is long memory a property of thin stock markets? international evidence using arab countries

Volume 1, Number 3 2003 Article 4

Review of Middle East Economics andFinance

Is Long Memory a Property of Thin StockMarkets? International Evidence Using Arab

Countries

Imed Limam, The Arab Planning Institute

Recommended Citation:Limam, Imed (2003) "Is Long Memory a Property of Thin Stock Markets? InternationalEvidence Using Arab Countries," Review of Middle East Economics and Finance: Vol. 1: No. 3,Article 4.

DOI: 10.2202/1475-3693.1015

Volumes 1-3 of Review of Middle East Economics and Finance were originally published by theTaylor & Francis Group.

Brought to you by | University of Newcastle, AustraliaAuthenticated | 134.148.29.34

Download Date | 3/13/14 9:39 AM

REV. MIDDLE EAST ECON. FIN., DECEMBER 2003, VOL. 1, NO. 3, 251–266

Is long memory a property of thinstock markets? International evidenceusing Arab countries

IMED LIMAM

The Arab Planning Institute, PO Box 5834, Safat-Code 13059,Kuwait (e-mail: [email protected])

The paper analyzes the long memory property of stock index returns in14 markets with diverse levels of development. While the sample includesthe developed stock markets of Japan, UK and USA, it also includes, inaddition to the emerging markets of Brazil, India and Mexico, thoseof eight Arab countries as benchmarks of thin markets with the aim ofinvestigating the link between fractional integration dynamics in stockreturns and the level of stock market development. Using parametric andsemi-parametric estimation procedures, the results show that the propertyof long-range dependence in stock index returns tend to be associated withrelatively thin stock markets. Evidence from the Arab countries seems tosuggest that long-memory might also be linked to the peculiar character-istics and the environment within which each stock market operates.

Keywords: long memory; stock markets; stock returns

JEL Classification: C22–G12

1. Introduction

There is ample evidence in recent literature pointing to the importance oflong-range dependence or long memory processes in describing financial dataand particularly stock market returns (Greene and Fielitz, 1977; Aydogan andBooth, 1988; Lo, 1991; Cheung et al., 1993; Ding et al., 1993; Mills, 1993;Crato, 1994; Cheung and Lai, 1995; Chow et al., 1995; Barkoulas andBaum, 1996; Lobato and Savin, 1997; Henry, 2002). The relevance oflong memory processes in modeling long-term properties stems from thefact that many financial time series, although appearing to be stationary,exhibit a dependence among distant observations. This has many importantimplications for modeling financial variables, notably stock prices.

If information accrues to market participants, or they adjust to it onlygradually, successive returns would tend to be dependent showing persistenceor long memory. This represents evidence against the weak form of efficiencythat is implicitly assuming no memory in the series of price changes and the

Review of Middle East Economics and Finance ISSN 1475-3685 print/ISSN 1475-3693 online# 2003 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/1475368032000158241



inability of investors to use past information to predict future returns so as tobe able to realize abnormal profits.1

In addition, as argued by Beran (1992), long memory can seriously under-mine many classical statistical inferences and the usefulness of conventionallinear models as accurate tools to forecast the behavior of processes with longmemory. More specifically, Lo (1991) points out the implications of longmemory on many statistical inferences in several financial areas such as, capitalasset, arbitrage and derivatives pricing theories.

The empirical evidence related to long memory dynamics in stock marketreturns is mixed with regard to finding overwhelming support of the presenceof long memory. Many studies (Lo, 1991; Mills, 1993; Crato, 1994; Barkoulasand Baum, 1996 and Henry, 2002, among others) related to developed stockmarkets, such as in the USA and UK, failed to find evidence of long memoryin stock returns. The available evidence on less developed markets is rathersupportive of the existence of long memory dynamics in stock returns(Barkoulas et al., 1996; Sadique and Silvapulle, 2001; Wright, 2001; Henry,2002).

The absence of long memory dynamics can be rationalized for developedstock markets on the grounds that they are informationally efficient. Prices tendto reflect all publicly available information and any new one is fully arbitragedaway. Thin markets, on the other hand, are characterized by various institu-tional rigidities that perpetuate informational inefficiency and asymmetry.

Inappropriate information acquisition and dissemination about firmsissuing equities, lack of adequate regulatory environment, especially in relationto property rights and protection of creditors were found to be strongly associ-ated with low levels of financial and stock market development (Levine, 1999).In addition, the presence of price manipulations, use of inside information,and the inadequacy of important institutional aspects in relation to listingrequirements and the absence of specialized brokers, tend to be typicalcharacteristics of thin markets. These characteristics encourage speculativeactivities and may explain the departure of stock prices in these marketsfrom their fundamentals and their slow adjustment to new information.

Although the empirical literature points to the possible link between thelong memory property and level of development of stock markets, this linkhas not been clearly established. Few studies, including Harvey (1995) andBekaert and Harvey (1995), have reported persistence in the stock returns ofemerging markets more pronounced than those in developed ones. The serialcorrelation coefficients for stock returns in emerging markets were found to bestatistically more significant than their developed counterparts pointing to abetter predictability, and hence more inefficiency, in the former than in thelatter. However, while simple autocorrelation analysis is useful in detectinglong-run dependence if the pattern of dependence is periodic and consistentover time, it is less useful a tool if this dependence is not periodic. Direct testsof long memory are more useful in the sense that they take into account bothperiodic and non-periodic forms of dependence.

