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Lazăr Dorina

Babes-Bolyai University, Faculty of Economics and Business Administration, Teodor Mihali 58-60, 400591 Cluj-Napoca, Romania, Tel: 40 + 0264 41.86.52, E-Mail: dlazar@econ.ubbcluj.ro

Ureche Simina

Babes-Bolyai University, Faculty of Economics and Business Administration, E-Mail: urechesimina@yahoo.com

Abstract

This paper tests weak-form market efficiency of eight emerging markets: Romania, Hungary, Czech Republic, Lithuania, Poland, Slovakia, Slovenia, Turkey. To test for linear dependences in the returns series we employ Ljung-Box test and serial correlation LM test. To test for nonlinear dependences the BDS test and runs test were used; BDS test is applied on the residuals series generated by ARMA models. The used tests determines empirically the presence of linear and nonlinear dependences, for most of the returns series. For the adjusted returns series the main dependences found are nonlinear, while the observed returns series are characterised by linear and nonlinear dependences. Most of these emerging equity markets are not weak-form efficient.

Keywords: Efficient market hypothesis, Emerging markets, Serial Correlation LM test, BDS test

1. Introduction

Testing of the financial markets efficiency is an important issue for investors and policymakers dealing with emerging equity markets. An efficient capital market is necessary and useful for a functioning market economy, inducing an efficient capital assignation within an economy. There for, an efficient capital market is concerning the macroeconomic level as well as the administration of the financial assets portofolio.

The efficient market hypothesis asserts that financial markets are efficient as concerning the information. The current stocks prices reflect all the known information, useful for their prediction. The information channels are efficient as long as the information is spreading rapidly and new information becomes public quickly. These new information will lead to purchasing and selling which will affect the price until it corresponds to the new value of the company. There for, the information will be quickly assimilated to the new stock price. The share price may be at any time a correct estimation of the future share prices, described as a random walk behavior. The presence (or absence) of a random walk has important implications for investors (Worthington and Higgs, 2006).

Depending on the information set available, the financial theory is based on three forms of efficiency, as follows. Weak efficiency holds if the asset price immediately incorporates the information contained in the asset history. Semi-strong efficiency holds if all the public information is incorporated into the asset price. Strong form efficiency holds if all the information, public or private is incorporated into market prices.

The subject of this paper is weak-form market efficiency. In an efficient (weak-form) market stock returns are unpredictable. Testing of this efficiency form is assimilated with tests concerning the predictibility of stock returns. If stock prices are not generated by a random walk process, meaning there are recurrent patterns in asset prices, than the future returns may be predicted by the historical sequence of returns. A useful rating, regarding the predictibility of asset returns, generates the following random walk hypothesis (Campbell et al., 1997):

− random walk hypothesis (RW1) with independent and identically distributed increments; − random walk hypothesis (RW2) with independent but not identically distributed increments; − the weakest form of the random walk hypothesis include processes with dependent but uncorrelated

increments (RW3).

Tests used in most studies are aplied to RW1 and RW3 hypothesis.

This paper will verify the efficiency of capital market for 8 emerging economies: Romania, Czech Republic, Hungary, Lithuania, Poland, Slovakia, Slovenia, Turkey. A number of recent studies focused on emerging equity markets; the results are different depending on the country and the aplied methodology. Worthington and Higgs (2006) have studied the weak-form market efficiency of twenty-seven emerging markets in different regions. The serial correlation and runs tests conclude that most emerging markets are weak-form inefficient. Kvedaras and Basdevant (2002) have tested the efficiency of financial markets in the three Baltic States drawing conclusion that that financial markets are, with some turbulence, approaching weak form of efficiency.

The efficiency of capital markets in emerging economies increase over time, as a result of gradual liberalization. Harrison and Paton (2004) examined the evolution of stock market efficiency in the Bucharest Stock Exchange using a GARCH model on daily price data. They found strong evidence of inefficiency in the Bucharest Stock Exchange, the lagged stock price index beeing a significant predictor of the current price index. The level of inefficiency appears to diminish over time. Testing the efficiency of emerging markets should take into account some of the following characteristics: infrequent trading, high volatility, unlinearity of the share price variation (Todea, 2005).

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2. Empirical methodology and data

The data used for this study are the market value-weighted equity indices (BET for Romania, cz_px50 - Czech Republic, hu_bux - Hungary, lt_liting - Lithuania, pl_wig - Poland, sk_sax - Slovakia, si_sbi - Slovenia, tr_nati100 – Turkey). The data consist of monthly values of these indices

1. The time series cover a period of

time from december 1995 to february 2007 for all the above mentioned countries, except Romania. Because of the considerably increasing investors interest and trade rate since 2000, a period of time since january 2000 until february 2007 was considered for Romania.

We are considering the continuously compounded return or log-return tR , defined by:

11)ln()1ln( −− −==+= tttttt CCccrR (1)

where )ln( tt cC = is the logarithm of the index price observed at time t. The equation of the random walk

with drift process is:

ttt CC εµ ++= −1 or ttt CR εµ +=∆= (2)

where µ is the drift parameter, tR representing the change in the index and tε the random error term. In the

RW1 random walk hypothesis the tε are independently and identically distributed (IID) with mean 0 and

variance 2σ .

