF and the PP,the unit root hypothesis was rejected (accepted) at the firstdifference (at levels) and demonstrated that the Emiratesstock price index followed a random walk. The results ofthe Perron (1997)[28]model showed the presence of struc-tural breaks in the Emirates stock price index on 1/22/2006for both (IO1 and IO2) and on 6/1/2005 for the additivesOutlier model. In brief, all models supported the unit rootand the RWH which was consistent with the weak-form

efficiency hypothesis which could attract foreign portfolioinvestment, encourage foreign portfolio investment, encour-age the pricing and the availability of capital.

Butler and Malaikah (1992) [6] tested the EMH in theMiddle East (Saudi Arabia and Kuwait). They employed aserial correlation method and run tests over the period 1985to 1989, the results of which suggested that institutionalfactors affected operational inefficiency in the Saudi Ara-

bia stock exchange market. This result was less pronouncedin the Kuwaiti stock market. Serial correlation significancewas revealed in many Kuwait stocks, a result which wasfurther confirmed by Al-Loughani (1995)[3].

Squalli (2005) [33] employed a variance ratio test anddaily sectorial indices for the period 2000 to 2005 to inves-tigate market efficiency in selected sectors of the Dubai fi-nancial market and the Abu Dhabi securities exchange. Theresults showed that the RWH in all sectors of the UnitedArab Emirates (UAE) was rejected, with the exception ofthe Dubai banking sector and Abu Dhabi insurance sector.

Chancharat and Valadkhani (2007) [10]tested the RWHin the presence of structural breaks for 16 markets. Thetests developed Zivot and Andrews (1992) [39] and Lums-daine and Papell (1997) [22] were used in the study. The

RWH was accepted for 14 markets according to the Zivotand Andrews test and rejected for five markets accordingto the Lumsdaine and Papell test.

Ozdemir (2008) [27] investigated weak-form market ef-ficiency in Turkey using different methods (a ADF test, aunit root with two structural breaks, a run test and a vari-ance ratio test) for weak data over the period 1990-2005 inthe Istanbul Stock Exchange Market (ISE) and concludedin favor of the weak efficiency hypothesis. Abraham et al.(2002) [1] used the Beveridge-Nelson decomposition of in-dices and advanced mixed results to measure efficiency inthe Kuwaiti, Saudi and Bahraini markets.

Yang et al. (2008)[37] analyzed the temporal evolution ofstock market efficiency in the U.S., Japan, and Korea (Stan-dard and Poors 500 index, Nikkei 225 Stock Average, andthe Korean Composite Stock Price Index) using entropydensity2. The authors argued that the entropy density in-creased over time and consequently the markets becamemore efficient.

Bentes et al. (2008) [5] used conditionally heteroscedas-tic models like ARCH, GARCH, IGARCH and FIGARCH,and entropy measures like the Shannon entropy, Renyi en-tropy and Tsallis entropy to investigate long memory andvolatility clustering for the S&P 500, NASDAQ 100 andStoxx 50 indexes over the period 2002-2007. The resultsshowed evidence of nonlinear dynamics.

Dragota et al. (2009) [13]employed a Multiple VarianceRatio to test the RWH in the Romanian market. Using dailyand weekly returns for 18 companies listed on the first tierof the Bucharest stock exchange and the indexes of Roma-nian Capital Market over the period (first listing until the

end of 2006), the results supported the RWH. However, theRomanian market was found to be weakly efficient and re-turn forecasting was impossible to establish based on pastreturns. Zunino et al. (2009) [40] used forbidden patternsand permutation entropy concepts to quantify stock marketinefficiency. It was found that the degree of market ineffi-ciency was positively correlated with a number of forbid-den patterns and negatively correlated with the permuta-tion entropy. The results also showed that these two phys-ical concepts were helpful in discriminating stock market

2 The authors used some others statistical measures like probability distribution, scaling property of standard deviation, statisticalcomplexity, and autocorrelation function.

IJMSEM email for contribution: [email protected]


3/12

International Journal of Management Science and Engineering Management, 7(1): 53-63,2012 55

Table 1 Descriptive statistics

Countries Mean Median Maximum Minimum Standard

deviationSkewness Kurtosis Jarque-Bera P-value

EGYPT 0.000644 0.000000 0.092859 0.090046 0.016905 0.159546 7.037774 1716.419 0.000000

MOROCCO 0.000368 0.000117 0.062507 0.048187 0.009408 0.076783 7.097145 1758.765 0.000000

S. AFRICA 0.000373 0.001150 0.076363 0.130200 0.016999 0.623740 6.992878 1830.862 0.000000

CHINA 8.24E 05 8.1 4E 05 0.118180 0.144419 0.020548 0.038952 6.794926 1507.388 0.000000INDIA 0.000668 0.000995 0.098967 0.120975 0.017060 0.460392 7.369030 2085.832 0.000000

