Oil Sector Spillover Effects to the Kuwait Stock Market under Uncertainty

The purpose of this paper is to identify the connection between oil prices and the performance of oil and gas, industry and services sectors. The paper is supported by the granger causality and Engle and Granger cointegration tests. The research findings do not support a long-run association between Brent oil prices excluding the case of the Oil and Gas sector index; however, short-run dynamics were recognized. There is no unidirectional causality found in any case. The outcomes of the GARCH model show stable results for all three sectors.


Introduction
In recent years, literature has been dedicated to oil prices affecting macroeconomic factors in developed nations (Killian, 2009). Among the existing literature, attention is being focused on interlinkage among oil prices and stock markets. Besides that there is no theoretical pattern that characterizes the interlinkage between the financial markets and oil, empirical research reveals that instability in oil prices impact firms' performance, cost, and incomes, which thereafter impact stock market returns. Most of the literature has information on the interlinkage between the oil and equity markets in oil-dependent economies, like the united states (US), where raise in oil prices have unfavorable economic impacts. When oil price boosts, oil-importing economies can experience heavy negative results and economic recession (Federer, 1996). However, the impression of oil prices on oil-rich countries is different, a surge in oil prices recovers the balance of trade, causing a greater current account surplus, and an upgrading foreign asset position (Abdelaziz et al., 2008). For this reason, this paper investigates the affiliation between equity markets and oil prices from the perspective of oil-exporting countries such as Kuwait.
Kuwait is considered to be one of the main oil exporters on world energy markets, and the variation in equity returns on Kuwait's stock markets is likely to be sensitive to differences in oil prices. Also, Kuwait's stock markets are prone to regional political events that separate them from developed and emerging markets. The recent global trend of rising oil prices is bringing more cash flows to Kuwait, which is having a positive effect on stock market listed sectors. Consequently, recognizing shifts in oil prices on Kuwait's stock market returns at the sectoral level allows investors to make more focused investment choices and to provide new evidence for policymakers monitoring stock markets. As such, a study involving the Kuwait stock market and the stock index at the sectoral level should be of great interest.
The interlinkage between oil prices and equity market behavior has enjoyed a considerable level of attention among the researchers (Arezki et al., 2017;Al-Qudsi & Ali, 2016;Guesmi et al., 2018) debate that the fluctuation of oil prices is a risk factor causing market contagion towards stock markets with origins on oil price volatility. Oil prices can impact equity markets through various methods, as rising oil prices can boost interest rates lead to control inflationary pressures, increase inputs costs which will reduce gains that affect negatively on the stock returns (Jiang et al., 2017;Grima & Caruana, 2017;Adrangi et al., 2014;Ansani & Daniele, 2012;Filis et al., 2011). Narayan & Gupta (2015) used the least square estimation and utilizing monthly data for 150 years and their result in favor of nonlinear likelihood, proposing that inverse oil prices predict US stock return. Cunado & de Gracia (2014) confirmed the influence oil prices shocks on 12 oil-dependent European countries (Belgium, Austria, Finland, Denmark, Germany, France, Italy, Luxembourg, Spain, Portugal, the Netherlands, and the UK). They used monthly data for the period from February 1973 to December 2011. The outcome has shown that oil price changes in Belgium, Denmark, Finland, France, Italy, Luxembourg, the Netherlands, Portugal, Spain, and the United Kingdom have a significant negative impact on stock returns, as regards to the global oil price. Narayan & Sharma (2014) investigated the oil price fluctuation that impacts the stock returns. They utilized daily returns of 560 listed firms on the Stock Exchange (New York), and they were separated into 14 sub-sectors. The outcomes reveal that the fluctuation in oil price impacts a firm's returns differently based on their sectors. Azar & Basmajian (2013) used three types of non-linearity to analyze the effect of the price of oil shocks on the stock markets of the two largest and most liquid GCC equity markets, Kuwait and Saudi Arabia. The study found that oil price shocks do not affect the Kuwaiti stock market, either linearly or non-linearly, while the Saudi market non-linearly reacts to oil price variations in the US S & P 500. Kumar & Maheswaran (2013) explored if oil price instability has an impact on the Indian stock market's indices on a sectoral -like financial, metal and commodities, services and industry. The result showed that the industrial sector returns are directly impacted by oil price fluctuations.