On the other hand, most of the recent studies, including Sadiqueand Silvapulle (2001), Wright (2001) and Henry (2002), aiming at providing

252 I. Limam



international evidence on the long run memory property in stock returns, havesamples of emerging markets that can hardly be classified as thin in terms ofsize and liquidity.

The objective of the paper is to test stock index returns for long memoryusing data from a sample of 14 stock markets with a wider developmentspectrum in terms of size, liquidity and importance in the economy, as anattempt to provide further international evidence on the link between longmemory in stock returns and the level of stock market development. Whilethe sample includes the developed stock markets of Japan, the UK and theUSA, it also includes, in addition to the emerging markets of Brazil, India andMexico, those of the eight Arab countries of Bahrain, Egypt, Jordan, Kuwait,Morocco, Oman, Saudi Arabia and Tunisia, as benchmarks of thin markets.

The next section of the paper presents a short description of the relativecharacteristics of the Arab stock markets in comparison with the other marketsin the sample in terms of size and liquidity. The third section describes the dataand methodology and Section 4 presents the results. The final section isdevoted to some concluding remarks.

2. Arab stock markets in international perspective

Over the decade of the 1990s, Arab stock markets have witnessed significantgrowth owing to the many reforms undertaken by these countries.2 At thenational level, stabilization and structural adjustment programs were imple-mented in most of these countries starting from the mid-1980s. These programsinvolved, in addition to measures aiming at stabilizing the macroeconomicenvironment, structural measures with a bearing on stock market developmentincluding liberalization of the financial sector, relaxation of foreign directinvestment regulations, and privatization of state-owned enterprises (Husseinet al., 1999). Many steps were also taken to improve the institutional andlegislative infrastructure of Arab stock markets, especially in relation to infor-mation disclosure, listing requirements, clearing and settlement systems andforeign ownership.

However, despite the recent rapid growth in their size, liquidity and impor-tance in the economy, Arab stock markets remain very thin relative to otheremerging and developed markets. Table 1 shows the relative size and liquidityindicators of the eight Arab stock markets in comparison with those of theemerging markets of Brazil, India and Mexico; and the developed markets ofJapan, the UK and USA.

The total value of market capitalization of the eight Arab markets for theyear 2000, was $US143 483 million, slightly above that of the Mexican market,and representing about the market capitalization value of the sole stock marketof India, two thirds that of Brazil and less than 1% that of the USA. The othermarket size indicator—number of domestic listed companies—shows alsothat Arab stock markets remain a limited source for mobilizing capital anddiversifying risk.

The liquidity indicators, total value traded as share of GDP and the turn-over ratio, defined as the value of shares traded as a percentage of marketcapitalization, point to the limited ability to easily buy and sell stocks in

Long memory in Arab stock markets 253



254

I.Lim

am

Table 1. Relative size and liquidity indicators of Arab stock markets.

Country

Market capitalization ($US millions) Market capitalization (%GDP) Stocks traded (%GDP) Turnover ratio Listed companies

1990 2000 1990 2000 1990 2000 1990 2000 1990 2000

Bahrain 3 174 6 624 73.7 83.1 na 3.1 na 3.7 30 40Egypt 1 765 28 741 4.1 29.1 0.3 11.3 7.3 38.7 573 1071Jordan 2 001 4 943 49.8 59.3 10.1 5.0 20.3 8.4 105 163Kuwait 11 068 18 814 60.9 55.0 4.9 11.1 8.0 20.3 54 86Morocco 966 10 899 3.7 32.7 0.2 3.3 5.4 10.0 71 54Oman 1 061 3 463 9.4 29.4* 0.9 13.0* 9.6 44.2 55 139Saudi Arabia 48 213 67 171 40.8 38.8 1.9 10.0 4.7 25.8 59 74Tunisia 533 2 828 4.3 14.5 0.2 3.2 4.7 22.1 13 44Brazil 16 354 226 152 4.0 38.0 1.0 17.0 24.0 43.0 581 459India 38 567 148 064 12.0 32.0 7.0 48.0 66.0 134.0 2 435 5 937Mexico 32 725 125 204 12.0 22.0 5.0 8.0 44.0 32.0 199 179Japan 2 917 679 3 157 222 96.0 65.0 53.0 56.0 44.0 70.0 2 071 2 561UK 848 866 2 576 992 86.0 182.0 28.0 130.0 33.0 67.0 1 701 1 904USA 3 059 434 15 104 037 53.0 154.0 30.0 324.0 53.0 201.0 6 599 7 524

*Refers to 1999.Source: World Bank (2002) and ESCWA (1995).

Brought to you by | University of N

ewcastle, Australia

Authenticated | 134.148.29.34D

ownload D

ate | 3/13/14 9:39 AM

Arab markets relative to other markets. In addition, the relatively lower turn-over ratio points to possible higher transaction costs.

Relatively few studies have analyzed informational efficiency in Arab stockmarkets.3 Sourial (2002) is, however, the only study related to an Arab countryto establish the presence of long memory process for the case of the Egyptianstock market. In this paper, a test for the presence of long memory dynamics isconducted for the eight included Arab stock markets in conjunction with sixemerging and developed markets.