PAKISTAN 0.000243 0.000474 0.142051 0.157272 0.021075 0.582262 9.461630 4510.257 0.000000

INDONESIA 0.000225 0.000523 0.237737 0.430810 0.033227 1.070731 25.69696 54377.58 0.000000

KOREA 0.000640 0.000657 0.268808 0.216664 0.028005 0.184111 13.05005 10581.67 0.000000

MALAYSIA 0.000223 0.000000 0.258537 0.369670 0.020421 0.945062 66.00754 415729.7 0.000000

PHILIPPINES 7.26E 0 5 0 .0 00 00 0 0 . 21 97 17 0.092424 0.018783 1.039567 16.76995 20290.37 0.000000

TAIWAN 6.01E 05 3.52E 05 0.086510 0.130481 0.018186 0.123771 6.761228 1486.524 0.000000

THAILAND 0.000184 0.000172 0.181001 0.180845 0.023427 0.634131 13.08312 10805.43 0.000000

JORDAN 0.000379 0.000000 0.073713 0.094366 0.011147 0.392837 13.40510 11391.93 0.000000

TURKEY 0.000463 0.000522 0.220148 0.274195 0.034581 0.253300 9.537513 4498.427 0.000000

HUNGARY 0.000570 0.001155 0.124161 0.190124 0.019935 0.681615 11.60025 7932.948 0.000000

POLAND 0.000423 0.000595 0.119464 0.115906 0.019712 0.125560 5.652566 742.7504 0.000000

RUSSIA 0.000455 0.001264 0.242200 0.280966 0.032897 0.438820 13.12374 10803.61 0.000000

CZECH. R 0.000886 0.001108 0.089267 0.073933 0.016386 0.173237 5.246147 540.4110 0.000000

ARGENTINA 0.000219 0.000262 0.163412 0.336472 0.024890 1.357661 24.96665 51256.50 0.000000

BRAZIL 0.000484 0.001368 0.173349 0.176509 0.023769 0.222592 9.134779 3958.351 0.000000

COLOMBIA 0.000515 0.000330 0.164922 0.129676 0.017123 0.038464 12.98707 10436.08 0.000000

MEXICO 0.000536 0.000956 0.144457 0.217589 0.018653 0.385254 15.54593 16530.12 0.000000

PERU 0.000654 0.000630 0.106478 0.093377 0.015635 0.256927 7.360889 2017.316 0.000000

CHILE 0.000294 0.000393 0.070071 0.093769 0.012119 0.364330 6.936274 1676.636 0.000000

VENEZUELA 0.000180 0.000000 0.347299 0.451583 0.029991 0.826622 38.56505 132623.3 0.000000

TUNISIA 0.000384 0.000160 0.030405 0.021246 0.004445 0.409859 6.201521 1118.562 0.000000

dynamics. Zunino et al. (2010) [41] used the complexity-

entropy causality plane to distinguish the stages in stockmarket development, which showed that such a statisticalphysics approach was useful, allowing for a more refinedclassification of stock market dynamics.

Al Janabi et al. (2010) [2] tested for informational effi-ciency in the six emerging markets of the Gulf CooperationCouncil (GCC) with respect to oil and gold price shocks.A bootstrap simulation technique was used for the period2006-2008. They concluded that the GCC stock marketswere weakly efficient with regard to oil and gold prices.From this research, it was concluded that the gold and oilprice index information cannot improve GCC stock marketindex forecasting.

Wang et al. (2010) [35] examined the Shanghai indexEMH from the period December 1990 to December 2008 us-

ing both Hurst exponents, DME and DMEF methods. Theempirical results revealed that the degree of efficiency im-proved after the reforms. More precisely, the price-limitedreform ameliorated the efficiency in the long term whereasthe extent was narrow in the short term.

More recently, Yang et al. (2011) [38]analyzed the tem-poral evolution of statistical quantities such as the cumula-tive distribution function of volatility, the autocorrelationfunction, the detrended fluctuation analysis of log returns,and entropy density for 10 markets. They found patterns

and long-range correlations until the mid-1990s. In con-

trast, the long-range correlations for most markets short-ened, and the patterns weakened in the 2000s. The improve-ment in communication infrastructure such as the internetand internet-based trading systems, which help facilitatethe rapid dissemination of information, were offered as ex-planations for the results.

3 Methodology

3.1 Data description

In this study the daily closing spot prices relative totwenty-six emerging stock exchange markets3 were consid-ered for the period 1997-2007. The choice of emerging mar-kets is justified by the rapid economic growth experiencedin these markets and their economic structure as well asthe convergence toward a developed market. The emerg-ing stock markets have meaningful investment opportuni-ties such as more predictable returns, and lower correla-tions than developed market returns, so investors reducetheir risks through international portfolio diversification.The continuously compounded daily returns were computedas follows:

rt = 100 ln

PtPt1

, (1)

3 Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India, Indonesia, Jordan, Korea, Malaysia, Mexico,Morocco, Pakistan, Peru, Philippines, Poland, Russia, South Africa, Taiwan, Thailand, Tunisia, Turkey, and Venezuela.

IJMSEM email for subscription: [email protected]


