Day of the week effect in central European stock markets/Efekt dne tydnu na kapitalovych trzich ve stredni Evrope.
Some decades ago, the Efficient market hypothesis (hereafter EMH) remarkably influenced financial theory and practice. The main contribution to the theory is often attributed to Fama's survey study  where the efficient capital markets were promoted. In efficient markets, asset prices reflect the best estimation of market participant regarding the expected risk and return of the assets while the information currently known about the asset is taken into account. Hence, all assets in the market will be appropriately priced offering adequate level of expected return to risk. In particular, it is stated in  that EMH can be distinguished in three versions depending on the nature of the information subset of interest: (i) strong form, (ii) semi-strong form, (iii) weak form. The weak form claims that asset prices already correspond with all past publicly available information. The semi-strong form states both that prices reflect all publicly available information and that prices instantly change to reflect new public information. The strong form additionally claims that prices instantly reflect even hidden or 'insider' information.
However, many studies found empirical evidence against validity of the semi-strong and weak forms of EMH. As it is pointed out in  or , many financial economists and statisticians began to believe that stock prices are at least partially predictable. Such contradictions in asset pricing are considered as anomalies. If the anomalies appear regularly in trading with stocks and can influence stock market returns they are usually referred to calendar anomalies. Calendar anomalies rest on the basic assumption that the past behaviour of a stock's price is rich in information pertaining to its future behaviour. In other words, the study of calendar anomalies suggests that investors could use these results on anomalies to predict stock market movements on given days .
The most important examples of calendar anomalies in stock markets are day of the week effect, twist of the Monday, turn of the month, turn of the year and holiday periods. The present paper is focused solely on day of the week effect (hereafter DWE). We can distinguish several approaches to the effect in literature. The original understanding of DWE was formulated in  as evidence of large stock market decrease between the Friday close and the Monday close. By contrast, it is suggested in  that returns on Monday are lower than those for Tuesday through Friday. Finally, DWE according to  is simply that weekdays differ in their returns.
The Central European (hereafter CE) countries have made significant progress towards integration with the world economy over the past 15 years. Although the CE stock markets are inevitably involved in the process of convergence and integration they have a brief history compared to mature markets in Europe and the United States. Likewise, as compared to other international markets, the liquidity of the CE markets is lower, and their size relatively small [1i]. According to the World Federation of Exchanges, the CE stock markets represented 0.5 % of the world stock market capitalization in 2010.
We focus on stock markets in the Czech Republic, Hungary and Poland. Data from the World Bank suggest that the market capitalization as a percentage of GDP decreased during the period 2006-2010 from 34.1 % to 22.4 % in the Czech Republic, from 37.2 % to 21.2 % in Hungary, and from 43.6 % to 40.6 % in Poland. Despite this unfavourable development these markets are the largest, most liquid and most integrated in the CE region. It is reported in  that the three analysed CE markets have strong presence of foreign institutional investors and large volumes traded by foreign investors. Furthermore, spillovers as well as macroeconomic announcements from developed markets do impact the three CE markets under investigation. Therefore, we believe that these markets are the best candidates for analysis of stock market calendar anomalies in the CE region.
The aim of the paper is to estimate DWE in the stock markets in the Czech Republic, Hungary and Poland over the period of six years (April 2006-March 2012). The present paper substantially contributes to the existing literature as it covers the most recent period and the markets that have not been in the centre of researchers' interest. Since the analysed period includes the global financial crisis the paper also reveals the influence of the financial crisis and its phases on presence and character of DWE.
The paper is structured as follows. In Section 1, we review the relevant literature. In Section 2, we introduce and describe the dataset and specify the model used in estimation. In Section 3, we present and discuss the results obtained from estimations. The last section concludes the paper with summary of crucial findings.
1. Review of Relevant Literature
The empirical literature is rich on studies that examine DWE and other calendar anomalies in matured and developed stock markets as well as emerging markets in Asia or Latin America. However, we are aware of only few studies that address DWE in the CE stock markets. Some of these papers, in addition, do not focus strictly on the CE region but incorporate the CE markets to a larger group of analysed markets. Various techniques and approaches were applied by researchers with no general consensus on the best method to be used for DWE estimation. All studies geographically relevant to the present paper are listed and summarized in Tab. 1.
