“Testing the linkages of Arab stock markets: a multivariate GARCH approach”

The authors undertook to examine 720 monthly observations of activity in 15 Arab stock markets over four years (from 2014 to 2017) to identify the dynamic linkages among those markets. To achieve this, several forms of the Generalized Auto- Regressive Conditional Heteroskedasticity (GARCH) model were utilized. Both panel and individual stationarity, in addition to cointegration tests, were employed to highlight the interaction between these markets. The results suggest that Arab stock markets have weak linkages with the exception of those of the Gulf Cooperation Council (GCC). The authors also find out that the TARCH, EGARCH, PARCH, and Component GARCH (1,1) models are suitable in terms of passing the econometric analysis tests. Nevertheless, they conclude that the EGARCH model is the most appropriate for capturing the cross-market dynamic linkages, thereby outperforming the other GARCH specifications under study. The empirical findings bear special implica-tions for economic literature regarding linkages of stock markets in the Arab world. the stock markets of the remaining Arab countries under study, the GCC markets are closely interrelated, which makes them potentially more open to investor risk diversification. Furthermore, this study demonstrates that most Arab stock markets are particularly influenced by those in Dubai and Saudi Arabia, which are found to be the most sensitive to events that occur within the GCC. This research makes three additions to the present body of literature; the first one is the exploration of the relationship between stock markets in the developing part of the world, which retains various investment characteristics that are distinct from those in the developed countries. Secondly, this paper examines the time-var-ying linkages among these markets. Thirdly, this study employs a multitude of GARCH-type models to identify the most appropriate method for pinpointing the dynamics of how the targeted stock markets interact.


INTRODUCTION
The growing importance of Arab stock markets has given impact to a new avenue of research in analyzing the relationship among market indices; not only because emerging stock markets play a crucial role in global monetary intermediation, but also for their role in facilitating a growing number of economic transactions and providing an essential channel for the flow of capital. More broadly, the analysis of historical price index movements enables the investors to support their decision-making process. In addition, the market index provides the investors with a historical overview of stock market performance and is widely used to measure how well individual portfolios perform. Monthly data series were gathered for 15 emerging Arab economies to explore the relationship between their stock market prices. The results suggest that, unlike the stock markets of the remaining Arab countries under study, the GCC markets are closely interrelated, which makes them potentially more open to investor risk diversification. Furthermore, this study demonstrates that most Arab stock markets are particularly influenced by those in Dubai and Saudi Arabia, which are found to be the most sensitive to events that occur within the GCC. This research makes three additions to the present body of literature; the first one is the exploration of the relationship between stock markets in the developing part of the world, which retains various investment characteristics that are distinct from those in the developed countries. Secondly, this paper examines the time-varying linkages among these markets. Thirdly, this study employs a multitude of GARCH-type models to identify the most appropriate method for pinpointing the dynamics of how the targeted stock markets interact.