4/12


0

200

400

600

800

1000

1200

500 1000 1500 2000 2500

EGYPT

100

200

300

400

500

600

500 100 0 1500 2000 2500

MOROCCO

100

200

300

400

500

600

500 1000 1500 2000 2500

SOUTHAFRICA

0

20

40

60

80

100

120

500 1000 1500 200 0 2500

CHINA

0

100

200

300

400

500

600

700

500 1000 1500 2 000 2500

INDIA

0

40

80

120

160

200

240

500 100 0 1 500 200 0 2500

PAKISTAN

0

100

200

300

400

500

600

700

500 1000 1500 2 000 2500

INDONESIA

0

100

200

300

400

500

500 1000 150 0 2 000 2500

KOREA

50

100

150

200

250

300

350

400

500 1000 1500 2000 2500

MALAYSIA

50

100

150

200

250

300

350

400

500 1000 1500 2 000 2500

PHILIPPINES

120

160

200

240

280

320

360

400

440

500 100 0 1 500 200 0 2500

TAIWAN

0

50

100

150

200

250

300

500 1000 1500 2000 2500

THAILAND

50

100

150

200

250

300

350

400

500 1000 1500 2000 2500

JORDAN

0

100

200

300

400

500

600

700

800

500 100 0 1 500 2000 2500

TURKEY

0

200

400

600

800

1000

1200

1400

500 1000 1500 2000 2500

HUNGARY

200

400

600

800

1000

1200

1400

1600

1800

500 1 000 1500 2000 2500

POLAND

0

200

400

600

800

1000

1200

1400

1600

5 00 1 000 1500 2000 2500

RUSSY

0

100

200

300

400

500

600

700

800

900

5 00 1000 150 0 2 000 2500

CZECH REPUBLIC

0

500

1000

1500

2000

2500

3000

3500

500 1000 1500 2000 2500

ARGENTINA

0

1000

2000

3000

4000

500 1000 1500 2000 2500

BRAZIL

0

100

200

300

400

500

600

700

500 100 0 1 500 200 0 2500

COLOMBIA

0

1000

2000

3000

4000

5000

6000

7000

500 1000 1500 2000 2500

MEXICO

0

200

400

600

800

1000

1200

1400

1600

500 1000 1500 2000 2500

PERU

0

400

800

1200

1600

2000

2400

500 1000 1500 2000 2500

CHILE

40

80

120

160

200

240

280

500 1000 1500 2000 2500

VENEZUELA

800

1200

1600

2000

2400

2800

500 1000 1500 200 0

TUNISIA

Fig. 1 Time-variations of daily indices spot prices

where rt and Pt are the percentage return and the indexclosing price on day (t), respectively.

3.2 Descriptive statistics

3.2.1 Normality tests

Descriptive statistics for all the daily returns are in Tab.

1.However, all index returns share similar statistical prop-erties. More precisely, all index returns did not correspondto a normal distribution assumption. According to theJarque-Bera test statistic, the null hypothesis of Gaussiandistribution was undeniably rejected. Descriptive graphs fordaily price levels, and daily returns for the market indexesare in Figs.1 2.Volatility clustering is apparent for all thereturn time series revealing the presence of heteroscedastic-ity.

3.2.2 Unit root analysis

Before fitting the time series, tests were done to check thepresence of unit roots and to test stationarity. Tab.2showsthe results of the Phillips-Perron (1988) [29]tests. These PPtests rejected the unit root hypothesis for all market dailyreturns4. So, from this it appears that all stock exchangemarket return time series are governed by an I(0) processwhich has no long-range memory.

3.3 The modified Shannon entropy

The Shannon entropy attributed to Claude Shannon(1948) [32]. The concept of entropy can be used where prob-abilities can be particularly defined and can be of greatassistance when examining financial chronics. In contrastto the GARCH models, the Shannon entropy captures theincertitude (randomness) of a financial time series withoutimposing any constraints on the theoretical probability dis-

4 These unit root and stationary test results could should be considered with caution because as these tests have beenwere laterrefined by several authors including Ng and Perron (2001) [28]). Moreover, some authors (see among others, Tanaka (1999) [34])have shown that most of these procedures have very low power if the alternatives are in a fractional form.



5/12


-.10

-.05

.00

.05

.10

5 00 1 000 1500 2000 250 0

EGYPT

-.06

-.04

-.02

.00

.02

.04

.06

.08

5 00 1000 1500 2000 2 500

MOROCCO

-.16

-.12

-.08

-.04

.00

.04

.08

500 1000 1500 2000 2 500

SOUTHAFRICA

-.15

-.10

-.05

.00

.05

.10

.15

500 1000 1500 2000 2500

CHINA

-.16

-.12

-.08

-.04

.00

.04

.08

.12

500 1000 1500 2000 2500

INDIA

-.16

-.12

-.08

-.04

.00

.04

.08

.12

.16

5 00 1 000 1500 2000 250 0

PAKISTAN

-.5

-.4

-.3

-.2

-.1

.0

.1

.2

.3

5 00 1000 150 0 2000 2500

INDONESIA

-.3

-.2

-.1

.0

.1

.2

.3

500 1000 1500 2000 2500

KOREA

-.4

-.3

-.2

-.1

.0

.1

.2

.3

500 100 0 1 500 2000 2500

MALAYSIA

-.10

-.05

.00

.05

.10

.15

.20

.25

500 1000 1500 2000 2500

PHILIPPINES

-.15

-.10

-.05

.00

.05

.10

5 00 1 000 1500 2000 250 0

TAIWAN

-.2

-.1

.0

.1

.2

5 00 1000 150 0 2000 2500

THAILAND

-.12

-.08

-.04

.00

.04

.08

500 1000 1500 2000 2500

JORDAN

-.3

-.2

-.1

.0

.1

.2

.3

500 1000 1500 2000 2500

TURKEY

-.20

-.15

-.10

-.05

.00

.05

.10

.15

500 1 000 1500 2000 250 0

HUNGARY

-.15

-.10

-.05

.00

.05

.10

.15

5 00 1 000 1500 2000 250 0

POLAND

-.3

-.2

-.1

.0

.1

.2

.3

5 00 1000 150 0 2000 2500

RUSSY

-.08

-.04

.00

.04

.08

.12

500 1000 1500 2000 2500

CZECH REPUBLIC

-.4

-.3

-.2

-.1

.0

.1

.2

500 1000 1500 2000 2500

ARGENTINA

-.20

-.15

-.10

-.05

.00

.05

.10

.15

.20

500 1000 1500 2000 2500

BRAZIL

-.15

-.10

-.05

.00

.05

.10

.15

.20

5 00 1 000 1500 2000 250 0

COLOMBIA

-.3

-.2

-.1

.0

.1

.2

5 00 1000 150 0 2000 2500

MEXICO

-.12

-.08

-.04

.00

.04

.08

.12

500 1000 1500 2000 2500

PERU

-.12

-.08

-.04

.00

.04

.08

500 1000 1500 2000 2500

CHILE

-.5

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

500 1000 1500 2000 2500

VENEZUELA

-.03

-.02

-.01

.00

.01

.02

.03

.04

500 1000 1500 2000

TUNISIA

Fig. 2 Time-variations of daily indices returns

tribution. This metric was used to both check the efficiencymarket weak-form hypothesis and to rank between markets.