Methodology and Models Selection
Various econometric models were implemented to test the interlinkage among oil prices and the following sector indexes of the Kuwaiti equity market: Oil and Gas, Industry and Services. Daily data of prices (Brent) were gathered from Energy Information Administration-EIA (USA) and stock prices were obtained from the Kuwait stock market over the period from January 2012 to December 2017. stock prices are converted into returns by using natural logarithms -SRt = ln (SPt)-ln (SPt-1); similarly, Brent oil prices are also transformed into returns BRt = ln (BPt)-ln (BPt-1) Where SR = stock return SP = stock price BR = Brent oil returns BP = Brent oil price

Preliminary Tests
A vector autoregressive (VAR) framework was implemented to ensure choosing the optimum number of lags in econometric modeling. The method of lag selection is important and needs attention because the use of lags might have a direct influence on the estimation progression. On the other side, a small number of lags can lead to autocorrelation in the model. Also, a lengthier lag increases the size of the parameter affecting the degree of freedom that raises massive issues about the estimated model (Ivanov & Kilian, 2005).
The ADF test was implemented based on the equation given below: To cross-check the results of the ADF method, the Phillips and Perron (PP) test, alike to the ADF test, but adding an automated amendment of the DF protocol to enable correlated error named as the Kwiatkowski -Phillips -Schmidt -Shin test, which makes a null hypothesis, arguing that an obvious time series is smooth around a deterministic pattern. Three stationarity tests were considered for robustness purposes and due to significant levels of criticism associated with the performance of the ADF test.

Testing For Long-Run Dynamics
Two cointegration techniques (Johansen-Juselius and Engle-Granger) were used to test the presence of long-run testing among oil prices and Kuwait stock prices. The literature in the field informed the selection of the cointegration techniques with studies investigating the long-run association among stock markets and oil prices with an interest in the GCC nations (Bouri et al., 2016;Chau et al., 2014;Imarhiagbe, 2010;Miller & Ratti, 2009;Arouri & Fouquau, 2009;Granger et al., 2000). Other researchers have developed studies testing cointegration among stock prices and oil prices in a broader context, like, for example (Muhtaseb & Al-Assaf, 2017;Bahmani-Oskooee & Saha, 2015;Asteriou & Bashmakova, 2013;Constantinos et al., 2010). These researches offer new evidence on the significance of the specific econometric models, and as such, they contribute to ensuring that the selected research framework to support this study is appropriate. Engle & Granger (1987) endorse a two-step process for cointegration study that involves the estimation equation of the base-line equation listed below: The OLS residuals from the equation above are a measure of disequilibrium The baseline of the Johansen and Juselius (JJ) (1990) test is as follows: Where Zt and μt are explained as (m x 1) vectors. The Johansen (1988) approach includes the estimation of eq. 4 and the analysis of the rank of matrix Pk. Precisely, if rank (Pk) is equal to 0, there will be no stationary linear grouping of variables in Zt, there is no cointegration of the predictors. Since the matrix rank is a non-zero number of Eigenvalues (r), the quantity of the variables representing the number of cointegrating vectors. Two cointegration techniques were considered to allow cross-checking of the research outcomes.

Testing For Short-Run Dynamics
Granger causality uses linear prediction to determine if some event occurs before another (i.e., if we find Granger causality in one way only). The traditional Granger test was applied to understand if there is a sign of a pivotal link among the variables in a static dimension. To bring a dynamic dimension to the study, the causality frequency domain was considered to help to examine frequency-varying causal effects. Breitung & Candelon's (2006) study is centered on previous work by (Hosoya, 1991;Geweke, 1982) that measured the vector comprising of with a finite-order of VAR characteristic of order p. A brief insight into the test is presented below.
With ( ) = Θ( ) −1 −1 and G is the lower triangular matrix of the Cholesky decomposition ′ = Σ −1 such that ( ′ ) = and = . The causality test developed by Geweke (1982) can then be written as: Within this outline no causality from to at frequency tallies to the condition | 12 ( − )| 2 = 0. Breitung and Candelon's (2006) main contribution is to demonstrate that this situation leads to Where, Θ ,12 is the (1,2)the element of Θ , such that a sufficient set of conditions for no causality is given by Consequently, it is possible to test the null-hypothesis showing no Granger causality at the frequency π using the generic F-test for the linear restriction imposed by the VAR member of order p, that tracks the distribution of F(2, T-2p) for each π, where T represents numbers of series (Breitung & Candelon, 2006). The selected methodological framework helped to identify the existence of long and short-run dynamics among oil prices (Brent Index) and the Kuwait Stock Exchange (KSE) by using well-known and established econometric models.