LITERATURE REVIEW
Previous works have focused their attention on stock market indices and their bearing on different macroeconomic variables, rather than the relative relationship between the markets. However, studies that are more recent have shifted towards addressing several methods of testing the relationship among stock markets themselves, particularly in emerging countries. For instance, Al-Najjar (2016) uses symmetric and asymmetric GARCH modeling in his study of the fluctuation of prices in the Amman stock market, covering the lengthy period between 2005 and 2014. Having applied ARCH, GARCH, and EGARCH, it was found that the dynamic traits of the Jordanian stock market were effectively captured by the symmetric ARCH/GARCH models, whereas the EGARCH model failed to yield any evidence of existing leverage effects in stock returns. Rehman and Hazazi (2014) point to certain stock markets building a rapport over the years, including those of the US, Japan, the UK, and the GCC. They also indicated that the Saudi index had gradually seen a decrease in volatility. Surprisingly, no evidence of a significant causal relationship was found to exist between the stock markets under investigation. Although Hatemi (2012) stated that the US and UAE stock markets show little integration, this study, upon carrying out asymmetric causality tests, finds these markets to be integrated. Abdmoulah (2010) applied the GARCH-M (1,1) approach in order to scrutinize the markets of 11 Arab countries, using the data gathered over ten years. The study finds that all markets were significantly responsive to prior shocks in addition to being inefficient. Al-Fayoumi et al. (2009) investigate the dynamic interactions among the daily returns of the Amman Stock Exchange indices using the multivariate cointegration and the causal linkages among general, financial, industrial, and services indices. The authors find that the indices are related via one cointegrating vector in the long run, while the services index is the least integrated with the other sectors. Click and Plummer (2005) test for the integration of five ASEAN stock markets using the cointegration technique to detect the long run interactions. Their results infer that national borders do not serve to segment markets, and there is indeed a level of cointegration. Assaf (2003) employed an autoregressive vector analysis in order to examine how GCC markets interact with regard to stock market returns. His findings suggested that interdependence does exist and that all of the markets reacted to any common feedback. Bahrain's market was shown to carry a major influence over the remaining Gulf markets, while the market in the Kingdom of Saudi Arabia was revealed to respond slowly to any unexpected activity in neighboring markets.
Previous studies have fallen short in testing the interrelationship among Arab stock market indices. Moreover, there is very little empirical evidence concerning the overall linkages between Arab stock markets. In contrast, the integration and linkages between the markets of developed countries are the subject of a large body of literature, including some important and more relevant studies, where the examination of returns across these markets has been investigated. For instance, Samadder and Bhunia (2018) examine the linkages among the selected Asian stock markets by means of cointegration and causality analysis, using time series data. The primary findings reveal that Asian stock markets are interconnected in the long run, exhibiting both bidirectional and unidirectional causality among them. Moreover, Khalil (2014) reached a similar conclusion regarding the Karachi market and other Asian stock markets. Valera, Holmes, and Hassan (2017) used a panel GARCH approach to pinpoint the correlation between the fluctuation of interest rates and stock market uncertainty. Their research revealed that high level of uncertainty in the stock market causes interest rates to fall, as well as offering econometric evidence of positive relationships between uncertainty in the stock market and volatile interest rates. Al Nasser and Hajilee (2016) applied bounds testing approach when examining five stock markets in three developed markets, looking for cointegration and error-correction modeling to identify the time-varying relationship between the two sets of markets. Evidence points to both developed and emerging countries experiencing the short-run integration between stock markets. A multitude of GARCH-type models is commonly applied to examine the global and regional stock market volatility spillovers. For example, Hansen and Huang (2016) applied a Realized Exponential GARCH framework to Dow Jones Industrial Average stocks, in addition to a fund that is run over the stock exchange and used to follow the activity of the S&P500 index. The model was designed to account for multiple volatility measures in a return series. It can be seen that single measure specifications are overwhelmed by those with multiple realized measures. Bentes (2015) highlighted that Portuguese, Spanish, Japanese, UK, and US stocks are interrelated. Beirne et al. (2010) employed a Tri-variate VAR-GARCH(1,1)-inmean model for 41 emerging market economies (EMEs) in Asia, Europe, Latin America, and the Middle East to uncover the existence of regional as well as global return spillovers in most emerging markets, albeit to varying degrees. The Egyptian and Israeli stock markets came under the scrutiny of Floros (2008) who measured volatility by employing a wide range of GARCH specifications. The study finds the Egyptian index to be the most volatile, namely due to the price uncertainty in the Egyptian market over the specified period. The results of the abovementioned studies strongly indicate that cross-market linkages differ in nature depending upon the countries and region under examination.
In terms of causality and cointegration, Dasgupta (2014) reports the presence of an ongoing bidirectional effect between the Indian and Brazilian stock markets. Moreover, there is a domino effect whereby stock prices in Moscow's market rise and fall in response to changes in Brazil, which, in turn, are influenced by movements in China. According to Iqbal and Rafiq (2011), there is no significant cointegration between the stock markets in India, Pakistan, and the United States. The authors applied Granger-causality testing and reported findings of unidirectional causality affecting the stocks on the Indian market, with the influence coming from the US. Another study, authored by Joshi (2011), reveals that stocks in the Indian market adjust faster than those of any other stock market, including those in the US, Brazil, Mexico, and China. Kenourgios and Samitas (2011) applied Monte Carlo simulations, cointegration tests, and regime-switching models, in order to examine the dynamics between the emerging stock markets in the Balkan countries of Bulgaria, Croatia, Romania, Serbia, and Turkey and the developed markets in the UK, Germany, Greece, and the US over the period from 2000 to 2006. The main findings demonstrate the evidence of a long-run cointegrating rela-tionship between the named Balkan stock markets, and between them and the developed stock markets. Chinzara and Aziakponoy (2009) show that returns linkages exist between the equity market of South Africa and the Chinese, Australian, and US stock markets. The researchers analyze daily stock returns for the period from 1995 to 1997, using a univariate GARCH and a multivariate VAR framework. Moreover, the study finds that the volatility is inherently asymmetric and relatively stable over the selected period, and no evidence is found in favor of the risk-premium hypothesis. A. Masih and R. Masih (1999) examine the short-and long-term dynamic linkages between four member states of the Organisation for Economic Co-operation and Development and emerging stock markets in Asia. Specifically, the study examines the dynamic causal linkages between the aforementioned markets and utilizes both a VAR model and a vector error-correction model to measure the extent of their dynamic interdependencies. By studying the daily stock prices for the period 1992 through 1997, evidence was found to support the concept that the targeted markets experienced a significant short-and long-term relationship. Regarding the Southeast Asia region, the Hong Kong market was found to occupy the dominant role, in that it is a driving force behind the volatility that may occur in the region. This finding also suggests that the Asian markets in question tend to be regionally integrated and globally segmented.
Almost all of the above studies have applied simple correlation, cointegration, Granger causality, VAR etc. to inspect the degree of inter-linkages among international stock markets. The literature review above indicates contradictory evidence regarding international stock market linkages. The results of which depend upon data, methodology, time period, and framework used. In addition to the aforementioned research papers, there is a large abundance of recent studies such as Chen, Tian, and Zhao (2017), Guo (2017), Al-Najjar (2016), Basher and Sadorsky (2016), Gabriel (2012), Teresiene (2009), Guo and Neely (2008), and many others that also employ a wide variety of GARCH-family models to investigate the linkages, integration, and cointegration among stock returns. However, the literature remains short of studies, which document the interrelationship among stock indices in Arab markets.