According to Risso (2008) [30], the modified Shannonentropy is defined as follows

H= 1

log2(n)

ni=1

pilog2pi

, (2)

where n is the total number of sequences, pi is the proba-

bility of sequence i= 1,2, , n and l og2 is the logarithmbase2, which is used because the information is measuredin bits. The convention 0 log20 = 0 is adopted.

To calculate the Shannon entropy H-statistic, the follow-ing steps were conducted. First, the time series was sym-bolized to derive more information. In this study, the timeseries contained positive and negative index returns. In thiscase, zero symbols were assigned to the negative returns,the number one (1) symbol to the positive returns with zerobeing the breaking point between the two. The zero repre-sented a drop in prices (referred to as bear market) while

the number one (1) represented a rise prices (referred toas bull market). So, from these, the original returns timeseries was converted into a symbolic time series involvingonly two values (0 and 1).

rt > 0, st = 1rt 0, st = 0

(3)

In expression(3),r t ands t denote the indices return seriesat time t and its corresponding symbolic series respectively.

The second step of choosing the optimal sequence orlength5. However, a sequence of five days was set as anentropy of six days had approximately the same result asfive days; H(L = 5) H(L > 5). The total number of se-quences was given by n = 2L =25 =32, where L is a lengthor a sequence of days (L= 5).

In the third step, the probability distribution of each se-quence i was calculated. The probability of sequence i wasthe total quantity of sequencei divided by the whole period.

5 A sequence or length L ofm days is a sequence or length ofm consecutive returns.



6/12


Table 2 PP unit root tests

CountriesIndex series Return series

Intercept Trend and

interceptNone Intercept

Trend and

InterceptNone

EGYPT 0.423893 47.62156

MOROCCO 1.497596 41.0566

S. AFRICA 1.326623 46.17912

CHINA 0.175536 43.31700

INDIA 2.518131 46.58373

PAKISTAN 2.64733 47.65622

INDONESIA 1.823252 44.30675

KOREA 0.936046 46.03422

MALYSIA 2.186765 44.19613

PHILIPPINES 0.559478 42.16723

TAIWAN 2.462995 48.01041

THAILAND 2.803366 41.75280

JORDAN 1.022909 49.74087

TURKEY 0.971085 47.53552

HUNGARY 1.228158 46.82859

POLAND 0.561376 46.00306

RUSSIA 1.924193 47.36685

CZECH. R 5.541759 45.18803

ARGENTINA 0.895647 49.11196

BRAZIL 1.153497 45.66158

COLOMBIA 1.426862 40.83004

MEXICO 1.020625 46.69633

PERU 5.418627 45.51433

CHILE 0.809273 41.30271

VENEZUELA 4.277928 50.10688

TUNISIA 4.546649 31.86900

Critical values

3.432761(1%)

2.862491(5%)2.567321(10%)

3.961699(1%)

3.411597(5%)3.127668(10%)

*** Denotes statistically significant parameters at the 1% level.

* Denotes statistically significant parameters at the 10% level.

The modified Shannon entropy Hoscillated between zeroand one. The maximum incertitude was obtained when theevents were equiprobable (p1 = p2 = = pn = 1/n).When the Hequals one and the entropy attains its maxi-mum, the index price shows randomness and the market isconsidered efficient. In contrast, the minimum incertitudewas when (p1 or p2 or pn = 0 or 1). When the Hequalszero and the entropy reaches its minimum, the market is in-efficient. Therefore, the presence of patterns was detected.

To study the stock market efficiency daily evolution, atime-window of 100 observations was employed allowing thecapture of the locality, as shown in Fig. 3.Grech and Mazur(2004) [16] argued that the time-windows should be smallto detect the locality.100 observations lead to the detectionof the effect of major events on weak-form market efficiency.The Shannon entropy coefficient was shown to have goodsample properties over short data horizons.

Then, a rolling sample approach6 was used. The samplewas rolled one point forward eliminating the first obser-

vation and including the next one for re-estimation of theShannon entropy. This procedure was repeated until theend of the entire selected sample.The application of therolling approach was shown to capture the persistence ofstock price deviation from a random walk over time.

4 Empirical results and interpretations

The estimation of the Shannon entropy over differentrolling time-windows from moment 1 to the end of sample

allowed thousands of time-varying H series to be obtained.The descriptive statistics for the modified Shannon entropyexponent for all markets are given in Tab. 3.

From this data, the minimum of Shannon entropy ex-ponent was 0.918 for the Tunisian stock market and themaximum was 0.953 for Argentinian market. The Jorda-nian stock market was the most volatile with the risk (interms of the standard deviation) of this market being 5.30%in contrast to 0.12% for the Brazilian market. The Skewnessand Kurtosis measures indicated that all series didnt follow

6 Cajueiro and Tabak (2005) [9], Cajueiro et al. (2009)[7], Lim (2007) [19], Lim et al. (2008)[21], Risso (2008) [30]have commonlyused the rolling sample approach to preserve the dynamic aspect of efficiency.



