Kurdistan Journal of Applied Research (KJAR) Print-ISSN: 2411-7684 | Electronic-ISSN: 2411-7706 Website: Kjar.spu.edu.iq | Email: kjar@spu.edu.iq Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 95 An Approach To Study The Effects of GBP/USD Exchange Rate and Gold Prices on Brent Oil Prices Using Autoregressive Distributed Lag (ARDL) Shaho Muhammad Wstabdullah Muhammed Ali Kamal Department of Statistics and Informatics Department of Computer Science College of Administration and Economics College of Basic Education University of Sulaimani University of Sulaimani Sulaimani, Iraq Sulaimani, Iraq shaho.wstabdullah@univsul.edu.iq muhammed.kamal@univsul.edu.iq Hozan Khalid Hamarashid Department of Information Technology Computer Science Institute Sulaimani Polytechnic University Sulaimani, Iraq Hozan.khalid@spu.edu.iq Article Info ABSTRACT Volume 7 - Issue 2- December 2022 DOI: 10.24017/Science.2022.2.8 Article history: Received: 14/11/2022 Accepted: 02/01/2023 The Autoregressive Distributed Lag (ARDL) is possible when cointegration analysis is applied to experimentally to shape the relationship between the variables without considering the regressors are stationary at its first difference or level, there is an integration of order one or both of the variables are mixed. Being based on one equation framework is a benefit of using the ARDL model, in order to take sufficient lags’ number and directing process data generation process in a modelling framework that goes from general to specific. The aim of this study is to focus on the trend of the relation between the GBP/USD rate and Brent Oil prices, which is done through the adoption of dependent variable which the oil price and the independent variable which is the dollar exchange rate. Another target of the research is to show the relationship between gold price and oil prices. The result shows that there are a number of likely influenced variable through by which the dollar-pound rate has effects on the demand and supply of oil as a result of its prices. That is done through the analysis of the relations between the variables of the study. Moreover, correlation coefficient values are given that there exists a positive explanatory correlation between the variables of the study. On the whole, there exists a positive long-term equilibrium relation between the GBP/USD exchange rate, price of oil and price of gold. Any change in the exchange rate of GBP/USD is causing the changes in prices of Brent oil. Consequently, the results are consistent with and not consistent with other researches that show opposite relationship. Keywords: Autoregressive Distributed Lag, Oil Prices, GBP/USD exchange rate, Gold prices Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 96 1. INTRODUCTION According to [1] the ARDL model is thought to be a standard squares regression where both explanatory and response variables fall behind as regressors. Despite of its usage in both econometrics and statistics for tens of years, the ARDL model only became popular recently as a way to examine cointegration between variables which were extended by [2] after their suggestion by[3].There are many techniques for cointegration in the literature, among those [4] consider the expression of “cointegration” as a technique being used for the reflection of the equilibrium long-term among the variables which tend to meet with time, while ARDL approach is known to be the newest technique of cointegration to check equilibrium and dynamic relations between explanatory and response variables. Some instances cointegration techniques are those which [2][5] supposed. The usage of the ARDL model started as they realized that the variables to be studied are found to be non-stationary and there is an integration of the same order between them, after that there is a possibility to study the cointegration relationship (i.e the likelihood the variables move with each other) by the ARDL approach between explanatory and response variables in long-term. The adoption of ARDL is possible when cointegration analysis is applied to experimentally to shape the relationship between the variables without considering the regressors are stationary at its first difference or level, there is an integration of order one or both of the variables are mixed [2]. Being based on one equation framework is a benefit of using the ARDL model, in order to take sufficient lags’ number and directing process data generation process in a modelling framework that goes from general to specific[6]. In addition to all these, the argument by [7] states that the cointegration test of Johansen needs a big sample in order to get reasonable, although, it indicates that ARDL approach works better with a the sample of a small [8]. 