To test for serial dependence in the returns tR the Ljung-Box Q-statistics is used, based on autocorrelation

coefficients2. The Q-statistic at lag k is a test for the null hypothesis that there is no autocorrelation up to order k.

In case of independently and identically distributed returns the Q statistic is asymptotically distributed as a2χ

variable with degrees of freedom equal to the number of autocorrelations. Thus, this is a test for the strongest form of random walk. Second, we use the serial correlation Lagrange multiplier (LM) test in equation (3), where the returns are represented by a moving average model MA(0). The null hypothesis of the LM test is that there is no serial correlation up to lag order k. The alternative includes both AR(p) and MA(p) error processes; the

LM test statistic is asymptotically distributed as a )(2 pχ .

Tests based on autocorrelation coefficients detect only linear autocorrelation. Emerging markets are typically characterized by a non-linear information behavior in stock prices (Todea, 2005).

To detect nonlinear correlations in the returns series we will perform BDS test (Brock, Dechert, Scheinkman and LeBaron, 1996); BDS is a powerful tool for detecting serial dependence in time series. This test is aplied to see if there is any non-linear dependence in the residuals series after the linear ARMA model has been fitted. The test statistic follows asymptotically the normal distribution. Under the BDS test, the null hypothesis is that the increments are independently and identically distributed (RW1 hypotesis), where the alternative hypotesis assumes a variety of possible deviations from independence including non-linear dependence. To define the test, the concept of integral correlation is used, which measures the spatial correlation among the points. The runs test relies only on the successive returns signs, without interest in their dimension and does not require assumptions about the distribution of the returns. A sequence with too many or too few runs suggests that the sample is not random.

In testing the efficiency of emerging markets, it is necessary to take into account some of their characteristics, like thin trading. Among the consequences of thin trading is the apperance of a serial correlation, studied by Miller, Muthuswamy and Whaley (1994). To remove the impact of this artificial correlation, a correction is aplied to the observed returns. The methodology proposed by Miller, Muthuswamy and Whaley suggests an autoregresive model AR(1) to separate the effect of infrequent trading.

3. Empirical results

Summary statistics concerning logarithmic returns for each of the emerging capital markets considered are provided in table 1.

Table 1. Descriptive Statistics for logarithmic returns in emerging capital markets

1 Source: Eurostat and Monthly Bulletins publicated by National Bank of Romania 2 autocorrelation coefficients define the linear correlationare between two observations of the returns time series tR at

different dates.

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Indicele Romania Hungary Poland Czech

Republic Slovenia Slovakia Turkey Lithuania

Mean 0.0323 0.0207 0.0145 0.0103 0.0109 0.0076 0.0347 0.0059

Std. Dev. 0.0911 0.0777 0.0639 0.0558 0.0538 0.0588 0.1202 0.0780

Skewness 0.4403 -1.1519 -0.1981 -0.2140 -0.2319 0.4838 0.1527 2.4608

Kurtosis 4.0029 10.546 3.2234 3.0915 8.5751 3.6982 4.4192 16.568

JB p-value 0.0273 0.0000 0.5612 0.5856 0.0000 0.0187 0.0027 0.0000

The lowest mean returns is observed in Lithuania, with a value of 0.592% and the highest mean returns are for the turkish index returns (3.479%). The market risk measured using standard deviation is signifiantly higher in Turkey and Romania, these capital markets being characterised by a higher volatility. A negative skewness shows that the lower deviations from the mean are larger than the upper deviations, indicating a greater probability of large deceases than rises. Kurtosis coefficients have values greater than 3, also the Jarque-Bera statistic is significant at 5% level, both indicate much higher distributions than the normal distribution; almost all markets exhibits significant deviations from normality.

Table 2 provides the statistics and p-values (in parentheses) for the tests of serial independence. To compute the adjusted returns, for each market an autoregresive model AR(1) was estimated. The Q-statistic indicates the rejection of the hypothesis according to the first 15 autocorrelation coefficients are significant for Hungary, Poland, Czech Republic, Slovakia, Turkey and Lithuania, if the observed returns are used; for the adjusted returns the autocorrelation coefficients are signifiant only for Lithuania; the results are valid at the 5% level of significance. For Hungary, Poland, Czech Republic, Slovakia and Turkey the initial correlation is artificial, being a statistical illusion brought about by thin trading. LM test points out a linear dependence between the adjusted returns for the hungarian market with a signifiance level of 5%. In conclusion, both tests indicates that thin trading has a significant effect on the efficiency of the studied stock markets.