7/12


Table 3 The modified Shannon entropy exponents for emerging stock markets

Countries Mean Median Maximum Minimum Standard

deviationSkewness Kurtosis Jarque-Bera P-value

EGYPT 0.923073 0.932053 0.990125 0.800551 0.038923 0.995516 3.524478 425.3413 0.000000

MOROCCO 0.928487 0.930704 0.989144 0.830628 0.031063 0.437128 2.676798 87.16800 0.000000

S. AFRICA 0.946675 0.951668 0.989396 0.845438 0.023100 1.077581 4.255331 624.1311 0.000000

CHINA 0.942773 0.947087 0.981977 0.854457 0.022497 0.932680 3.859727 423.2765 0.000000INDIA 0.936200 0.942713 0.981396 0.832848 0.030212 0.848235 3.179048 291.9767 0.000000

PAKISTAN 0.941448 0.946691 0.981777 0.835598 0.022826 1.442022 5.770345 1604.584 0.000000

INDONESIA 0.938324 0.938428 0.993847 0.854822 0.022909 0.303134 3.253848 43.34389 0.000000

KOREA 0.946703 0.950474 0.988215 0.879822 0.021513 0.899924 3.453264 3445.6381 0.000000

MALAYSIA 0.934620 0.941609 0.983157 0.816964 0.030715 1.286896 4.547964 905.0669 0.000000

PHILIPPINES 0.938684 0.945155 0.982706 0.854428 0.025286 0.882307 3.432168 331.1632 0.000000

TAIWAN 0.946750 0.949777 0.990176 0.835324 0.023033 1.173500 5.247926 1059.679 0.000000

THAILAND 0.940695 0.944713 0.985525 0.853042 0.024409 0.846339 3.547034 317.4951 0.000000

JORDAN 0.914453 0.931079 0.986905 0.680388 0.053080 1.406629 5.045660 1213.948 0.000000

TURKEY 0.945972 0.947732 0.982957 0.882786 0.018976 0.406412 2.622059 80.62004 0.000000

HUNGARY 0.949120 0.951087 0.985977 0.873609 0.019409 0.788418 3.948750 339.7830 0.000000

POLAND 0.948514 0.950474 0.993595 0.885430 0.021657 0.472635 2.713612 97.88041 0.000000

RUSSIA 0.947919 0.951486 0.987105 0.878428 0.021374 0.719172 3.092879 208.4384 0.000000

CZECH. R 0.945095 0.951932 0.987686 0.819073 0.028131 1.749427 6.590988 2522.097 0.000000

ARGENTINA 0.947287 0.953229 0.987738 0.857048 0.024025 0.920180 3.492893 364.1967 0.000000

BRAZIL 0.948827 0.951345 0.981247 0.888829 0.017082 0.608314 3.087910 149.2872 0.000000

COLOMBIA 0.922693 0.926141 0.982558 0.747844 0.037958 1.253755 5.927346 1490.648 0.000000

MEXICO 0.940345 0.944629 0.983886 0.856455 0.022660 1.011291 3.878266 487.8398 0.000000

PERU 0.939593 0.943312 0.982622 0.842688 0.026186 0.669450 2.996721 179.8642 0.000000

CHILE 0.929149 0.933869 0.990905 0.745213 0.035575 1.661011 8.016292 3631.968 0.000000

VENEZUELA 0.943734 0.946757 0.980215 0.857442 0.021972 0.825897 3.635011 314.2099 0.000000

TUNISIA 0.916511 0.918676 0.984215 0.813043 0.035843 0.442804 2.649225 89.03330 0.000000

a normal assumption. Skewness was asymmetric and nega-

tive for all markets, which showed that the series had a longleft tail distribution. Kurtosis was less than 3 for the Moroc-can, Turkish, Polish, Peruvian and Tunisian series implyingthat the tails taper down more rapidly than the normal dis-tribution (leptokurtic distribution). The series distributionfor all indexes werenot normally distributed. Fig. 3presentsthe daily efficiency measure time-paths for emerging mar-kets. As shown in this figure, the normality distributionand the stationarity hypothesis for all time series can berejected, which shows that these Shannon entropy expo-nents are time-varying. The obtained results are not dueto noise in the data time series. The best tool for rankingefficiency markets is the median H of modified Shannonentropy.

As mentioned above, the Shannon entropy exponent be-havior exhibited a large deviation from the Gaussian distri-bution. For this reason, the meaningfulness of the empiricalresults was tested by employing a nonparametric statisticapproach. The nonparametric test results are shown in Tab.4.From this test, the equality of the median null hypothesiswas rejected for all series and was rejected for all series andwere proven to be significant.

As shown in Tab. 3, the efficiency level is time-varying.This result supports those of Yang et al. (2008)[37], Zunino et al. (2009, 2010) [40, 41] and Yang et al.(2011) [38]. The median of the modified Shannon entropyvalue (H) is larger for Argentinian market, which indicatesthat this market is more efficient. This result confirms those

obtained by Cajueiro and Tabak (2005)[9]. In contrast, the

Tunisian market was less efficient.Tab.5 shows the area ranking efficiency for the emerg-ing markets. According to this table, the modified Shannonentropy median value for Argentina (0.953) is the highestwhile the Colombian (0.926) is at the tail end of the LatinAmerican stock market ranking. For the Asian markets, theKorean market is the more efficient market and Indonesianmarket is the less efficient market. For South Africa andthe MENA region, the median Hfor South Africa is 0.951whereas for Tunisia it is 0.918. For the European region,the Czech market is the most efficient. The difference inthe efficiency degree between all indices can be explainedby the specific features of each market.

Table 4 Nonparametric tests of equality of medians

Method df Value P-value

Med. Chi-square 4 15.09091*** 0.0045

Adj. Med. Chi-square 4 9.325000* 0.0535

Kruskal-Wallis 4 22.23077*** 0.0002

Kruskal-Wallis (tie-adj.) 4 22.23837*** 0.0002

van der Waerden 4 22.01325*** 0.0002

*** Denotes statistically significant parameters

at the 1% level.

* Denotes statistically significant parameters

at the 10% level.



8/12


0.76

0.80

0.84

0.88

0.92

0.96

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

EGYPTT

.......Internet Bubble.......Asian financial crisis

0.80

0.84

0.88

0.92

0.96

1.00

98 99 00 01 02 03 04 05 06

MOROCCO

0.84

0.88

0.92

0.96

1.00

98 9 9 0 0 0 1 0 2 0 3 04 0 5 0 6

SOUTHAFRICA

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

CHINA

.......Asianfinancial crisis

0.80

0.84

0.88

0.92

0.96

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

INDIA

0.80

0.84

0.88

0.92

0.96

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

PAKISTAN

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

INDONESIA

mnimum efficiencyOctober 2005.......