1.1 Objective of the research The aim of this study is to focus on the trend of the relation between the GBP/USD rate and Brent Oil prices, which is done through the adoption of dependent variable which the oil price and the independent variable which is the dollar exchange rate. Another target of the research is to show the relationship between gold price and oil prices. 1.2 Hypothesis • There exists a correlation between the prices of Gold and the prices Brent oil. • There is a correlation between the exchange rate of GBP/USD and the prices Brent oil. • There exists a relation that is sourced from the prices of gold toward the prices of Brent oil. • Any increase or decrease in the exchange rate of GBP/USD will cause important changes in the prices of Brent oil in the long run. • There exists a relation that is sourced from the exchange rate of GBP/USD towards THE prices of Brent oil. 2. LITERATURE REVIEW The study conducted by [9] which is one of the most recent studies using ARDL, searches for another treatment for spurious regression, that is caused by the unit root and analysis of cointegration, these are frequently used for the treatment of spurious regression but because of some specification as, innovation process distribution, structural breaks choice of the deterministic part and autoregressive lag length choice, they are not stable. The research which for the most part concentrated on Monte Carlo simulations, discovered that the main reason of spurious regression is caused by variables that are missing in the values of lag, which the treatment is an alternative method that leads us to the variable that is missing and as a result to ARDL model. As a conclusion the study comes up with the confirmation that we can benefit from ARDL as different way to the spurious regression problem. [10] which benefited from using a small T (number of time periods) and a big N (number of cross section data), concentrated on a single estimation equation of ARDL model from panel Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 97 data. While Micro panel data on individuals and firms are represented by the mentioned structure, to acquire consistent parameter estimates, the estimation ways don’t need the time dimension to be bigger. Single equation models with internal independent variables and dynamics autoregressive, the estimators of Generalized Method of Moments (GMM) which were extensively used in this situation, are the focus eras of the study. Two instances are put into the discussion as a simple autoregressive model for rates of investment and a basic production function, using firm-level panel data. The conclusion from the paper is that to get consistent parameter estimation an extensive range of microeconomic applications, we can benefit from using GMM estimators. Although these estimators may face biases of large finite sample, when the estimator of consistent GMM is compared to an estimator of a simple kind such as the level Ordinary Least Square, these biases can be detected and prevented in experimental studies [11]. Financial and economic with statistics indicators are the three topics that most ARDL research is done about. The research which studies the long-term relation between the rate of inflation and its factors in Iran using ARDL is done by [12]. The study concluded that the most statistically significant reasons affecting the rate of inflation in the country are the liquidity, inflation (imported), the exchange rate and the GDP. The ARDL cointegration technique is used by[13] to study the relation between the Chinese share market and the rate of exchange. The conclusion of the study is that the stock market is affected positively by the rate of exchange and money supply. The approach of ARDL bounds testing was used by[14] to investigate relations between the rates of inflation and the reserves of foreign exchange in Pakistan, for almost half a century (from 1960 to 2007). The paper concluded that a long-term cointegrating relation between the rates of inflation and the reserves of foreign exchange in the country.