The first serious attempt to investigate DWE in the CE emerging stock markets is . They study DWE in eight stock markets during the period 22 September 1997-29 March 2002 and come to the following conclusions. Monday returns were negative and significant for the Czech and Romanian stock markets. Wednesday returns were significantly positive for the Slovenian market. The DWE was not revealed in the Polish and Slovak stock markets.
The study  focuses on even larger group of 11 emerging stock markets in Central and Eastern Europe. The authors use data on stock market indices from inception of each market's major index to 6 September 2002. They test the classical hypothesis that stock returns are significantly lower or negative on Mondays relative to other weekdays. Their results indicate negative Monday returns in six markets but only returns in Estonia and Lithuania are significantly negative. After application of supplementary tests the authors conclude that no evidence of DWE in form of Monday anomaly was found.
In , various calendar anomalies in the Czech Republic, Slovakia and Slovenia are examined. The results are also rather sceptical on existence of DWE and other effects. They find only very weak evidence of the January effect, DWE, and the turn of the month effect. Moreover, the effects have different characteristics based on the differences in the stock markets. As regards to DWE, they only revealed a weak existence in mean return for Slovenia, but in opposite direction than theory suggests.
The focus of  is primarily on developed European markets but the paper analyses also the Czech stock market as the only example of emerging CE markets. The results obtained are in accordance with above cited studies since the Czech market as one of the two did not exhibit any evidence of DWE. The authors of  used a battery of parametric and non-parametric tests on daily returns of 15 European stock markets in the period 1997-2004. Application of the Kruskal-Wallis test provided no evidence of the day of the week effect in the Czech Republic's stock market.
By contrast,  focus on the same period 1997-2004 and investigate the seasonality and nontrading effect in stock market indices of the Czech Republic, Germany, Hungary and Poland. They used the PAR-PGARCH model and revealed significant day of the week effects in the mean of returns on the Czech and Polish index, and significant seasonality in the volatility of the Hungarian index. High frequency data from the Warsaw stock exchange is used in  to verify daily and hourly calendar effects. Based on estimations of robust regression models they conclude that positive DWE for Monday and persistent and positive open jump and end of session effects are present in the Polish stock market.
In , calendar anomalies in 20 emerging stock markets from different continents are investigated and results suggest that DWE is present in market returns for three countries and in market volatility for five countries. Only one country reports DWE in both return and variance specifications. None of the CE markets examined in the present paper showed DWE evidence at 1% significance level that is recommended by the authors for estimations with time series with thousands of daily observations.
Similarly to most of the previous studies,  finds no strong and convincing evidence of calendar effects across the group of analysed countries. European stock markets seem to be mostly immune to DWE. The only effect that is shared by more countries is the tendency for lower returns in the holiday months of August and September. However, all the revealed calendar anomalies are basically country-specific. Similar conclusion is presented in  as they point out that DWE is rather local than regional of global phenomenon. The results for CE stock markets only indicate an increase of conditional volatility on Wednesday for Hungary.
The evidence on DWE in CE and Turkey's stock markets before and during financial crisis is compared in [i]. Application of regression models with dummy variables leads to conclusion that DWE was present only in the Czech (decreasing Monday effect) and Hungarian (increasing Friday effect) stock markets during the crisis. It was impossible to find any aspect common for all CE markets in the estimation results. Results of  also confirm rather sporadically evidence of DWE in CE stock markets. Moreover, substantial differences among countries prevent authors from drawing any general conclusion. The only notable feature of the results is that the Monday effect in volatility (variance) tends to be present in more indices in the post accession than in the pre accession EU period.