3. Methodology and data

3.1. MethodologyA series is said to have long memory if its autocorrelation coefficients, �jremain significant at long lags. More specifically, a series is said to have longmemory if:4

S� ¼ limk!1

Xk

j¼�k

�j��

¼ 1 ð1Þ

Long-term dependence or long-memory processes have been modeled in theliterature by the fractionally integrated ARMA models (ARFIMA) developedby Granger (1980) and Granger and Joyeux (1980). The ARFIMA (p, d, q)model is given by:

�ðLÞð1� LÞd ðyt � �Þ ¼ �ðLÞ"t, "t � iidð0, �2" Þ ð2Þ

where L is the lag operator, �ðLÞ ¼ 1� �1L� �2L2� � � � � �pL

p, �ðLÞ ¼1þ �1Lþ �2L

2þ � � � þ �qL

q, and ð1� LÞd is the operator that accounts forthe long memory of the process defined as:

ð1� LÞd ¼ 1� dLþdðd � 1Þ

2!L2

�dðd � 1Þðd � 2Þ

3!L3

þ � � � ¼X1

k¼0

�ðk� dÞLk

�ð�dÞ�ðkþ 1Þ

ð3Þ

where �ð:Þ is the gamma function defined as �ðgÞ ¼R1

0 xg�1e�xdx.The process yt would be stationary and invertible if the roots of �ðLÞ and

�ðLÞ lie outside the unit circle and dj j < 0:5. Hosking (1981) has shown thatfor 0 < d < 0:5, S� defined in equation (1) does not have a finite sum and theprocess is said to exhibit long memory or persistence but would revert to itsmean. In this case, the Autocorrelation Function (ACF) of the process declinesat a hyperbolic rate to zero but the rate of its decay is slower than the corre-sponding I(0) process with the same ARMA parameters. On the other hand, if�0:5 < d < 0, S� tends to a constant and the process has short memory. In thiscase, the process is also said to be anti-persistent or to have intermediatememory.5 Anti-persistence means that if returns increase in a given period,they are very likely to decrease in the next and vice versa.

For 0:5 < d < 1, the process is non-stationary and for �1 < d < �0:5, itdoes not have an invertible representation. In both cases the ACF still decaysto zero and the process reverts to its mean. Finally, for dj j > 1, the process is




not mean-reverting in the sense that any shock to the process will displace itfrom its starting point.

Many estimation procedures have been suggested in the literature to esti-mate ARFIMA models with each having its merits and relative weaknesses.6

These procedures can be classified into two-step procedures and maximumlikelihood (MLE)-based procedures. They can also be classified into param-etric or semi-parametric depending on the degree of their reliance on specificstatistical distributions. In order to account for the variation in quality ofthese estimation procedures under different assumptions, three estimationprocedures will be used in this paper.

The first proposed estimation procedure has been suggested by Geweke andPorter-Hudak (1983), GPH hereafter. It is a two-step procedure where thefractional integration parameter, d, is estimated first, and then the AR andMA parameters of the ARFIMA model are estimated after adequate transfor-mation of the data based on the estimate of d. The second estimation procedureused in the paper is due to Robinson (1992), who suggested estimating dindirectly, through the Hurst exponent H (Hurst, 1951).

Given the potential bias of the previous estimation procedures, Li andMcLeod (1986) and Sowel (1992), respectively, have suggested the joint esti-mation of the ARFIMA parameters through the MLE procedure; this will beused as the third estimation procedure.

3.2. The dataThe data used relate to weekly stock index returns conventionally defined asthe log-difference of the weekly stock price indices in the fourteen stock mar-kets in the sample spanning the period September 27, 1994 to April 24, 2002.The stock price indices used are listed in table 2.

The data on Arab stock markets are from various issues of MEED (MiddleEast Economic Digest), while data on emerging and developed stock marketsare from various issues of the Economist magazine.

256 I. Limam

Table 2. Stock price indices used in the study.

Country Stock price index Abbreviation

Bahrain Bahrain Stock Exchange Index BSEEgypt Capital Market Authority Index CMAJordan Amman Stock Exchange ASEKuwait Kuwait Stock Exchange Index KSEMorocco Casablanca Finance Group CFGOman Muscat Securities Market Index MSMSaudi Arabia National Center for Financial and

Economic Information IndexNCFEI

Tunisia Bourse des Valeurs Mobilieres de Tunis Index BVMTBrazil Bolsa de Valores de Sao Paulo (Sao Paulo Stock Exchange) BOVESPAIndia National Stock Exchange of India NSEMexico Bolsa Mexicana de Valores (Mexico Stock Exchange) BMVJapan Tokyo Stock Exchange NIKKEIUK London Stock Exchange FTSE100USA Dow Jones Industrial Average DJIA



Table 3 displays descriptive statistics of the returns data in the 14 markets.Although no marked difference can be discerned among the different countriesin the sample with respect to average returns, volatility—as measured by thestandard deviation of returns—is relatively lower in the group of Arab coun-tries. This contrasts with previous evidence presented by authors includingHarvey (1995) and Bekaert and Harvey (1995), suggesting that returns volatil-ity in developing markets tends to be higher than that observed in developedmarkets. This can be explained by the relatively thin trading in Arab countriesas evidenced by the low turnover ratios in these markets.