[15] implemented research using the approach of ARDL bounds testing for a period of 28 years from 1982 to 2010 to study how volatility of oil prices affects the rate of inflation in Taiwan. The conclusion of the paper indicates to a relation between the two but of a long-term and in addition to that the paper concluded any global increase in the prices of oil causes inflation merely in the long-term. 3. METHODS AND MATERIALS 3.1 Data Collection The data to investigate the impact of the Exchange Rate of GBP/ USD and the prices of Gold on the prices of oil from 2000 to 2022 on a monthly basis in the world were collected from various sources such as the Exchange Rate of GBP/ USD (E.X): the exchange rate of the United States. Dollar against a Great Britain currency (Pound), the prices of Brent oil (B.O.): Brent Oil barrel price. (G.P) Price of Gold per ounce in US dollars (USD/OZ). The response and explanatory variables are compounded monthly and based on nominal values (01/2000- 08/2022). The data were collected from [16]. 3.2 Methods An ARDL methodology is being adopted to investigate the long-term relation between the response and explanatory variables under examination [2]. The time series not being integrated from the second degree or more I (2) is the only criterion that makes this test different from the other tests of its kind. Although, the method of self-regression accepts chains of stability at the levels of I (0) and I (1) or both together. Prior to the equation analysis, we should be ensured that the variables under study are stationary; which means our variables do not have unit root problem. Later on, the co-integration test of (ARDL) is implemented while estimation of the model in short and long term and the test of Granger causality are done. Lastly, the results of the analysis are shown as followings. The Autoregressive Distributed Lag model adopts the following form: ln〖BO〗_t=δ_0+∑_(k=1)^n▒〖δ_1k ∆ln〖BO〗_(t-k)+ ∑_(k=1)^n▒〖δ_2k ∆ln〖ED〗_(t-k) 〗〗+∑_(k=1)^n▒〖δ_3k ∆ln〖GP〗_(t-k)+π_1 ln〖BO〗_(t-1) 〗+π_2 ln〖ED〗_(t-1)+π_3 ln〖GP〗_(t-1)+εt ……………….. (1) Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 98 Δ shows variables differences of the first level, the response variable parameter (B.O.) decelerated for a single period to the left side of the equation; π indicates long-run relations parameter, (δ) represents first differences parameters for the short period where random stroke errors and segment are represented by ԑ and δ0 respectively. The first step in the ARDL bounds testing approach is to estimate equation (1) by Ordinary Least Squares (OLS) in order to test for the existence of a long-run relationship among the variables by conducting an F-test. Estimation of the above equation is the first step of the testing approach which is done by (OLS) so that we can test if there is long-term relation between the variables through applying an F-test to determine the lagged levels coefficients for response and explanatory variables in joint significance. H_0: π_1=π_2=π_3=0 H_1: π_1≠π_2≠π_3≠0. A test for co-integration is provided by two asymptotic critical values bounds when the explanatory variables are I(d), while (0≤d≤1): the smallest value representing the regressors are I(0), and the largest value representing the regressors are I(1). Regardless, the integration orders of the time series null hypothesis is being rejected if the F-statistic value is greater than the upper critical value. On the other hand, null hypothesis is being accepted if the F-statistic value is smaller than the lower critical value. Finally, the result is inconclusive if the F-statistic value is in the range between the upper and lower critical values [17]. 