After the review of relevant literature one can conclude that the existing studies generally found none or little evidence of DWE in the CE stock markets under examination. This conclusion prevailed regardless the methodology and econometric techniques applied. The present paper contributes to existing literature on DWE as it covers the most recent period and the markets that have not been in the centre of researchers' interest. Since the analysed period includes the global financial crisis the paper also reveals the influence of the financial crisis and its phases on presence and character of DWE. The findings can be worth to market participants for their investment decisions.
2. Overview of Stock Markets, Data Description and Model Specification
This paper employs the daily closing values of the stock market main indices in the Czech Republic, Hungary and Poland. Namely, we use the Prague Stock Exchange Index (PX), the Budapest Stock Exchange Index (BUX) and the Warsaw Stock Exchange Index (WIG). The time series of the indices' closing values were collected from the Patria financial database. We consistently use five observations per week and the returns for non-trading days are calculated using the closing price indices from the last trading day. This approach is followed in order to avoid possible bias from the loss of information due to public holidays.
The period under estimation starts on April 2006 and ends on March 2012. Hence, we have 1565 daily returns for each stock market in total. The whole estimation period was divided into six sub-periods to capture individual phases of the financial crisis. The pre-crisis period (Period 1) is from April 2006 to March 2007. The phase of crisis initialization (Period 2) starts in April 2007 and ends on 14 March 2008. The crisis culmination (Period 3) lasts from 17 March 200i to end of March 2009. The phase of crisis stabilization (Period 4) covers the period from April 2009 to March 2010. The post-crisis phase (Period 5) starts in April 2011 and ends on 31 March 2011. Finally, the debt-crisis phase (Period 6) is from April 2011 to March 2012. Although the phasing of the analysed period is rather arbitrary it reflects generally accepted turning points in the timeline of the financial crisis. Although the recent sovereign-debt crisis that hit many countries in the euro area is sometimes considered as a crisis of specific kind we incorporate it to the analysis as the last phase. We believe that the financial crisis remarkably contributed to uncovering of the structural economic problems that stay behind the sovereign-debt crisis.
Fig. 1 depicts development of the stock market indices over the entire period of analysis. One can clearly observe that the main development trends are synchronized in all stock markets. Nevertheless, in spite of sharing the trends, the markets did not respond to domestic and international impulses uniformly and the overall change of stock market indices differ significantly. The only market with positive change is the Polish one (+0.97 %). The other two markets recorded substantially negative change: -36.49 % for the Czech and -18.97 % for the Hungarian stock market.
For better understanding of the market development as well as results of DWE estimations we also provide a basic description of the analysed CE stock markets that captures the period of estimation. In Tab. 2, we present overview of market capitalization, annual turnover, number of trades and number of companies that are listed in official stock market of the exchange. Although all exchanges also offer trading with bonds, derivatives, exchange-traded funds and other securities and financial instruments but the respective figures are not reported in the paper as we focus solely on stock market. The Warsaw Stock Exchange is the leading stock market in CE region according to all parameters used in comparison. However, the Prague Stock Exchange has the highest average volume of transaction realized in the market. Hence, the Czech market seems to be used more by larger portfolio or institutional investors than small and individual investors.
[FIGURE 1 OMITTED]
Following the standards used in literature, daily returns are calculated as first difference in natural logarithms and then multiplied by 100 to approximate percentage changes:
[R.sub.t] = ln([I.sub.t]/[I.sub.t-1]) x 100 (1)
where [I.sub.t] and [R.sub.t] refer to the stock market index closing value and the daily return on day t, respectively. The calculated daily returns are depicted in Fig. 2. The vertical lines in graphs delimitate the six phases of the financial crisis.
[FIGURE 2 OMITTED]
Although a higher volatility and serious fluctuations of daily returns are observable in all stock markets during the phase of crisis culmination the Polish market seems to be least affected by the crisis. By contrast, one can observe many extreme daily returns considerably exceeding the usual levels in the Czech and Hungarian markets. All markets demonstrate a clear tendency to restoration of standard behaviour patterns in the course of Period 4 and Period 5. By contrast, Period 6 brought a new wave of instability into stock markets as the sovereign-debt crisis in the euro area expanded in the second half of 2011. It is evident from the graphs that the Hungary's stock market displayed the highest volatility at this time as Hungary has to face the most serious problems with sovereign and private sector debt in the group of CE economies. The differences among the phases of financial crisis can be also documented by comparison of the average daily returns and standards deviations. The graphs in Fig. 3 show the average daily return and standard deviation for all markets in individual periods.