Table 2. Tests for independence in emerging capital markets: Ljung-Box test, LM test, runs test

Indices Romania Hungary Poland Czech

Republic Slovenia Slovakia Turkey Lithuania

Q-statistics 20.149

(0.166)

25.434

(0.044)

25.208

(0.047)

30.969

(0.009)

15.635

(0.407)

40.567

(0.000)

35.651

(0.002)

36.631

(0.001)

LM-test

5.51082

(0.0635)

17.7918

(0.0003)

12.0804

(0.0023)

17.2274

(0.0001)

3.8182

(0.1482)

21.2110

(0.0000)

14.3214

(0.0007)

11.4179

(0.0033)

Runs test 0.103

( 0.918 )

-2.673

( 0.008 )

-2.793

( 0.005 )

-2.502

( 0.012 )

-3.877

( 0.000 )

-2.931

( 0.003 )

-2.191

( 0.028 )

-4.812

( 0.000 )

Adjusted returns

Q-statistics 20.819

(0.143)

18.334

(0.246)

13.236

(0.584)

24.525

(0.057)

13.249

(0.583)

11.926

(0.685)

21.960

(0.109)

27.154

(0.028)

LM-test 5.7170

(0.0573)

8.9625

(0.0113)

0.9673

(0.6165)

3.8445

(0.1462)

1.4071

(0.4948)

0.0658

(0.9676)

3.0242

(0.2204)

2.3969

(0.3016)

Runs test 0.523

( 0.601 )

-0.928

( 0.353 )

-1.222

( 0.222 )

-2.020

( 0.043 )

-2.488

( 0.013 )

0.267

( 0.789 )

0.958

( 0.338 )

-4.291

( 0.000 )

Notes: Q-statistics is computed for a lag =15. Ljung-Box and LM tests were performed using Eviews 5.1; for the nonparametric runs test it was used SPSS 11.0.

Using the non-parametric runs test the results show that the succesive returns are not independent for all the markets, except Romania. After the correction the test points out that the adjusted returns are dependent for the following markets: Czech Republic, Slovenia, Lithuania, therefore these markets are inefficient. The test statistic has an asymptotic normal distribution. The resulting negative values indicate positive serial correlation.

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Table 3. BDS test for nonlinear dependence in returns on emerging markets

Indicele Romania Hungary Poland Czech

Republic Slovenia Slovakia Turkey Lithuani

BDS test

Dimension

2

3

4

5

0.4270

0.2126

0.1801

0.1822

0.0000

0.0001

0.0001

0.0001

0.0052

0.0135

0.0237

0.0246

0.2698

0.0416

0.0225

0.0176

0.0000

0.0000

0.0000

0.0000

0.2151

0.0565

0.0080

0.0035

0.0001

0.0005

0.0001

0.0000

0.0000

0.0000

0.0000

0.0000

Adjusted returns

Dimension

2

3

4

5

0.3757

0.1317

0.0916

0.1013

0.0033

0.0268

0.0240

0.0086

0.0041

0.0048

0.0063

0.0065

0.0755

0.0094

0.0136

0.0267

0.0250

0.0001

0.0000

0.0000

0.0987

0.0822

0.0204

0.0109

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

Notes: for BDS test the distance used for testing proximity of the data points was specified as a fraction of pairs, with a value of 0.6. BDS test was aplied using Eviews 5.1.

To each of these returns series, we fit an ARMA(p,q) model. In this way the linear serial correlation was removed from the data or at least diminished. Results of the BDS test are reported in table 3, both for observed indices and indices after corrected for infrequent trading.

All markets are characterised by nonlinear dependences in case of the observed returns, except Romania. When the tests are aplied on the corrected returns results show that the returns are not independent in the following markets: Slovenia, Lithuania, Slovakia, Turkey, Romania and Poland. The results of this study are in accordance with the results in the literature for similar emerging markets (Hseih, 1991; Brooks, 1996), the returns are nonlinearly related in general.

The used tests determines empirically the presence of linear and nonlinear dependences, for most of the returns series. For the adjusted returns series the main dependences found are nonlinear, while the observed returns series are characterised by linear and nonlinear dependences. Most of these emerging equity markets are not weak-form efficient.

Bibliography

1. Brock W. A., Dechert W. D., Scheinkman J. A. and LeBaron B., “A Test for Independence based on the Correlation Dimension”, Econometric Reviews 15, 1996, 197-235.

2. Brooks C., “Testing for Non-linearity in Daily Sterling Exchange Rates, Applied Financial Economics, 6(4), 307-317.

3. Campbell J.Y., Lo A.W. and MacKinlay A.C. (1997), “The Econometrics of Financial Markets”, Princeton University Press, Princeton, 1997.

4. Harrison B. and Paton D., “Transition, the Evolution of Stock Market Efficiency and Entry into EU: The Case of Romania”, Economics of Planning, 37, 2004, 203–223.

5. Hseih, D.A., “Chaos and Nonlinear Dynamics: Application to Financial Markets, Journal of Finance, XLVI (5), 1991, 18379-1877.

6. Kvedaras V. and Basdevant O., “Testing the Efficiency of Emerging Markets: the Case of the Baltic States, 2002,

7. Miller M., Muthuswamy J. and Whaley R., “Mean reversion of standard and Poor’s 500 index basis changes: Arbitrage-induced or statistical illusion”, Journal of Finance, 49, 1994, 479-513.

8. Todea A., “Eficienta Informationala a Pietelor de Capital”, Editura Casa Cartii de Stiinta, Cluj-Napoca, 2005.

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