3.3 Stationarity Tests The Dickey-Fuller test is one of the most common tests to examine the unit root test. The simplest formula of this test dates back to 1979 named as the test of Simple Dickey- Fuller (D.F.), estimating the Autoregressive Model of first-order AR (1) is the basis of the test as follows: ∆X_t=αx_(t-1)+ε_t ……………. (2) Where ε_t shows the stochastic error with the following conditions supposedly: E(ε_t )=0,var(ε_t )=E(X_t-μ)=σ^2,Cov(ε_i,ε_j )=0 i≠j, e_t follows normal distribution According to [18] under the above assumptions a suitable estimation technique is the least square estimation as the estimation is straightforward. If the value of α equals to 1, the variable (X_t) has a unit root and its non-stationary then it is called the White Noise Error Term. If we subtract (X_(t-1)) from both sides of the above equation, it will be as follows: ∆X_t=(α-1〖)X〗_(t-1)+ε_t …….. (3) The equation becomes as follows if we set (α-1 = p) ∆X_t=pX_(t-1)+ε_t Using OLS method for estimation, the three models become as follows: ∆X_t=pX_(t-1)+ε_t ……… (4) ∆X_t=θ_0+pX_(t-1)+ε_t ……… (5) ∆X_t=θ_0+θ_1+pX_(t-1)+ε_t …….. (6) All the above have been done so we can test the following null hypothesis: Null hypothesis H0: p = 0 (1) Alternative hypothesis H1: p ≠ 0 (2) The time series is non-stationary at the level if P = 0 is calculated to be ∆x_t=ε_t. If the conditions for the alternative hypothesis are applied, the time is called stationary and it is of order I (0). Taking the first difference or second differences we can make the time series stationary. That is when the time series under study is said to be stationary. In case of a Serial Correlation, the Dickey-Fuller test in its simple formula is not reliable and appropriate to examine if the time series is stationary or not. That is when the test of Augmented Dickey-Fuller should be used which is based on estimating of the following models: ∆X_t=pX_(t-1)+∑_(j=2)^p▒〖φ_j ∆pX_(t-j+1) 〗+ε_t…….. (7) ∆X_t=θ_0+pX_(t-1)+∑_(j=2)^p▒〖φ_j ∆pX_(t-j+1) 〗+ε_t ………. (8) Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 99 ∆X_t=θ_0+θ_1 t+pX_(t-1)+∑_(j=2)^p▒〖φ_j ∆pX_(t-j+1) 〗+ε_t…….. (9) Firstly, the optimal lag (p) is chosen which leads to the removal of the self-correlation with stochastic errors using specific tolls in statistics. The two criteria of Akaik and Schwarz are the most significant of these tools. However, there will be a false significance of the parameters if there exist a too short lag length that is caused by the information which is not explained. The Akaike information criteria (AIC) which is a statistical method is often used to determine the lags number. This method is a way of balancing between the underfitting case and overfitting case. As it does not depend on accepting or rejecting the null hypothesis, the Akaike information criteria are not a classic hypothesis test. It depends on scoring system and choosing the “most suitable” model as follows: AIC=-2log(L)+2m …… (10) Where m represents the number of parameters and the estimated model likelihood function of log value. Hannan Quinn criterion (HQ) and Bayesian Information criterion (BIC) which are the other frequent lag selection criteria are used as followings: BIC=-2log(L)+ m log(n) ……. (11) HQ=-2log(L)+ 2m log (log(n)) ……. (12) Where n denotes the number of observations or the sample size. 4. RESULTS AND DISCUSSION The description of the main statistics measurement such as mean and standard deviation etc. for the variables are shown in table 1: Table1: Main descriptive statistics Variables Abbreviation Mean Standard Deviation Maximum Minimum Oil Price BO 4.0766 0.49690 4.94 2.95 Gold Price GP 6.7857 6.3077 7.59 5.56 Exchange Rate EX 1.2021 0.16044 1.58 0.85 As shown in the table (1) that the mean and standard deviation of oil price are (4.0766, 4.94) respectively, (6.76857, 6.3077) for gold price and (1.2021, 0.16044) for exchange rate. Table 2: Correlation matrix of variables Variables Abbreviation BO GP EX Oil Price BO 1 0.733 ** 0.721 ** Gold Price GP 0.733 ** 1 0.416 ** Exchange Rate EX 0.721 ** 0.416 ** 1 ** significance with alpha equals 0.01. Table 2 indicates that there is a positive correlation between the rate if exchange and the price of oil with statistically significance because p-value of it were less than 0.05. There is a moderate correlation coefficient between the price of oil and the rate of exchange with statistically significance and almost approximately high correlation between gold price and oil and price. According to the result of correlation coefficient is that the problem of multi-collinearity does not exist among explanatory variables because the result for all were less than 0.08. 