Volatility Measurement
Variant prices, as well as stock trading fluctuations, are recognized as financial market uncertainty. The biggest concern about volatility is the decline in market trading (Ibbotson, 2011). To understand market risk, understanding of volatility is very important. Current research uses data on returns on the stock exchange that are deliberated more volatile and vulnerable to any economic shock that is worth seeing. However, it is also important to consider that Kuwait has a more volatile market, as it will help to better understand the dynamics of the local stock market. Another way to track market volatility is to look at frequent stock market movements (Barnes, 2017). To comprehend potentially unstable variance, a well-equipped Autoregressive Conditionally Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models are implemented to explain gradual increments invariance over time. Autoregressive Conditional Heteroscedasticity (ARCH) models have commonly applied models coming into the field as these methods are known as autoregressive in square returns and the volatility of the following period depends on information from that period in these models. To understand these types of models, there are two sections (Agung, 2009).
The 1 st component is known as the conditional mean, which is equivalent to a traditional equation of regression. The 2 nd part known as the conditional variance formula, where the focus is on modeling the mean equation's time-reliant variance. Information for which the variances of the residual terms are not equal, and that the residual terms can rationally be predicted to be greater for some points or information ranges than for others, is considered to be heteroscedastic (Paul, 2007). A normal linear regression, i.e.
= + + where the residual variance, i.e., is constant, is said to be homoscedastic and the ordinary least square method for estimating α and β is applied in such a system.
Let us consider that the return on an asset is given as: Where is a sequence of N(0, 1) i.i.d. random variables. Then, we determine the residual return at time t, rt − µ, as:

=
In an ARCH(1) model, which was first developed by Engle (1982), we have that: Where α0 > 0 and α1 ≥ 0 have a positive variance and α1 < 1 has a stationary variance. For an ARCH(1) model, if the residual return is high in magnitude, the forecast for the conditional volatility of the next cycle will be large. Therefore, the derived returns are provisionally normal (provisional to all data up to t−1, the one-time normally distributed returns) and this condition can be relaxed under normality assumption. It is also important to note that the returns, rt, are not correlated but not i.i.d. Therefore, it is not difficult to detect a time-varying 2 outcomes in big tails in the unconditional distribution of as opposed to a normal distribution (Campbell et al., 1997).
The kurtosis description is given as: If considered as normally distributed and it is around 3. In such an occurrence, we have that: We indicate here that an ARCH (1) is akin to an AR (1) equation on squared errors, 2 . This can be reviewed in the description of the forecast error (conditional), or the dissimilarity, between residual return (squared) and squared residual return (conditional expectation), given as: Where It − 1 is the evidence at time t -1 and vt stand as an uncorrelated zero-mean series. The ARCH (1) equation develops as follows: This is an AR (1) method for squared residuals. The existing study is established on daily frequency-based stock returns (financial data), so an ARCH would give deep prudence in analyzing the nexus of Brent oil returns and stock returns. Over the past two decades, the ARCH family of parametric nonlinear time series models was developed to specifically address volatility data trends (Paul, 2007).

Generalized Autoregressive Conditional Heteroscedasticity (GARCH)
Generalized models of Autoregressive Conditional Heteroskedasticity (GARCH) help locate financial markets where patterns of volatility may change. It suggests that the behavior of returns becomes more unsettled in periods of international instability, financial crises or conflict, economic uncertainty, etc., and has a lower level of volatility in times of relative calm and s table economic era. The following equations outline the typical GARCH model Where SRx is the stock return of asset X and SRy is the stock return of asset Y and the serially correlated errors is termed by a Moving Average (1) process, which is given as: In this analysis, the typical GARCH model is modified to introduce volatility in stock returns. For GARCH models, which require robust t-statistics from the Bollerslev-Wooldridge and the Jarque-Bera test for normality, residual diagnostic methods are performed. The statistics of the Ljung-Box (LB) help detect if there are any residual linear or nonlinear LB statistics and dependencies in the error terms that are calculated for the given equations because these statistics help to determine whether to accept the assumption of constant correlation overtime. If the specification of the variance equation is done correctly, then no ARCH should be found in the standardized residuals.