On the other hand, the figures confirm some of the well established empiricalproperties of return distributions namely, excess kurtosis and skewness,hence pointing to the divergence from normality.7 This establishes therelative merit of estimation procedures, such as GPH, that are robust tonon-normality.

4. Empirical results

As a first step toward exploring the statistical properties of the return series andto pre-test for the presence of long memory, a battery of tests is conducted. Thefirst set tests for the presence of unit roots in the returns series. The rejection ofthe unit root hypothesis is suggestive of random walk and hence of no memoryin the returns series. The three unit root tests used in the paper are theAugmented Dickey–Fuller (1981), Kwiatkowski et al. (1992), and Phillips–Perron (1988), referred to hereafter as ADF, KPSS and PP, respectively.

Another indirect test to detect long-range dependence is the modifiedrescaled range statistics, R/S, suggested by Lo (1991). The main merit of thistest is that it can better distinguish between long-range and short-rangeprocesses than the original rescaled range statistic.

Acceptance of the assumption of stationarity, using the previous tests, doesnot exclude the presence of a systematic pattern or some form of dependence inthe data. The presence of such properties might signal long memory. For thisreason, the paper also provides the RUNS test for randomness and the BDStest, suggested by Brock et al. (1996), for a wide range of non-independence inthe data such as linear and non-linear dependence and chaos.

The first three columns in table 4 provide the results pertaining to the unitroot tests. As can be seen from this table, the hypothesis of unit root in stockreturns is generally rejected by all three tests for all 14 markets in the sample.8

This represents evidence in favor of a random-walk model in stock prices and,hence, of the weak form of efficiency. However, the absence of unit root is notnecessarily evidence against long memory.9 Hassler and Wolter (1994), forinstance, have shown that the ADF and PP tests of unit roots have weakpower against the alternative of fractional integration. In return, Lee andSchmidt (1996) have shown that the KPSS test has more power than theprevious tests for �0:5 � d � þ0:5 and, therefore, is more appropriate inchoosing between short and long memory processes, especially for largesample size. They also show that KPSS has similar power properties to Lo’sR/S test.




258

I.Lim

am

Table 3. Descriptive statistics of stock returns data.

Country Mean Median Maximum Minimum Std dev. Skewness Kurtosis Jarque�Bera*Number ofobservations

Bahrain 0.000 0.000 0.066 �0.063 0.015 0.108 6.712 225.219 391Egypt 0.002 0.001 0.091 �0.056 0.019 1.198 7.228 380.833 387Jordan 0.000 �0.001 0.063 �0.054 0.016 0.432 4.720 60.399 391Kuwait 0.002 0.001 0.064 �0.083 0.018 �0.329 5.169 83.685 391Morocco 0.001 0.000 0.098 �0.082 0.018 0.585 7.870 391.88 375Oman 0.000 0.000 0.153 �0.077 0.026 0.917 7.985 459.637 391Saudi Arabia 0.002 0.002 0.068 �0.083 0.019 �0.166 5.275 86.112 391Tunisia 0.002 0.000 0.108 �0.109 0.024 0.399 7.818 388.59 391

Brazil 0.002 0.009 0.312 �0.277 0.063 �0.498 8.180 448.710 387India �0.001 0.001 0.158 �0.134 0.040 0.255 3.965 19.200 387Mexico 0.003 0.000 0.148 �0.230 0.045 �0.180 5.624 113.10 387

Japan �0.001 �0.002 0.117 �0.098 0.031 0.248 4.131 24.606 387UK 0.001 0.002 0.060 �0.085 0.021 �0.203 3.601 8.480 387USA 0.001 0.002 0.070 �0.092 0.023 �0.453 4.561 52.51 387

*Large values of the Jarque-Bera statistic mean departure from normality.


ewcastle, Australia


ownload D

ate | 3/13/14 9:39 AM

Longmem

ory

inArabsto

ckmarkets

259

Table 4. Stochastic properties of stock returns.

Country ADF* KPSSy PPz R/S§

RUNS BDS

Number of runs Z-statisticTwo-tailedsignificance BDS statistic Z-statistic p-value epsilon

Bahrain �15.31 0.23 �0.80 1.80 155 �4.20 0.00 0.07 6.94 0.00 0.02Egypt �8.09 0.13 0.90 1.51 170 �2.34 0.02 0.11 11.23 0.00 0.02Jordan �19.68 0.08 �1.28 1.14 203 0.72 0.47 0.01 1.32 0.19 0.02Kuwait �17.14 0.45 0.52 2.17 170 �2.51 0.01 0.05 6.40 0.00 0.02Morocco �17.48 0.69 0.18 1.79 151 �3.87 0.00 0.10 8.78 0.00 0.02Oman �16.38 0.49 �0.59 1.97 136 �6.11 0.00 0.14 13.93 0.00 0.03Saudi Arabia �16.95 0.17 0.76 1.15 179 �1.46 0.14 0.04 5.40 0.00 0.03Tunisia �12.10 0.25 0.46 1.77 161 �3.54 0.00 0.12 9.46 0.00 0.03