4.1 Unit root tests The conduction of this test is needed to make sure that response and explanatory variables are not integrated of second difference I (2), The time series not being integrated from the second degree or more I (2) is the only criterion that makes this test different from the other tests of its kind. Although, the method of self-regression accepts chains of stability at the levels of I (0) and I (1) or both together [2]. The unit tests of response and explanatory variables show in the table 3 and table 4. Table 3 illustrates the test of Augmented Dickey-Fuller result and table 4 illustrates the test of Phillips-Perron result. The null hypothesis is that the time series a stationary in level and first difference or both. Result shows that the null hypothesis accepts Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 100 because p-value was less than 0.05 in first difference. The results are similar with the test of Augmented Dickey-Fuller and the cointegration tests of ARDL can be proceed with these tests because response and explanatory variable are stationary in first difference. Table 3: Unit root test of Augmented Dickey-Fuller Variable ADF Test Stat * 1%level ** 5% level P-value At level (0) Ln BO -2.297963 -3.454443 -2.872041 0.8299 Ln EX -1.689155 -3.454353 -2.872001 0.4449 Ln GP -0.753304 -3.454353 -2.872001 0.8299 1 st Difference I(1) Ln BO -12.39297 -3.45444 -2.872041 0.000 Ln EX -16.30667 -3.45444 -2.872047 0.000 Ln Gp -18.63172 -3.45444 -2.872041 0.000 Table 4: Unit root test of Augmented Dickey-Fuller - Phillips-Perron Variable ADF Test Stat * 1%level ** 5% level P-value At level (0) Ln BO -2.037016 -3.454443 -2.872001 0.2709 Ln EX -1.791431 -3.454353 -2.872001 0.3844 Ln GP -0.651940 -3.454353 -2.872001 0.8552 1 st Difference I(1) Ln BO -12.39471 -3.45444 -2.872041 0.000 Ln EX -16.31323 -3.45444 -2.872041 0.000 Ln Gp -18.71194 -3.45444 -2.872041 0.000 4.2 Normality test It is indicated in the table (5) that the value of Jarque- Bera equals to 1.430124 and the probability of it is 0.491024 which is greater than the common alpha 0.05. Thus, residuals are normally distributed. Table 5: Normality test Mean Std.Dev Skewness Kurtosis Jarque-Bera Probability 3.69 0.05321 -0.251234 4.21354 1.430124 0.491024 4.3 Correlation LM Test It is clear in the table (6) that the null hypothesis (there is no serial correlation exist in the model) were rejected because p-value of Obs*R-squared were less than the common alpha 0.05 and accepts the alternative hypothesis (there is serial correlation exist in the model). In conclusion, there is serial correlation exist in the model. Table 6: Breusch-Godfrey Serial Correlation LM Test F-statistics 3.01243 Prob (2, 261) 0.1425 Obs*R-squared 11.9824 Prob.Chi-Square (2) 0.00597 4.4 Heteroskedasticity Tets It is clear in the table (7) that there is no heteroskedasticity problem exists in the model because the prob. Chi squar (6) of Obs*R-squared were greater than 0.05. Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 101 Table 7: Breusch-Pagan-Godfrey F-statistics 1.69576 Prob (6, 263) 0.2096 Obs*R-squared 12.98542 Prob.Chi-Square (6) 0.2199 Scaled explained SS 3.74521 Prob.Chi-Square (6) 0.9487 4.5 Lag Selection After we have found the order of integrating, two- steps of cointegration of ARDL procedure is applied. In the first stage, likelihood ratio (LR) criteria, SBC (Schwarz Bayesian Criterion) and AIC are used to determine the length of optimal lag of vector autoregressive. Table 8 illustrates the optimal lag chosen for vector autoregressive, it is crucial that we can choose high enough lag to make sure that the optimal order is not exceeding it. Five vector autoregressive (VAR (p)) p = 0,1,2,3,4 models are expected from 2000 to 2022. Because of minimization of the lost in the degree of freedom and the selection of smallest possible lag length, Schwarz Bayesian