[FIGURE 3 OMITTED]
Whereas the standard deviation in Period 1 and Period 2 are very similar in all markets the average daily returns differ and Period 2 exhibits negative returns. Culmination of the financial crisis brought to the stock markets substantial volatility and remarkably negative average daily returns. The stabilization and post-crisis phases are characteristic of gradually decreasing of volatility to the pre-crisis levels. The rebound of returns in Period 4 was followed by stagnation in Period 5. The analysed stock markets became more homogeneous in Period 6 and showed very similar negative average daily returns with slightly increased standard deviations. Hence, none of the individual periods is similar to the others and, subsequently, the estimations of DWE are conducted separately for each period.
Many alternative approaches and estimation techniques have been applied in literature to examine DWE. The classical methodology used in pioneer studies is the conventional OLS regression model with appropriately defined five dummy variables, each for one day of the week. Estimation of such regression model should be accompanied by a means test. This is necessary to verify if the returns are independent of the day they come from or they are characterised by statistically similar mean returns. Although this approach has been used extensively in previous research it suffers from two serious problems.
First, the residuals from the regression model can be autocorrelated, which results in misleading the inferences. This problem can be solved by extension of the model with lagged returns (e.g. one week lag). Second, there is no reason to assume that the variance of residuals will not vary over time. As it has been often documented by empirical evidence, the variance of residuals is not constant and possibly time-dependent. In this respect, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is able to capture the time-varying variability in the variance of the residuals. This approach has the advantage that the conditional variance can be expressed as a function of past errors. These models assume that the variance of the residual term is not constant through time.
In the present paper, we used the GARCHM (1,1) model in the following specification:
[R.sub.t] = [[alpha].sub.0] MO + [[alpha].sub.TUE] TU + [[alpha].sub.THU] TH + [[alpha].sub.FRI] FR + [lambda][h.sub.t] + [[epsilon].sub.t] (2)
[h.sup.2.sub.t] = [alpha] + [[delta].sub.MON] MO + [[delta].sub.TUE] TU + [[delta].sub.THU] TH + [[delta].sub.FRI] FR + [beta][[epsilon].sup.2.sub.t-1] + [gamma][h.sup.2.sub.t-1] (3)
where [R.sub.t] represents daily returns of an examined index. MO, TU, TH and FR are the dummy variables for Monday, Tuesday, Thursday and Friday, while we exclude the Wednesday's dummy variable from the equation to avoid the dummy variable trap. Further, [h.sub.t] is the conditional variance, [[epsilon].sub.t] denotes the residual term and X is a measure of the risk premium, as it is possible that the conditional variance (proxy for risk) can affect stock market returns. If [lambda] is positive the risk-averse agents must be compensated to accept the higher risk.
Given the fact that more risky assets may provide higher average returns we included the conditional variance in the conditional mean equation and used the GARCH-M model. Since our analysis is focused on very turbulent period of financial crisis we believe that it is worth to examine DWE not only in returns but also in volatility. Hence, we included the dummy variables also in the variance equation. Such a modification of the standard GARCH-M specification accounts for the possible stationary effects within the variance equation. Our approach finally leads to complex assessment of DWE in CE stock market indices as it captures both key factors of investments, i.e. return and risk.
[FIGURE 4 OMITTED]
3. Estimation Results
Before reporting results of our GARCH-M models' estimations we present a detailed graphical illustration of average daily returns in individual days of the week structured by periods and stock markets. The graphs in Fig. 4 show how different are the analysed periods.