Brazil �13.33 0.07 �0.25 1.19 182 �1.00 0.32 0.09 9.65 0.00 0.70India �20.28 0.07 �1.32 1.17 201 0.68 0.50 0.02 2.16 0.03 0.06Mexico �19.75 0.05 0.15 1.17 181 �1.37 0.17 0.03 3.79 0.00 0.06

Japan �20.20 0.08 �0.24 1.18 191 �0.31 0.76 0.02 2.46 0.01 0.04UK �20.91 0.50 0.43 1.43 195 0.15 0.88 0.05 7.26 0.00 0.03USA �19.76 0.40 1.12 1.33 187 �0.43 0.67 0.04 5.40 0.00 0.03

*Mackinnon (1991) critical value at 5% level is –2.87.yKPSS critical value at 5% level is 0.463.zPP critical value at 5% level is –14.0.§The R/S critical values at the 5% significance level are 0.809 and 1.862.


ewcastle, Australia


ownload D

ate | 3/13/14 9:39 AM

Column 4 in table 4 provides the Lo’s R/S statistic. A statistically insignif-icant R/S statistic is evidence of short memory or mean-reversion, while a largevalue of the statistic is consistent with return persistence. The R/S is a two-tailed test whose critical levels are given in Lo’s (1991, table 2, p. 1288) paper.The critical values for the 5% significance level are 0.809 and 1.862, respect-ively. The computed R/S statistics are consistent with the assumption of longmemory in the case of Kuwait and Oman. The markets of Bahrain, Moroccoand Tunisia represent borderline cases of long memory. The evidence is, on theother hand, consistent with the assumption of short memory in the rest ofthe markets.

It should be pointed out that the result of the R/S test is to be readwith caution as it is consistent with fractional alternatives provided that�0:5 � d � þ0:5. In addition, in case of flat-tailed distribution of the returns,the test could lead to more rejection in favor of d<0 and less rejection in favorof d>0 (Mills, 1993 and references therein).

Table 4 also provides the non-parametric RUNS test to detect randomnessin the data of stock returns. A number of runs, or successions of returns withthe same positive or negative sign, that is either too small (clustering) or toolarge (repeated alternating pattern) is an indication of possible lack of random-ness. The runs test is a two-tailed test based on a Z-score such that a lowvalue of this score is consistent with randomness and a high value is evidenceagainst it. The results seem to suggest that while the arrangements of stockreturns in the developed and emerging markets are random, they do not seemto be so for the Arab stock markets in the sample, save for Jordan and SaudiArabia where the hypothesis of randomness could not be rejected at the 5%significance level.

The results of the BDS test show that the assumption of identically andindependently distribution (iid) of the returns is rejected, at the 5% significancelevel, in all markets except Jordan, where the assumption of iid failed to berejected as evidenced by the low values of the Z-statistic or equivalently by ap-value higher than 0.05.10

In order to estimate the fractional differencing parameter d, 16 combina-tions of ARIMA (p,d,q) have been tried with p and q taking each integer valuesbetween zero and three. The estimation of the parameters is conducted usingthe MLE method developed by Sowell (1992) and provided in the ARFIMAcomputer software developed by Doornik and Ooms (2001) within the OXprogramming language developed by (Doornik, 2001). The reported valuesof d are those corresponding to the model specification holding the lowestvalue of the Akaike Information Criterion (AIC).

In order to account for some of the specific properties found in the dataunder study, such as non-normality, estimates of d through the semi-parametric estimation methods of GPH and Robinson, and using theLMM2 software developed by Davidson (2002) within the OX package, arealso reported. The GPH estimation is performed using three different valuesfor n, the number of ordinates in the periodogram.

Table 5 presents the estimation results. As can be seen from the reportedfigures the estimates of d across the three estimation methods are fairly close to

260 I. Limam



each other. Overall, the results suggest that long memory in stock returns is a

property of thin, rather than developed, stock markets. In line with previous

results, stock index returns in developed markets are not found to have long

memory. The estimated fractional differencing parameter d for Japan, the UK

and USA are found to be close to zero. For Japan, the estimated value of d

is not significant pointing to short memory. For the UK and the USA the

estimated values of d are also not significant but tend to be negative, suggesting

the presence of anti-persistence. This result is in line with other studies,

such as Barkoulas and Baum (1996) and Henry (2002) to name just a few,

who also found anti-persistence in many stock index returns in the UK and US

markets.

The results pertaining to the three emerging markets of Brazil, India, and

Mexico, are similar to those of developed markets in the sense that they are not


Table 5. Estimates of the fractional integration parameter d.