Criterion is for lag selection. As a result, lags two are selected in this research. Table 8: Selection of Optimal Lag Lags LR FPE AIC SC HQ 0 NA 1498861 22.7385 22.77448 22.75018 1 2505.751 104.6792 13.16452 13.38694 13.22984 2 33.46569 * 98.38573 * 13.10249 * 13.38694 13.21679 3 6.040995 102.8597 13.55325 13.55325 13.31018 4 7.206401 107.0148 13.18636 13.71462 13.39863 4.6 Stability Tests According to [19] the CUSUM square (CUSUMSQ) test and the cumulative sum of recursive residuals (CUSUM) are applied to study the stability of the model. CUSUM test helps to indicate if there is systematic change in the regression coefficients. The parameters of the null hypothesis are stable and the ones of the alternative hypothesis are not. Consequently, in the beginning of the figure, the blue line is not within the red lines but later it is within the two red lines, which implies that the parameters are going to be stable. CUSUM of square test helps in indicating if there is a sudden change in the coefficients of regression. If we interpret that, in the beginning the blue line was within red lines and then it was within the red line, it means at first that the null hypothesis were accepted and the alternative hypothesis is rejected, but it was going to be stable because the blue line was going be within the red lines. -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 25 50 75 100 125 150 175 200 225 250 CUSUM of Squares 5% Significance -60 -40 -20 0 20 40 60 25 50 75 100 125 150 175 200 225 250 CUSUM 5% Significance Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 102 Figure1: CUSUM Test Figure2: CUSUM of Squares Test 4.7 Co-integration Rank  H0: There exists no co-integration relationship (no long- term relationship between response and explanatory variables)  H1: There exists at least one co-integration (long- term relationship between response and explanatory variables) Table 9: Unrestricted Co-integration Hypothesized Eigenvalue Trace Statistic 0.05 Critical Value Prob. ** None * 0.081792 30.00113 29.79707 0.0474 At most 1 0.016753 7.217613 15.49471 0.5525 At most 2 0.010086 2.706767 3.841466 0.0999 Hypothesized Eigenvalue Trace Statistic 0.05 Critical Value Prob. ** None * 0.081792 22.78351 21.13162 0.0290 At most 1 0.016753 4.510847 14.26460 0.8019 At most 2 0.010086 2.706767 3.841466 0.0999 Table (9) displays the Johnson test in co-intergration test under 95% of confidence level. As the p-value was greater than the common alpha 0.05 or the value of statistics was more than the common alpha 0.05, the null hypothesis There exists no co-integration relationship (no long- term relationship between response and explanatory variables) is rejected and the alternative hypothesis There exists at least one co-integration (long- term relationship between response and explanatory variables) is being accepted. Consequently, there is long-run relation among the response and explanatory variables. 6.264 6.268 6.272 6.276 6.280 6.284 6.288 A R D L (2 , 1 , 1 ) A R D L (2 , 2 , 1 ) A R D L (3 , 1 , 1 ) A R D L (2 , 1 , 2 ) A R D L (2 , 0 , 1 ) A R D L (2 , 3 , 1 ) A R D L (3 , 2 , 1 ) A R D L (2 , 2 , 2 ) A R D L (2 , 1 , 3 ) A R D L (3 , 1 , 2 ) A R D L (4 , 1 , 1 ) A R D L (2 , 1 , 4 ) A R D L (2 , 4 , 1 ) A R D L (3 , 0 , 1 ) A R D L (2 , 0 , 2 ) A R D L (2 , 3 , 2 ) A R D L (3 , 3 , 1 ) A R D L (2 , 1 , 6 ) A R D L (6 , 1 , 1 ) A R D L (2 , 2 , 3 ) Akaike Information Criteria Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 103 Figure 3: Akaike information criteria appropriate the test of lag periods From Table 5 and Figure 3, it is obvious that the most suitable models using AIC are ARDL (2, 1, 1) for Oil price, LGold price, LGBP/USD, respectively. 4.8 Co-integration test of ARDL After establishing the long-run cointegration relation, the estimation of equation (2) was done. Table 10 shows the results acquired by normalizing oil prices in the long term. We can notice significant effects of independent variables lags on the oil price. First and second lag of oil price have a statistically significant impact at 1% confidence level. First and second lag of gold price have a statistically significant impact on oil price too which shows as a highly statistically significant impact from first and second lag of exchange rate of LGBP/USD. In addition, the negative value of gold price and exchange rate in the first lag means that those have a negative impact on oil price in the first lag. Table 10: ARDL co-integration test Variable Coefficient Std. Error T- Statistic Prob.