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

98 9 9 0 0 0 1 0 2 0 3 04 0 5 0 6

KOREA


0.80

0.84

0.88

0.92

0.96

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

MALAYSIA

.......Asianfinancial crisis.......11/09/2001 terrorist attacks

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

PHILIPPINES

.......Asiancrisis .......11/09/2001 terrorist attacks

0.80

0.84

0.88

0.92

0.96

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

TAIWAN

.......Asianfinancialcrisis

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

THAILAND


0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

98 9 9 0 0 0 1 0 2 0 3 04 0 5 0 6

JORDAN

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

TURKEY

.......20/11/2000 Turkeycrisis

......crash19990.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

HUNGARY

......Internet Bubble

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

POLAND

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

RUSSIA

......17/08/1998 Russia crisis

2003 USA militaryin Iraq....

0.80

0.84

0.88

0.92

0.96

1.00

98 9 9 0 0 0 1 0 2 0 3 04 0 5 0 6

CZECHREPUBLIC

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

ARGENTINA

Argentina crisis......

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

BRAZIL

.......Brazil cri sis

0.70

0.75

0.80

0.85

0.90

0.95

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

COLOMBIA


0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

MEXICO

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

98 9 9 0 0 0 1 0 2 0 3 04 0 5 0 6

PERU

0.70

0.75

0.80

0.85

0.90

0.95

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

CHILE


0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

9 8 9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6

VENEZUELA

.......Asianfinancial crisis.......USA militaryin Iraq

....11/09/2001 terrorist attacks

0.80

0.84

0.88

0.92

0.96

1.00

98 99 00 01 02 03 04 05 0 6

TUNISIA

Fig. 3 Daily efficiency measure time-paths for emerging markets

Table 5 Ranking for emerging stock markets

Asia HMedian Latin America HMedian S. AFRICA & MENA HMedian Europe HMedian

KOREA 0.950474 ARGENTINA 0.953229 S. AFRICA 0.951668 CZECH R. 0.951932

TAIWAN 0.949777 BRASIL 0.951345 TURKEY 0.947732 RUSSIA 0.951486

CHINA 0.947087 VENEZUELA 0.946757 EGYPT 0.932053 HUNGARY 0.951087

PAKISTAN 0.946691 MEXICO 0.944629 JORDANIE 0.931079 POLAND 0.950474PHILIPPINES 0.945155 PERU 0.943312 MOROCCO 0.930704

THAILAND 0.944713 CHILE 0.933869 TUNISIA 0.918676

INDIA 0.942713 COLOMBIA 0.926141

MALAYSIA 0.941609

INDONESIA 0.938428



9/12


Table 6 Argentinas financial crisis and weak-form market efficiency

Variable Coefficient Std. deviation t-Statistic P-value

Intercept 16.300 35 1 .78389 1 9.1375 27 0.0000

Shannon entropy 16.859 41 1 .87844 8 8.975181 0.0000

Mean dependent var 0.577658 S.D. dependent var 0.494035

S.E. of regression 0.486144 Akaike info criterion 1.327545

Sum squared resid 568.6248 Schwarz criterion 1.332351Log likelihood 1596.365 Hannan-Quinn criter 1.329293

Restr. log likelihood 1639.936 Avg. log likelihood 0.662942

LR statistic 87.14387 McFadden R-squared 0.026569

Probability (LR stat) 0.000000 Total observations 2408

*** Denotes statistically significant parameters at the 1% level.

In addition, the European area is the more efficient whilethe South Africa and MENA region are the most inefficient.The median of medians for the European region is 0.9512while for the South Africa and MENA region they are both0.931. The Asian region is in second place (0.9451) whilethe Latin American zone is third (0.9446).

As observed graphically, the emerging stock markets evo-

lution of efficiency is not similar, but have some character-istics in common. First, there was a sudden drop in theefficiency measures in August 1990, which coincided withthe Iraqi Invasion of Kuwait.

Furthermore, a minimum level of efficiency correspondedto crisis periods such as the1997 Asian financial crisis (forexample Chinese and Korean markets), the 2001 Argen-tinian economic crisis, the 2000 Turkish crisis, the 1998Brazilian crisis, and the 1998 Russian crisis. In September2001 and March 2003, the emerging markets efficiency wasat its lowest level, which was possibly due to the increasinguncertainties caused by the September 11, 2001 terroristattacks and the USA military action in Iraq (Gulf war).The EMH has direct consequences for portfolio managersin their trading strategy design and for financial managersfor equity financing decisions (Wang and Yang, 2010 [36]).

The results of these tests have several implications fortraders, portfolio managers and policymakers. For traders,by explaining the flow of information between emergingstock markets, while for portfolio managers it spells out thedynamic linkages between the emerging stock markets overtime allowing for the development of an appropriate hedg-ing strategy during difficult times such as crashes, financialcrises and economic crises. These findings also have someimplications for policymakers who watch the stock marketas an indicator of economic propensity. More importantly,the efficiency market pattern has strategic policy implica-tions. An inefficient stock market provides opportunities forprofitable transactions so having this kind of informationallows government authorities to determine when to reduceinterest rates, and also to evaluate the consequences of dif-

ferent economic policies such as money supply, exchangerates and inflation.

The efficiency dynamic was shown to b e dissimilar inall markets. Several factors may explain these findings.Cajueiro and Tabak (2004) [8] showed different levels ofefficiency over time and suggested that the informationspeed, capital follows and nonsynchronous trading mayaffect efficiency levels. According to Cajueiro and Tabak(2005) [9], the differences in microstructure market condi-tions may also explain differences in emerging market ef-ficiency. Charles and Darne (2009) [11] suggested that the

market deregulation explained the divergence in level effi-ciency between Brent and WTI (West Texas Intermediate)indices in the crude oil market.