Diagnostic Tests
Specific diagnostic tests are an important step towards modeling the time series. A list of the different residual diagnostic techniques used in the current study to verify the stability of the model and analysis. Such measures are discussed as follows. The residual test of the correlogram has used to evaluate the residual serial correlation. Jarque Bera has used to check residual normality and finally, the LM method applied to verify the ARCH effect. Figure 1 shows a persistent rise in Brent oil prices (BP) was experienced until the beginning of 2015. This is a situation that could be justified by the uncertainty over the side of oil supply related to the Arab Spring in 2011 abetted prices of oil return to preceding prices and levels stayed steady over three years (Bchir & Pedrosa-Gorcia, 2015). Afterward, the graph shows the price started to display a downward trend    In Figure 2 stock prices for oil and gas show a small upward trend in late 2012, which lasted until mid-2015, trailed by a steady decline for the remaining sample period. All of these fluctuations are linked to significant levels of volatility-related to each of the events that influence market performance over time. It can be found that the phenomenon is the same in both cases when contrasting stock prices with oil prices. Uncertainty over the supply side of the Arab Spring Revolution has allowed oil prices to remain stable for more than three years to return to previous levels and prices (Bchir & Pedrosa-Gorcia, 2015).

Empirical Findings
In Figure 3, Industry stock prices had a steady movement from 2012 until mid-2017 and an upward movement was observed after mid-2017. The industrial segment was the main sponsor for income growth in 2016. Profit for this sector was 181 million KD, up 49%, this increase was mainly due to setbacks in a large loss experienced in 2015 by one of the corporations (Kuwait Economic Brief, 2017). Figure 4 indicates that the service's stock price had a consistent downward trend after 2014. One of the sectors was primarily behind this drop, also several companies in the sector witnessed a decline in profit during all periods (Kuwait Economic Brief, 2017 Table 1 provides descriptive statistics for sector indexes. The SD for all explanatory predictors varies from 0.0238 to 106.003. The minimum standard deviation i.e. 0.0238 stands for Brent returns, which means that it has a lesser difference, and on the other hand, O & G (SP) has the highest SD of 106.003, which indicates a high level of variation. Significantly, the industrial mean value is high for all periods under study, and Brent return has the lowest mean. Skewness is noted that the value for all predictors is near zero excluding in the case of oil and gas returns, where it changes from an inverse one to a positive two. The coefficient of both Kurtosis and skewness (lower than 3) reveals that Brent prices and stock prices showing a platykurtic trend. Also, the values of the Jarque-Bera method are high for all predictors indicating that the series are non-normal. The result from the SIC method as shown in Table 2 demonstrates that the ideal number of lags is equal to one for all variables. The core idea of the estimation of these lags is to safeguard that the econometric equation is correctly accessible to minimize potential problems related to the model's misrepresentation. The model estimates will lead to spurious research results in the case of incorrect lag selection. A very minor lag length becomes a reason of autocorrelation that can lead to bungling estimators and, on the other side, a long lag length increases the size of the parameter, which decreases the degrees of freedom and consequences in huge standard errors and confidence intervals for the model's coefficients and the time that the model could not properly capture the dynamic variables (Füss, 2007). The second step is an Augmented Dicky Fuller (ADF) stationary test. The results indicate that the variables at levels are non-stationary, meaning that the first difference in the data is implemented and the ADF test applied again. In response to this step, all variables underneath are now a one-order I(1) integrated process, revealing that all series are stationary in the same order. The study used the Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests to test for robustness. The findings of PP and KPSS approaches are fully consistent with ADF.
Research results indicate no substantial evidence to improve the presence of a long-term connection between the stock and Brent prices excluding in the oil and gas sector where the Johanson test revealed a long-term linkage, but the Engle-Granger technique does not support this result because the results of the Johansen outcomes are in line with the Engle-Granger methodology based on a two-step format of estimation. The first stage is to produce the residuals and the second phase uses the residuals produced to approximate a regression of first-differentiated residuals on lagged residuals. Any mistake that happens in the first step will, therefore, be passed to the second step. In the Johansen cointegration test, however, this does not happen, and as such, the Johansen method is more powerful in conflict situations between the EG and the Johansen technique (Billgili, 1998). These results point to the general lack of a long-term equilibrium between oil and stock prices in Kuwait, which means that information contained in oil prices does not help predict future stock price movements and vice versa (Arouri & Fouquau, 2009;Zarour, 2006;Hammoudeh & Aleisa, 2004).
The causality test was used to detect whether Brent returns have a short-run impact on stock returns in the sector and vice versa. This experiment was used to demonstrate whether the returns from Brent could be a justification for a shift in stock returns as the Kuwaiti stock exchange market is highly sensitive to variations in oil prices. The result shows no evidence of