Country MLE*

GPHy

Robinsonyn¼T/4 n¼T/3 n¼T/2

Bahrain 0.196 0.209z 0.214z 0.204z 0.046(0.040) (0.073) (0.063) (0.054) (0.039)

Egypt 0.181z 0.298z 0.290z 0.236z 0.141z

(0.040) (0.073) (0.063) (0.054) (0.040)Jordan 0.003 0.072 0.060 0.050 0.044

(0.036) (0.073) (0.063) (0.054) (0.039)Kuwait 0.137z 0.106� 0.103� 0.086� 0.128z

(0.004) (0.073) (0.063) (0.054) (0.036)Morocco 0.109§ 0.109 0.094 0.061 0.194z

(0.038) (0.074) (0.063) (0.054) (0.040)Oman 0.157z 0.147§ 0.104* 0.118§ 0.043

(0.038) (0.073) (0.063) (0.054) (0.039)Saudi Arabia 0.119z 0.120� 0.056 0.052 0.082§

(0.042) (0.073) (0.063) (0.054) (0.039)Tunisia 0.196z 0.132§ 0.081 0.036 0.118z

(0.057) (0.054) (0.063) (0.054) (0.039)Brazil �0.025 0.001 0.002 �0.072 0.025

(0.050) (0.073) (0.063) (0.054) (0.036)India �0.038 �0.018 0.042 �0.016 �0.027

(0.042) (0.073) (0.063) (0.054) (0.036)Mexico �0.012 �0.013 0.003 0.007 0.024

(0.043) (0.073) (0.063) (0.054) (0.036)Japan �0.028 0.020 0.038 0.024 0.019

(0.041) (0.073) (0.063) (0.054) (0.036)UK �0.059 �0.039 0.008 �0.026 �0.187z

(0.039) (0.073) (0.063) (0.054) (0.036)USA �0.037 �0.096 �0.033 �0.018 �0.095z

(0.041) (0.073) (0.063) (0.054) (0.036)

Standard errors are in parentheses.*Estimates correspond to the optimal ARFIMA model based on the AIC criterion (see text).yStandard errors based on the imposed theoretical variance of the spectral regression error �2=6.z § � indicate statistical significance at the 1, 5, and 10% levels, respectively.



suggestive of long memory. The fractional integration parameters for these

markets are not significant and point to the insignificant presence of

anti-persistence.

The evidence from the eight Arab stock markets in the sample is strongly

supportive of the assumption of long memory. This result is consistent with the

characteristics of these markets. Thin trading and dominance of individual

investors, attributed to the lack of equity culture, can, to a large extent, explain

stock returns persistence in Arab markets (Sourial, 2002). Furthermore, the

relative weakness of the regulatory framework on issues related to information

dissemination, disclosure and transparency represent typical characteristics of

all Arab stock markets that have a direct bearing on informational efficiency.

In addition, Arab capital markets remain relatively closed to foreign investors.

Foreign ownership of domestic shares is often banned or restricted by explicit

ceilings. The lack of integration in international capital markets deprives Arab

stock markets from the informational discipline and alignment to international

standards that further openness would have entailed. Therefore, the lack of

openness is another factor that can explain informational inefficiency and

persistence in Arab stock returns.

Despite its relative thinness, Jordan is the only Arab market exhibiting short

memory. The relative efficiency of the Jordanian market can be attributed to a

large extent to the wide range of reforms undertaken since the mid-1990s to

substantially open up the stock market to foreign investors, to improve trans-

parency and disclosure and to organize the market in line with developed stock

markets (Alzoubi, 2000).

The results with respect to Egypt are in line with those of Sourial (2002) who

also found long memory using the IFC-Global index weekly returns instead of

the CMA index used in this paper. In addition to the factors mentioned earlier,

Sourial also explains the presence of long memory in the Egyptian market by

the relatively important number of non-traded shares.

Apart from the markets of Morocco and Tunisia who are also found

to exhibit long memory, the remaining Arab stock markets are all located in

oil-dependent countries. These countries incorporate the most significant mar-

kets in the Arab world, such as those of Saudi Arabia and Kuwait, in terms of

turnover and market capitalization. Stock market prices in these countries are,

to a large extent, driven by speculative activities of important individual inves-

tors animated in turn by excess liquidity and lack of investment opportunities

in the economy. These investors exert a great influence over stock trading and

prices.

On the other hand, the available evidence pertaining to these countries

suggests that variation in oil prices is one of the most important determinants

of future changes in stock returns. Oil prices affect profitability not only of the

business activities directly linked to oil, but also of other businesses through

their impact on the Government and private sector expenditures.11 In this

context, persistence in stock returns may reflect, in addition to the relative

thinness of the markets, a great deal of the dynamics specific to many Arab

oil-dependent economies.

262 I. Limam



5. Conclusion

Weekly stock index returns of fourteen developed and developing countriesspanning the period September 27, 1994 to April 24, 2002, have been tested forlong memory. Three parametric and semi-parametric estimation procedureswere used to robustly estimate the fractional differencing parameter andanalyze the link between the state of development of stock markets and theproperty of long memory. The results show a fairly strong support for theassertion that long memory is a property of stock returns in developing ratherthan developed markets. While short memory is found in the developed stockmarkets of Japan, the UK, and USA and the emerging markets of Brazil, Indiaand Mexico; long memory is associated with the thinner markets of the sample.Overall, the results show that fractional integration dynamics in stock returnsis strongly linked to the level of development in stock markets. Evidence fromthe Arab countries in general and oil-producing countries in particular, seemsto suggest that long-memory might also be linked to the peculiar characteristicsand environment of each stock market.

Acknowledgments

The author is grateful to Belkacem Labaas and Riad Dahel for providing partof the data, to Hassan Khudr for able research assistance and to an anon-ymous referee for constructive suggestions. The author is alone responsible forany remaining errors.