Aloui (2005) [4] argued that a lack of cultural equityslows investor reaction to information which could reduceefficiency. On the other hand, Oh et al. (2007)[26]tested ef-ficiency in European, North American, Asian, and African

foreign exchange markets and found that the European andNorth American markets are were more efficient than theAsian and African markets, concluding that differences inliquidity could explain the difference.

Lagorade-Segot and Lucey (2008) [18] showed that cor-porate governance (managerial liability and shareholderprotection) and market depth affected MENA market effi-ciency concluding that the differences in stock market sizeplayed a crucial role in the efficiency extent. Eom et al.(2008) [14] suggested that the financial market degree ofefficiency played a fundamental role when determining in-formation flow direction and concluded that informationflowed from the more efficient stock to the less efficientstock. Using a time-varying Hurst exponent, Cajueiro etal. (2009)[7] suggested that financial market liberalizationincreased the efficiency level of the Athens stock market.

4.1 Robustness: financial crisis and stock marketefficiency

In a further test the impact of Argentinas financial cri-sis7 on informational efficiency was studied. For this pur-pose, a logit model was employed. Suppose a variable ytakes a value of one (1) if there is a financial crisis and avalue of zero otherwise. The latent variable y is defined asfollows

yi =+ Hi+ i , (4)

where H is the efficiency measure and i is an error term.The observable variable y is given by

yi = 1, ifyi >0

0,otherwise

(5)

The present logit model is defined as follows

P(y= 1) = 1

1+e(+Hi) =

e(+Hi)

1+e(+Hi). (6)

Tab. 6 reports the regression of the logit model whichseemed to have a high significance. It can be concluded fromthis table that informational efficiency is negatively relatedto the probability of a financial crisis. The obtained resultscorroborated those of Lim et al. (2008)[21] and Risso (2008)[30].

7 See Setser and Gelpern (2006) [31] for more information about Argentinas financial crisis.



10/12


-

-

-

-

-

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

98 99 00 01 02 03 04 05 06

......Argentina financial crisis

......Brazil financial crisis

Full payment of the IMF's debt.......

Fig. 4 Time-varying efficiency for Argentina stock market

From Fig. 4, a significant fall in the Argentinian stockmarket efficiency level was experienced during the periodof crisis. However, financial liberalization, financial global-ization and market integration also increase the instabilityof stock markets. Hence, the market is more open to for-eign investors who influence private investment booms andincrease incertitude.

Increasing foreign portfolio investment and informationalasymmetries can reduce market efficiency and disrupt finan-cial market functions. These factors seemed to be determi-nant in the Argentinian financial crisis. Authorities would

need to implement reforms and introduce monitoring oncapital flows, and need to be aware as to how political andeconomic events affect the markets ability to allocate fundsto the most productive activities.

5 Conclusions

EMH is a key modern financial theory concept. Everyinvestor is interested in measuring the stock market ran-domness. The aim of this paper was to investigate weak-form efficiency in 26 emerging stock markets using a sym-bolic time series analysis and a modified Shannon entropy.Both a data time-window for 100 days and a rolling sam-ple approach were employed in order to study the marketefficiency daily evolution. The results showed that the Shan-non entropy exponent is time-varying, which suggested that

market efficiency is dynamic and evolves over time.The results also showed support for the findings of pre-

vious studies such as Al Janabi et al. (2010) [2], Cajueiroand Tabak (2005) [9], Cajueiro et al. (2009) [7], Charlesand Darne (2009) [11], Lagorade-Segot and Lucey (2008)[18], Lim (2007) [19], Lim et al. (2008) [21], Risso (2008)[30], Wang et al. (2010) [35] and Yang et al. (2011) [38].Previous research attributed the difference in stock marketefficiency degrees to factors such as market liquidity, mar-kets capitalization, and corporate governance. According tothe empirical results, the median H in Argentina was thehigher while the smallest median Hwas in Tunisia. Thus,the Argentinian market was considered the most efficientmarket while the Tunisian equity market was the least effi-cient. Efficiency was also measured across geographic areas.

The European region was found to be the most efficient,the South African and MENA regions the most inefficient.Finally, the results suggested that informational efficiencywas negatively related to financial crises.

In sum, the global efficiency of markets has importantimplications for both domestic and international investors,such as attracting domestic and foreign portfolio investmentand improving the resource allocation.

It will be interesting in the future to apply the modifiedShannon entropy to other financial time series such as ex-change and commodity markets or to test the relationshipbetween level efficiency and financial reforms using condi-tionally heteroscedastic models.

References

[1] Abraham, A., Fazal, J., and Sulaiman, A. (2002). Testingthe random walk behavior and efficiency of the gulf stockmarkets. The Financial Review, 37:469480.

[2] Al-Janabi, M., Hatemi, A., and Irandoust, M. (2010). Anempirical investigation of the informational efficiency of theGCC equity markets: Evidence from bootstrap simulation.International Review of Financial Analysis, 9: 4754.

[3] Al-Loughani, N. (1995). Random walk in thinly tradedstock markets: The case of kuwait. Arab Journal of Ad-ministration Science, 3:189209.

[4] Aloui, C. (2005). Long-range dependence in daily volatil-ity on tunisian stock market. Economic Research ForumWorking Paper, 40:325.

[5] Bentes, S., Menezes, R., and Mendes, D. (2008). Long mem-ory and volatility clustering: Is the empirical evidence con-sistent across stock markets? Physica A, 387:38263830.