Data
We employ monthly observations for 15 Arab stock indices covering the period from January 2014 to December 2017. Unfortunately, for other Arab countries such as Iraq, Libya, and others, there was a short time series that, if included, would lead to serious optimization problems for estimating the models and this would significantly weaken the analysis and interpretation of the results. Therefore, the data for these countries are completely excluded from this study. Table 1 describes the statistical characteristics of monthly stock indices for each market in question, which are based on data retrieved from the Arab Monetary Fund. The indices consist of monthly closing prices, are stated in US dollars, and are market capitalization weighted, using a chained Paasche Method. The results in Table 1 suggest, in terms of the mean volume, that among the Arab countries, Qatar, Dubai, and Morocco possess the biggest stock markets, while the smallest are those of Syria, Tunisia, and Egypt.

Methodology
The methodology used follows a generalized autoregressive conditional heteroscedastic (GARCH) framework. Specifically, under discussion are TARCH, EGARCH, PARCH and Component GARCH (1,1) models with generalized error distribution. These models are applied extensively for modelling the linkages of stock indices, particularly in the literature on developed countries. Prior to applying the GARCH-based models, some tests are required for exploring the relationship across the selected indices. Considering the weight carried by the order of integration of a time series for the analysis, the study applies a number of statistical tests. In the first set of tests, the null hypothesis is defined as the presence of a unit root against the alternative of stationarity of a given stock index. This test is carried out for both panel and individual data. For the panel analysis, we compute four types of panel unit root tests. The first is the Levin, Lin, and Chu (2002) test, for which the null hypothesis is that panel data has a unit root, assuming a common autoregressive parameter for all panels. The remaining three tests assume an individual unit root process, which includes the unit root test proposed by Im, Pesaran,   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   ABU   300   320   340   360   380   400   420   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   AMM   100   120   140   160   180   I II III IV I II III IV I II III IV I II III IV   2014 I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   DUB   100   120   140   160   180   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   EGY   100   120   140   160   180   200   220   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   KHA   280   320   360   400   440   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   KUW   250   300   350   400   450   500   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   MU S   140   160   180   200   220   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   PAL   600   800   1,000   1,200   1,400   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   QAT   0   100   200   300   400   500   I II III IV I II III IV I II III IV I II III IV   2014  2015  2016  2017   SAU   72   76   80   84   88   92   I II III IV I II III IV I II III IV I II III IV   2014 (2008), and many others, we propose four GARCH-type models which can be written in the following forms:

Model 1. The Threshold GARCH (TARCH) Model
The generalized TARCH(p, q) model for the conditional variance can be expressed by: where µ is constant for all time.
These simple, yet powerful, GARCH-type models have been tried and tested over a long period and have shown themselves to be a valuable tool in integration and volatility modelling for numerous stock markets (Ardiaa & Hoogerheide, 2014). All of the four models outlined above are estimated for each stock index included in the study. For simplicity and ease of comparison, estimated coefficients, standard errors, z-statistics, and associated probabilities are not reported in the tables. However, the fundamental statistical properties generated by our model estimation, such as the log likelihood (LL), the Akaike information criterion (AIC), the Schwarz criterion (SC), the Hannan-Quinn criterion (HQC), and the adjusted R 2 , are reported in Section 4.3.

Tests
It is of prime importance to test the stationarity for empirical modelling when wishing to validate outcomes of such models, as if the time series is non-stationary, there will be several effects based on incorrectly assuming stationarity (Hendry & Juselius, 2000). More formally, it is important to investigate the stationarity of each series before doing any econometric analysis. This is essential for not violating the application of econometric techniques, related to testing stock market integration. The augmented Dickey-Fuller regression was implemented to compute the resulting data: For both equations (6) and (7), y and z are integrated at ( )  we can reject the null hypothesis at 1% level of significance, as all the probability values are very small, hence, the null hypothesis of a unit root is rejected. In summary, the results of the stationarity tests suggest that all variables are integrated of order one.