Notes1. For the various definitions of efficiency in financial markets, see Fama (1965).2. For a description of Arab stock markets, see, for instance, ESCWA (1995),

AMF(1997) and Naser and Younis (1997).3. See, for instance, El-Erian and Kumar (1995) for the case of six Middle Eastern

countries (Egypt, Iran, Jordan, Morocco, Tunisia and Turkey), Mohieldin andSourial (2000) for the case of Egypt; Al-Loughani (2000) for the case of Kuwait;Bouri (2000) for the case of Tunisia and Omet et al. (2002) for the case of Jordan.

4. Alternatively, the concept of long memory can be defined in frequency domain as asituation where the spectral density increases without limit around frequency zero.See Baillie (1996) for an extensive overview of the various relevant definitions andfurther references.

5. For d<0, the process is said to be anti-persistent and very often the label long-rangedependence is reserved for the case where d>0.

6. For a review of the different estimation procedures and their relative merits, seeBaillie (1996).

7. For further details on the properties of return distributions, see for instance, Mills(1999).

8. The ADF test is implemented by choosing lag length based on the SchwartzInformation Criterion and all three unit root tests are conducted by incorporatinga drift but no time trend.

9. The absence of unit root may be taken fairly as evidence against the existence ofsignificant shifts or structural change in the data. Since long memory and structuralchange can easily be confused, the rejection of the unit root hypothesis in this casereduces the risk of that confusion namely, the presence of long memory being blurredby the existence of significant structural change.




10. The reported values of epsilon (the distance used to test proximity of the data pointsin the sample) are those ensuring that a certain fraction of the total number of pairsof points lies within epsilon of each other. To maximize the power of the test manycombinations of values for epsilon and the embedding dimension, m, (the number ofconsecutive data points to be included in the computation of the BDS test) weretried. The results, not reported here for space consideration, were similar to those intable 4.

11. See Arifa et al. (2002) for further evidence.

ReferencesAl-Loughani, N., 2000, Recent trends and market inefficiency in the Kuwait stock

exchange: evidence in the post liberation era. In: Arab Stock Markets: RecentTrends and Performance, edited by R. Dahel (Kuwait: Arab Planning InstitutePublication), pp. 63–73.

Alzoubi, M. M., 2000, The Amman financial market: performance, recent trends anddevelopment. In: Arab Stock Markets: Recent Trends and Performance, edited by R.Dahel (Kuwait: Arab Planning Institute Publication), pp. 45–61.

Arab Monetary Fund (AMF), 1997, Arab Stock Markets in AMF Database: Their Birthand Development (Arabic document, Special Issue) (Abu-Dhabi: AMF).

Arifa, A., Ghali, K. and Limam, I., 2002, Investigating stock market dynamics in an oil-dependent economy: the case of Kuwait. Economic Policy and Analysis, 32 (2), 141–158.

Aydogan, K. and Booth, G. G., 1988, Are there long cycles in common stock returns?Southern Economic Journal, 55, 141–149.

Baillie, R. T., 1996, Long memory processes and fractional integration in econometrics.Journal of Econometrics, 73, 5–59.

Barkoulas, J. T. and Baum, C. F., 1996, Long term dependence in stock returns.Economics Letters, 53, 253–259.

Barkoulas, J. T., Baum, C. F. and Travlos, N., 1996, Long memory in the Greek stockmarket. Unpublished manuscript (Department of Economics, Boston College).

Bekaert, G. and Harvey, C. R., 1995, Time-varying world market integration. Journal ofFinance, 10 (2), 403–444.

Beran, J., 1992, Statistical methods for data with long-range dependence. StatisticalScience, 7 (4), 404–416.

Bouri, A., 2000, Stochastic properties of the Tunisian stock market. In: Arab StockMarkets: Recent Trends and Performance, edited by R. Dahel (Kuwait: ArabPlanning Institute Publication), pp. 111–129.

Brock, W., Dechert, D., Sheinkman, J. and LeBaron, B., 1996, A Test for independencebased on the correlation dimension. Econometric Reviews, 15 (3), 197–235.

Cheung, Y. W. and Lai, K. S., 1995, A search for long memory in international stockmarket returns. Journal of International Money and Finance, 14, 331–345.

Cheung, Y. W., Lai, K. S. and Lai, M., 1993, Are there long cycles in foreign stockreturns? Journal of International Financial Markets, Institutions andMoney, 3, 33–47.

Chow, K. V., Denning, K. C., Ferris, S. and Noronha, G., 1995, Long-term and short-term price memory in the stock market. Economics Letters, 49, 287–95.

Crato, N., 1994, Some international evidence regarding the stochastic memory of stockreturns. Applied Financial Economics, 4, 33–39.

Davidson, J., 2002, Long Memory Modelling Version 2, User’s Guide, available onlineat http://www.cf.ac.uk/carbs/econ/davidsonje.

Dickey, D. and Fuller, W., 1981, Likelihood ratio statistics for autoregressive time serieswith unit root. Econometrica, 49, 1057–1072.

Ding, Z., Granger, C. W. J. and Engle, R. F., 1993, A long memory property of stockreturns and a new model. Journal of Empirical Finance, 1, 83–106.

Doornik, J. A., 2001, Object-Oriented Matrix Programming using Ox (4th edn)(London: Timberlake Consultants Press).