While the markets seem to be quite homogeneous in some periods (e.g. Period 4 or Period 5) one can observe substantial differences in daily returns in the other periods. For example, during the period of crisis stabilization (Period 4) all markets exhibit Monday average return as the highest and Friday average return as the only negative in the week. Likewise, the size and order of remaining returns are very similar across the markets. By contrast, the period of crisis culmination, for example, brought a considerable diversity to daily returns. Although all daily average returns in Hungary and Poland are negative, the market declines the most on Thursday in Hungary and on Friday in Poland. On the other hand, the Czech market reports positive returns on Monday and Wednesday and most negative on Tuesday.
We estimated the GARCH-M (1,1) model according to the specification in (2) and (3) for all the countries and periods analysed. The obtained results are presented in Tab. 3-5. The upper part of the table summarizes results for the mean equation and the lower part reports the results for the variance equation.
We run a battery of standard tests to check descriptive validity and specification adequacy of estimated models. In particular, we applied the ARCH-LM test and Ljung-Box Q Statistics on the standardized residuals and standardized squared residuals with 5, 10, 15 and 20-day lags. The tests reject the presence of auto-correlated residuals ARCH effects and support model specification for almost all GARCH-M models estimated. To conserve the space the results of these specification tests are not reported but may be obtained from the authors upon request.
As regards to the day of the week effect in the mean equation, the individual meaning for each one of the dummy variables could reveal the presence of an atypical yield during a day of the week with respect to that of Wednesday. Although we found some weak evidence of the effect presence the results are rather mixed and one can reveal no common pattern for all three stock markets. In addition, evidence of DWE is not stable over time as the significance and sign of individual dummy variables differ across the periods.
The estimation results are inconsistent with the usual concept of the day of the week effect that has been empirically revealed in most studies where average Monday returns are usually significantly lower and average Friday returns significantly greater than the average returns for the other days of the week. We only found that Monday's dummy variable is significantly negative in the Czech stock market in the pre-crisis period and period of sovereign-debt crisis. On the other hand, the only evidence of DWE discovered in the Hungarian market is opposite as the Monday returns seems to be significantly higher in the period of crisis stabilization. The evidence on DWE we picked up in the Polish market does not correspond with theoretical assumption either since the Friday average yield is significantly lower in the period of crisis stabilization. We further observe sporadic and isolated evidence of DWE in estimation results. Significantly lower returns are found on Tuesday for Poland in the post-crisis period and for the Czech Republic during the period of crisis culmination. Additionally, we uncover also lower return on Thursday in the Czech market during culmination of the crisis.
In the variance equation of the modified GARCH-M (1,1) model we allow the conditional variance to change for each day of the week. This is the way how we can examine the day of the week effect in volatility. The highest volatility as suggested by estimated coefficients occurred during the crisis culmination. However, the day of the week effect was not detected in volatility in this period. We did not find any evidence of the effect in the Hungarian stock market volatility at all. Some evidence was revealed in the remaining two markets; however it is rather exceptional. Results show significant effect of Monday and Thursday on conditional variance (volatility) in Czech and Poland's markets. In particular, Monday increases stock market volatility in the Czech Republic in the pre-crisis period and in Poland in the phase of crisis stabilization. Thursday increases volatility in Poland before the crisis (Period 1) and also during the stabilization (Period 4). Last, we revealed that Friday significantly reduces volatility of the Polish stock market volatility in the last period of sovereign-debt crisis.
This paper investigates the possible existence and change in nature of DWE in three CE stock markets during the recent financial crisis. The sample covers six periods that cover individual phases of the crisis. This is the first study focused on the CE region that uses the most recent data and examines DWE in daily returns as well as daily returns' volatility. The results suggest that the analysed stock markets seem to be mostly immune to DWE. In all markets and periods, we revealed only rare occurrence of calendar anomalies. This weak evidence is not consistent over time because significance and signs of the respective parameters change across the periods. Furthermore, the estimated coefficients are often contrary to theoretical expectations and findings of classical studies in this field. This can be explained by the fact that even though the analyzed markets are matured and most liquid in the Central and Eastern Europe, they still fall behind world developed markets. They are very sensitive to various impulses including swings and discrepancies in trading volume. Hence, the occasionally revealed effects may be only stokes of luck of erratic movements in the stock market indices. Such a conclusion can be drawn on both daily returns and volatility. Our analysis, therefore, confirms conclusions of previous research, as referred to in this paper, that DWE is not typical for the CE stock markets. This characteristic did not change even during the financial crisis. There are two streams of future research we suggest. First, investigate other types of calendar anomalies such as month of the year effect or turn of the holiday effect. Second, apply models that allow for asymmetry like EGARCH or TGARCH.