Cointegration testing
In order to ascertain the existence of a panel cointegration relationship between the stock markets, the authors apply Pedroni's residual-based panel cointegration test (Pedroni, 1999(Pedroni, , 2004, with a maximum lag limit of 9 and four-panel statistics (rho, v, PP and ADF). For testing cointegration between each market and each other market, we perform Johansen's system cointegration test Note: * Levin, Lin, and Chu (2002) assume the common unit root process, while all other tests assume individual unit root process. (Johansen, 1991). Since the number of combinations is very large (i.e., 105 combinations), we summarize the results in one table. As shown in Table  4, all four statistics of Pedroni's test are not significant, implying the failure to reject the alternative hypothesis. This means that the null hypothesis of no cointegration cannot be rejected at the 0.05 level.
For bivariate markets, the study applies Johansen's system cointegration test (1995) for five deterministic trend cases, which rendered the number of cointegrating relations under each trend assumption, thus facilitating the assessment of how far the results are sensitive to the trend assumption. Table 5 summarizes the results for testing the number of cointegrating relations, using two sets of resultant statistics: the first reports the so-called trace statistics, while the maximum eigenvalue statistics are reported in the second (not shown in the summary). Based on the confirmation of both Trace and Maximum Eigenvalues tests, Table 5 shows that from 105 possible cointegration cases, only 37 exist, and mainly between some markets of GCC countries. Pairs marked "CO" are pairs that are cointegrated, while empty cells denote no cointegration. As can be seen from  that initiatives be implemented to achieve integration, which is a feasible aspiration. Currently, an international portfolio investor would find few benefits of holding a diverse international portfolio over a number of Arab stock markets.

Results of model estimation
Based on the concept of Chen and Zhao (2017), for capturing the effect among stock markets more accurately, we combine information theory and introduce transfer entropy to obtain cross-market effects among stock markets. For each market, 14 other markets are regressed on it using dynamic transfer entropy ML-ARCH-Normal distribu-tion (BFGS/Marquardt steps) with unconditional pre-sample variance.
The results of all four models used in this study, as presented in Tables 6, 7, 8, and 9, demonstrate that the highest cross-market effects are those for Qatar, Dubai, and Saudi Arabia, while the lowest cross-market effects are those for Tunisia, Damascus, and Beirut stock markets. This finding underlines the relevance of market integration based on geographical proximity, particularly in the case of the Arab Gulf markets. Furthermore, the findings indicate that there is a systematic bias to investor expectations. The recommendation is that future research should strive to explain these empirical regularities.

DISCUSSION
The rapid growth of emerging markets has given rise to a research interest in analyzing the interrelationships among stock market indices for their role in facilitating a growing number of economic transactions and providing an essential channel for the flow of capital. The analysis of historical price volatility enables the investors to support their decision-making process. Moreover, the market index provides investors with a historical overview of stock market performance and is considered a benchmark for evaluating the performance of individual portfolios. This paper seeks to measure the extent of the dynamic interactions among 15 selected Arab stock markets. We apply four GARCH-based models -namely, TARCH, EGARCH, PARCH, and Component GARCH(1,1) -to examine 720 monthly observations starting from the beginning of 2014 to the end of 2017. Both panel and individual stationarity, in addition to cointegration tests, are employed to capture the interactions across these markets. Even though these models are employed by numerous studies in the literature on developed countries, very few studies have addressed the case for emerging Arab stock markets. All of the four models used in this study sufficiently pass the econometric analysis criteria. However, the EGARCH model, in particular, outperforms the other GARCH specifications in explaining the cross-market dynamic linkages across the selected markets.

CONCLUSION
The empirical findings conclude that the studied markets are generally described by weak linkages. However, the strong linkages are largely explained by geographical proximity (or region) particularly in the case of the GCC stock markets. It is clear from the results that the stock markets in Saudi Arabia and Dubai hold significant sway over the remaining markets of the Arab world, which are found to be the most responsive to events that occur within the Arab Gulf. The abovementioned model specifications show that the highest pairwise stock market effects are observed for Qatar, Dubai, and Saudi Arabia, while the lowest cross-market effects are observed for the stock markets in Tunisia, Damascus, and Beirut stock markets. It can be concluded that Arab stock markets are economically fragmented and remain to be integrated. Finally, initiatives to integrate these markets may result in potential diversification benefits for investors. Moreover, our findings show that investors hold systematically biased expectations and the recommendation is that researchers take further steps to explain these empirical regularities.
The contributions of this paper are threefold. Firstly, this paper evaluates the interactions among stock markets in a developing part of the world that is described by idiosyncratic investment characteristics