[6] Butler, K. and Malaikah, S. (1992). Efficiency and ineffi-ciency in thinly traded stock markets: Kuwait and SaudiArabia. Journal of Banking and Finance, 16:197210.

[7] Cajueiro, D., Gogas, P., and Tabak, B. (2009). Does fi-nancial market liberalization increase the degree of marketefficiency? Does financial market liberalization increase the

degree of market efficiency?, 18:5057.[8] Cajueiro, D. and Tabak, B. (2004). Ranking efficiency for

emerging markets. Chaos, Solitions and Fractals, 22:349352.

[9] Cajueiro, D. and Tabak, B. (2005). Ranking efficiency foremerging markets II. Chaos, Solitions and Fractals, 23:671675.

[10] Chancharat, S. and Valadkhani, A. (2007). Testing for ran-dom walk hypothesis and structural breaks in internationalstock prices. University of Wollongong, Working Paper, 715.

[11] Charles, A. and Darne, O. (2009). The efficiency of thecrude oil markets: Evidence from variance ratio tests. En-ergy Policy, 37:42674272.

[12] Dickey, D. and Fuller, W. (1979). Distribution of the estima-tors for autoregressive time series with a unit root. Journalof the American Statistical Association, 74:427431.

[13] Dragota, V., Stoian, A., and et al. (2009). The develop-ment of the romanian capital market: Evidences on informa-tion efficiency. Romanian Journal of Economic Forecasting,2:147160.

[14] Eom, C., Jung, W., and et asl. (2008). Effects of time depen-dency and efficiency on information flow in financial mar-kets. Physica A, 387:52195224.

[15] Fama, E. (1991). Efficient capital markets: II. Journal ofFinance, 46:15751617.

[16] Grech, D. and Mazur, Z. (2004). Can one make any crashprediction in finance using the local hurst exponent idea?Physica A, 336:133145.

[17] Grech, D. and Mazur, Z. (2004). Can one make any crashprediction in finance using the local Hurst exponent idea.

Physica A, 336: 133145.[18] Lagoarde-Segot, T. and Lucey, B. (2008). Efficiency in

emerging markets-evidence from the MENA region. Insti-tutions & Money, 18:94105.

[19] Lim, K. (2007). Ranking market efficiency for stock mar-kets: A nonlinear perspective. Physica A, 376:445454.

[20] Lim, K. and Brooks, R. (2011). The evolution of stock mar-ket efficiency over time: A survey of the empirical literature.Journal of Economic Surveys, 25(1):69108.

[21] Lim, K., Brooks, R., and Kim, J. (2008). Financial crisisand stock market efficiency: Empirical evidence from Asiancountries. International Review of Financial Analysis, 17:571591.



11/12


[22] Lumsdaine, R. and Papell, D. (1997). Multiple trend breaksand the unit root hypothesis. The Review of Economics andStatistics, 79:212218.

[23] Malkiel, B. (2003). The efficient market hypothesis and itscritics. Journal of Economic Perspectives, 17(1):5982.

[24] Marashdeh, H. and Shrestha, M. (2008). Efficiency inemerging markets-evidence from the emirates securitiesmarket. Efficiency in Emerging Markets-Evidence from theEmirates Securities Market, 12:143150.

[25] Ng, S. and Perron, P. (2001). Lag length selection and theconstruction of unit root tests with good size and power.Econometrica, 15:15191554.

[26] Oh, G., Kim, S., and Eom, C. (2007). Market efficiency infreign exchange markets. Physica A, 382:209212.

[27] Ozdemir, Z. (2008). Efficient market hypothesis: Evidencefrom a small open economy. Applied Economics, 40(5):633641.

[28] Perron, P. (1997). Further evidence on breaking trend func-tions in macroeconomic variables. Journal of Econometrics,80:355385.

[29] Philips, P. and Perron, P. (1988). Testing for unit roots intime series regression. Biometrika, 75:335346.

[30] Risso, W. (2008). The informational efficiency and the fi-nancial crashes. Research in International Business andFinance, 22:396408.

[31] Setser, B. and Gelpern, A. (2006). Pathways through finan-cial crisis: Argentina. Global Governance, 12:465487.

[32] Shannon, C. (1948). A mathematical theory of communi-cation. The Bell System Technical Journal, 27:623656.

[33] Squalli, J. (2005). Are the UAE Financial Markets Effi-cient? PhD thesis, Zayed University. Working Paper, No.05-01.

[34] Tanaka, K. (1999). The nonstationary unit root fractionaltest. Econometric Theory, 15:549582.

[35] Wang, Y., Liu, L., and et al. (2010). Analysis of marketefficiency for the shanghai stock market over time. PhysicaA, 389:16351642.

[36] Wang, T. and Yang, J. (2010). Nonlinearity and intraday ef-ficiency tests on energy futures markets. Energy Economics,32:496503.

[37] Yang, J., Kwak, W., and et al. (2008). Increasing mar-ket efficiency in the stock markets. The European PhysicalJournal B, 61:241246.

[38] Yang, J., Kwak, W., and Kaizoji, T. (2011). Temporal evo-lution into more efficient market stock market. Physica A,390:20022008.

[39] Zivot, E. and Andrews, D. (1992). Further evidence on thegreat crash, the oil-price shock, and the unit-root hypothe-sis. Journal of Business and Economic Statistics, 10:251270.

[40] Zunino, L., Zanin, M., and et al. (2009). Forbidden pat-terns, p ermutation entropy and stock market inefficiency.

Physica A, 388:28542864.[41] Zunino, L., Zanin, M., and et al. (2010). Complexity-

entropy causality plane: A useful approach to quantify thestock market inefficiency. Physica A, 389:18911901.



12/12

Ranking Efficiency for Twenty-six Emerging Stock Markets

Documents

Transcript of Ranking Efficiency for Twenty-six Emerging Stock Markets