Research behind this paper was supported by the Student Grant Competition of Silesian University within the project SGSr25r2010 'Financial integration in the EU and its effect on corporate sector'.
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doc. Ing. Daniel Stavarek, Ph.D.
Silesian University in Opava
School of Business Administration in Karvina
Department of Finance
Ing. Tomas Heryan
Silesian University in Opava
School of Business Administration in Karvina
Department of Finance
Doruceno redakci: 17. 5. 2012
Recenzovano: 12. 6. 2012, 10. 7. 2012
Schvaleno k publikovani: 26. 9. 2012
Tab. 1: Summary of relevant literature Paper Method Patev et al.  OLS regression, GARCH-M Ajayi et al.  OLS regression Tonchev and Kim  OLS regression, GARCH Apolinario et al.  GARCH, T-GARCH Chukwuogor-Ndu  Kruskal-Wallis test Zikes and Bubk  PAR-PGARCH Yalcin and Yucel  EGARCH-M Strawinski and M-estimators and Slepaczuk  OLS regression Borges  (Bootstrap) OLS Regression, GARCH, Kruskal-Wallis test Hogholm et al.  Kruskal-Wallis one day ANOVA test Guidi et al.  GARCH-M Gajdosov et al.  OLS regression Paper Stock markets analysed Patev et al.  Romania, Hungary, Latvia, Czech Republic, Russia, Slovakia, Slovenia, Poland Ajayi et al.  Croatia, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Russia, Slovakia, Slovenia Tonchev and Kim  Czech Republic, Slovakia, Slovenia Apolinario et al.  Germany, Austria, Belgium, Denmark, Spain, France, Netherlands, Portugal, United Kingdom, Czech Republic, Sweden, Switzerland Chukwuogor-Ndu  Austria, Belgium, Czech Republic, Denmark, Germany, France, Italy, Netherlands, Russia, Slovakia, Spain, Sweden, Turkey, Switzerland, United Kingdom Zikes and Bubk  Czech Republic, Hungary, Poland, and Germany Yalcin and Yucel  20 countries (including Czech Republic, Hungary, Poland) Strawinski and Poland Slepaczuk  Borges  Austria, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Netherlands, Norway, Poland, Portugal, Spain, Switzerland, United Kingdom Hogholm et al.  18 European countries (incl. Czech Republic, and Hungary). Guidi et al.  Bulgaria, Czech Republic, Hungary, Poland, Romania, Slovakia, Slovenia Gajdosov et al.  Czech Republic, Hungary, Poland, Slovakia, Turkey Paper Period Patev et al.  09/1997--03/2002 Ajayi et al.  Launch of national index--09/2002 Tonchev and Kim  01/1999--06/2003 Apolinario et al.  07/1999--03/2004 Chukwuogor-Ndu  01/1997--12/2004 Zikes and Bubk  01/1997--06/2004 Yalcin and Yucel  Different start--03/2005 Strawinski and 02/1998--30/2008 Slepaczuk  Borges  01/1994--12/2007 Hogholm et al.  01/2000--12/2006 Guidi et al.  01/1999--01/2009 Gajdosov et al.  01/2005--11/2010 Source: Authors' elaboration Tab. 2: Elementary description of analysed stock markets 2006 2007 2008 Czech Republic--Prague Stock Exchange Market 34,693 47,987 29,615 capitalization (EUR mln) Turnover 28,361 35,954 33,764 (EUR mln) Trades 567,893 670,873 1,395,871 Listed 32 32 29 companies Hungary--Budapest Stock Exchange Market 31,687 31,528 13,326 capitalization (EUR mln) Turnover 22,525 34,403 20,916 (EUR mln) Trades 1,464,580 1,629,278 1,893,044 Listed 41 41 43 companies Poland--Warsaw Stock Exchange Market 112,826 144,323 65,178 capitalization (EUR mln) Turnover 40,401 61,152 45,478 (EUR mln) Trades 10,280,959 15,203,866 9,836,831 Listed 265 375 458 companies 2009 2010 Czech Republic--Prague Stock Exchange Market 31,265 31,922 capitalization (EUR mln) Turnover 17,472 15,258 (EUR mln) Trades 1,571,640 1,162,508 Listed 25 27 companies Hungary--Budapest Stock Exchange Market 21,093 20,624 capitalization (EUR mln) Turnover 18,957 19,925 (EUR mln) Trades 3,349,838 2,612,330 Listed 46 52 companies Poland--Warsaw Stock Exchange Market 105,157 142,272 capitalization (EUR mln) Turnover 38,819 52,260 (EUR mln) Trades 13,274,986 13,120,775 Listed 486 585 companies Source: Various issues of the European Exchange Report by the Federation of European Securities Exchanges Tab. 3: Estimation of GARCH-M model for the Czech stock market Period 1 Period 2 Period 3 Mean equation [[alpha].sub.0] 0.2507 (a) 0.1661 0.4752 (b) [[alpha].sub.MON] -0.2162 -0.3005 (b) -0.4818 [[alpha].sub.TUE] -0.2075 -0.1421 -0.9689 (a) [[alpha].sub.THU] 0.1466 -0.1803 -0.5479 (b) [[alpha].sub.FRI] -0.1610 -0.0018 -0.4645 [lambda] -0.0055 0.0243 -0.0076 Variance equation [alpha] -0.3189 -0.0233 0.2614 [[delta].sub.MON] 0.7307 (b) -0.4098 -1.4415 [[delta].sub.TUE] 0.5351 0.3349 -0.1869 [[delta].sub.THU] 0.8234 0.1663 -0.3647 [[delta].sub.FRI] -0.0722 0.1988 0.9855 [gamma] 0.1240 (b) 0.2032 (a) 0.1885 (a) 0.8231 (a) 0.8053 (a) 0.8292 (a) Period 4 Period 5 Period 6 Mean equation [[alpha].sub.0] 0.0344 0.1529 0.4134 [[alpha].sub.MON] 0.2968 0.1046 -0.8124 (a) [[alpha].sub.TUE] -0.1030 -0.3383 -0.6553 (b) [[alpha].sub.THU] -0.1949 -0.0539 -0.4901 (c) [[alpha].sub.FRI] -0.3867 -0.2347 -0.4514 (c) [lambda] 0.0809 0.0037 0.0074 Variance equation [alpha] 0.1432 0.4760 1.1935 [[delta].sub.MON] -0.7476 -0.1499 -0.1010 [[delta].sub.TUE] -0.1010 -0.5314 -1.6895 [[delta].sub.THU] -0.2208 -0.8497 -2.0295 [[delta].sub.FRI] 0.5149 -0.7067 (c) -1.6438 [gamma] -0.0391 (a) 0.1064 (b) 0.1516 (a) 1.0100 (a) 0.8713 (a) 0.8205 (a) Note: (a,b,c) denote significance at 1 %, 5 % and 10 % respectively Source: Authors' calculations Tab. 4: Estimation of GARCH-M model for the Hungarian stock market Period 1 Period 2 Period 3 Mean equation [[alpha].sub.0] 