264 I. Limam



Doornik, J. A. and Ooms, M., 2001, A Package for Estimating, Forecastingand Simulating ARFIMA Models: ARFIMA Package 1.01 for OX (NuffieldCollege, Oxford OX1 1NF, UK and Erasmus University, Rotterdam, TheNetherlands).

Economic and Social Commission for Western Asia (ESCWA), 1995, Stock Markets inthe ESCWA Region (New York: United Nations).

El-Erian, M. and Kumar, M., 1995, Emerging equity markets in middle eastern coun-tries. In: Development of Financial Markets in the Arab Countries, edited by theEconomic Research Forum for the Arab Countries, Iran and Turkey (Cairo).

Fama, E., 1965, The behaviour of stock market prices. Journal of Business, 38, 34–105.Geweke, J. and Porter-Hudak, S., 1983, The estimation and application of long memory

time series models. Journal of Time Series Analysis, 4, 221–38.Granger, C. W. J., 1980, Long memory relationships and the aggregation of dynamic

models. Journal of Econometrics, 14, 227–238.Granger, C. W. J. and Joyeux, R., 1980, An introduction to long memory time series

models and fractional differencing. Journal of Time Series Analysis, 1, 15–39.Greene, M. and Fielitz, B., 1977, Long term dependence in common stock returns.

Journal of Financial Economics, 4, 339–349.Harvey, C. R., 1995, Predictable risk and returns in emerging markets. Review of

Financial Studies, 8 (3), 773–816.Hassler, U. and Wolter, J., 1994, on the power of unit root tests against fractional

alternatives. Economics Letters, 45, 1–5.Henry, O. T., 2002, Long memory in stock returns: some international evidence. Applied

Financial Economics, 12, 725–729.Hosking, J. R. M., 1981, Fractional differencing. Biometrica, 68, 165–176.Hurst, H., 1951, long term storage capacity of reservoirs. Transactions of the American

Society of Civil Engineers, 116, 770–799.Hussein, O. I., Borniya, M. Y. and Al-Bitar, A. H., 1999, Arab stock exchange markets:

performance and challenges. In: Role of Private Sector in Arab Economies, edited byS. Makdisi (Abu-Dhabi: Arab Fund for Economic and Social Development andArab Monetary Fund Publication), pp. 179–221. [In Arabic.]

Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y., 1992, Testing the nullhypothesis of stationarity against the alternative of a unit root: how sure are we thateconomic time series have a unit root? Journal of Econometrics, 54, 159–178.

Lee, D. and Schmidt, P., 1996, On the power of the KPSS test of stationarity againstfractionally integrated alternatives. Journal of Econometrics, 73, 285–302.

Levine, R., 1999, Law, finance and economic growth. Journal of FinancialIntermediation, 8, 8–35.

Li, W. K. and McLeod, A. I., 1986, Fractional time series modeling. Biometrica,73, 217–221.

Lo, A. W., 1991, Long-term memory in stock market prices. Econometrica, 59,1279–1313.

Lobato, I. N. and Savin, N. E., 1997, Real and Spurious Long Memory Properties ofStock Market Data. Discussion Paper (University of Iowa: Department ofEconomics).

MacKinnon, J. G., 1991, Critical values for cointegration tests. In: Long-Run EconomicRelationships: Readings in Cointegration, edited by R. F. Engle and C. W. J.Granger (Oxford: Oxford University Press), pp. 267–276.

Mills, T. C., 1993, Is there long-term memory in UK stock returns? Applied FinancialEconomics, 3, 303–306.

Mills, T. C., 1999, The Econometric Modelling of Financial Time Series (2nd edn)(Cambridge: Cambridge University Press).

Mohieldin, M. and Sourial, M. S., 2000, Institutional aspects, distributional charac-teristics and efficiency of the Egyptian securities market. In: Arab StockMarkets: Recent Trends and Performance, edited by R. Dahel (Kuwait: ArabPlanning Institute Publication), pp. 1–44.




Naser, K. and Younis, Y., 1997, A review of ten Middle East stock exchanges. MiddleEast Business Review, 2, 63–89.

Omet, G., Khasawneh, M. and Khasawneh, J., 2002, Efficiency tests and volatilityeffects: evidence from the Jordanian stock market. Applied Economic Letters,9, 817–821.

Phillips, P. C. B. and Perron, P., 1988, Testing for a unit root in time series regression.Biometrika, 75, 335–346.

Robinson, P. M., 1992, Semiparametric analysis of long memory time series. Annals ofStatistics, 22, 515–539.

Sadique, S. and Silvapulle, P., 2001, Long-term memory in stock market returns: inter-national evidence. International Journal of Finance and Economics, 6 (1), 59–67.

Sourial, M. S., 2002, Long memory process in the Egyptian stock market returns.Journal of Development and Economic Policy, 5 (1), 65–88.

Sowel, F., 1992, Maximum likelihood estimation of stationary univariate fractionallyintegrated time series models. Journal of Econometrics, 53, 165–188.

World Bank, 2002, World Bank Indicators (CD-ROM) (Washington, D.C.: WorldBank).

Wright, J. H., 2001, Long memory in emerging market stock returns. Emerging MarketsQuarterly, 5 (1), 50–55.

266 I. Limam



is long memory a property of thin stock markets? international evidence using arab countries

Documents