0.1453 -0.0301 0.3017 [[alpha].sub.MON] -0.0871 -0.1756 -0.4817 [[alpha].sub.TUE] -0.0664 -0.0706 -0.2558 [[alpha].sub.THU] 0.1423 0.0279 -0.3560 [[alpha].sub.FRI] -0.0785 0.1330 -0.4671 [lambda] -0.0390 0.0619 -0.0159 Variance equation [alpha] -0.0530 0.3690 0.7635 [[delta].sub.MON] 0.3686 -0.2789 -1.1826 [[delta].sub.TUE] 0.2407 -0.1365 -0.7713 [[delta].sub.THU] 0.8060 0.0972 -1.5002 [[delta].sub.FRI] -0.7674 0.1882 -0.0623 [beta] 0.1021 (c) 0.3296 (b) 0.1499 (a) [gamma] 0.8597 (a) 0.5040 (a) 0.8549 (a) Period 4 Period 5 Period 6 Mean equation [[alpha].sub.0] -0.2076 0.3509 -0.2565 [[alpha].sub.MON] 0.8400 (b) -0.1264 -0.1878 [[alpha].sub.TUE] -0.1418 -0.3410 0.0731 [[alpha].sub.THU] -0.0819 -0.3711 0.0095 [[alpha].sub.FRI] -0.1925 -0.4008 0.3042 [lambda] 0.0930 -0.0562 0.0745 Variance equation [alpha] -0.8869 0.4917 0.0553 [[delta].sub.MON] 0.7112 -0.8914 0.3941 [[delta].sub.TUE] 1.7669 0.0681 0.1927 [[delta].sub.THU] 1.4529 -0.7542 -0.4619 [[delta].sub.FRI] 0.8716 -0.3911 -0.1990 [beta] 0.0704 (b) 0.1134 (a) 0.1199 (b) [gamma] 0.9164 (a) 0.8456 (a) 0.8701 (a) Note: (a,b,c) denote significance at 1 %, 5 % and 10 % respectively Source: Authors' calculations Tab. 5: Estimation of GARCH-M model for the Polish stock market Period 1 Period 2 Period 3 Mean equation [[alpha].sub.0] 0.0795 -0.3611 -0.0654 [[alpha].sub.MON] 0.0859 -0.0225 -0.1232 [[alpha].sub.TUE] 0.0011 0.1315 -0.1131 [[alpha].sub.THU] 0.1120 -0.0847 -0.1435 [[alpha].sub.FRI] 0.1063 0.0669 -0.2667 [lambda] -0.0118 0.2466 0.0210 Variance equation [alpha] -0.2778 -0.0309 -0.3452 [[alpha].sub.MON] 0.4720 -0.0815 1.3420 [[alpha].sub.TUE] 0.5753 0.3593 0.4270 [[alpha].sub.THU] 1.5929 (b) 0.5179 -0.3205 [[alpha].sub.FRI] -0.7755 -0.0083 0.7435 [beta] 0.0551 (c) 0.0914 (c) 0.1229 (b) [gamma] 0.8926 (a) 0.8479 (a) 0.8579 (a) Period 4 Period 5 Period 6 Mean equation [[alpha].sub.0] 0.2080 0.2156 0.0811 [[alpha].sub.MON] 0.1988 0.0821 -0.3219 [[alpha].sub.TUE] -0.1045 -0.3483 (b) 0.0500 [[alpha].sub.THU] -0.2830 -0.2034 -0.2129 [[alpha].sub.FRI] -0.5366 (b) -0.1168 -0.0395 [lambda] 0.2211 -0.0321 0.0171 Variance equation [alpha] -0.6168 -0.0305 0.4797 [[alpha].sub.MON] 1.0904 (a) 0.1141 -0.1963 [[alpha].sub.TUE] 0.2073 0.2113 -0.6240 [[alpha].sub.THU] 1.7767 (b) -0.0040 -0.5982 [[alpha].sub.FRI] 0.7921 -0.0690 -0.8653 (b) [beta] 0.0644 (c) 0.0610 (b) 0.0888 (b) [gamma] 0.9131 (a) 0.9067 (a) 0.8968 (a) Note: (a,b,c) denote significance at 1 %, 5 % and 10 % respectively Source: Authors' calculations
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|Author:||Stavarek, Daniel; Heryan, Tomas|
|Publication:||E+M Ekonomie a Management|
|Date:||Oct 1, 2012|
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