* LBO(-1) 1.109304 0.058376 19.00283 0.0000 LBO(-2) -0.205508 0.059017 -3.482171 0.0006 LGP 0.255899 0.120368 2.125970 0.0185 LGP(-1) -0.218031 0.110245 -1.977660 0.0411 LEX 0.820413 0.198258 3.810541 0.0002 LEX(-1) -0.628727 0.196142 -3.205468 0.0015 C -0.019040 0.070195 -0.271250 0.8764 R-squared 0.961099 Mean dependent var 65.80085 Adjusted R- squared 0.961099 S.D. dependent var 29.61642 S.E. of regression 5.563761 Akaike info criterion 6.296010 Sum squared resid 8141.281 Schwarz criterion 6.389302 Log likelihood -842.9613 Hannan-Quinn criter 6.333472 F-statistic 1226.534 Durbin-Watson stat 1.982265 Prob (F-statistic) 0.0000 4.9 F-Bounds Test As a result, we have reached an establishment that none of the selected series I(2) or above and the optimal lag order determination, long run cointegration presence test was done using bounds test. Table 11 illustrates the results of ARDL bound test of cointegration. F-statistics is greater (6.503655) than critical value of the upper bound, according to [2], (at 1% significance level) is 5.0. Therefore, there are enough reasons for the rejection of the null hypothesis which states no long-term relation at 1% significance level and probably there exists cointegration between variables under investigation. Table 11: Bound test results Test statistics Value K F-statistic 6.503655 2 Significance Critical value bounds I0 Bound I1 Bound 10% 2.53 3.25 5% 3.2 3.77 2.5% 3.45 4.28 1% 4.23 4.99 4.10 Long-Run Relationship Table 12 displays the long-run result. The Gold price coefficient is statistically significant with a value of 0.393679, which implies that an increase with the rate of 1% in supply of relative Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 104 gold price, causes an increase of 0.393619 in oil price in the long term. The relative coefficient of GBP/USD exchange rate is 1.317447 and it is significant, that indicates an increase of 1% in the relative GBP/USD exchange rate results in an increase of 1.317447 appreciation in oil price in the long term. Table 12: Estimated long run coefficients Variables Coefficient Long Run Coefficient Standard Error t-Statistics Prob. LGP 0.393619 0.110915 3.548827 0.0005 LEX 1.317447 0.446136 2.953016 0.0034 C -0.197918 0.720404 -0.274732 0.7837 4.11 Estimations of ARDL-based error correction model After estimating parameters of long-term, the estimation of short-term parameters is needed, specifically for the estimation of error correction model. In Table 13, it was found that error correction model parameters are significant at level of 1% and 5%. Short term and long term signals are positive as well excluding the parameter of error correction which equals to −0.096204. It was found that the statistically significance is at level 1% with a negative signal leads to an increase in the long term equilibrium relation. There is no mechanism for error correction in the model and the parameter is used to measure the returning speed in the long term to an equilibrium position. The returning speed to equilibrium position equals to −0.096204. Table 13: Estimations result of Long Run from ARDL-based error correction model Selected Model ARDL (2, 1, 1) Variable Coefficient Std. Error T-statistic Prob. D(LBO(-1)) 0.205508 0.058424 3.517545 0.0000 D(LGP) 0.255899 0.137735 2.857907 0.0165 D(LEX) 0.755470 0.194697 3.880234 0.0001 CointEq (-1) -0.096204 0.024762 -3.885118 0.0001 4.12 Granger Causality test Table 14 shows a summary of a unidirectional causal relation that was seen between the oil price and GBP/USD exchange rate, which is significant at 1.83%, as the p-value is smaller than 5%. It illustrates that the exchange rate of GBP/USD has effects on of Brent oil price, but price of Brent oil has no effect on the GBP/USD exchange rate. Table 14: Granger causality test of Brent oil price and GBP/USD Null Hypothesis Obs F-Statistic Prob L EX does not Granger Cause LBO 269 4.05930 0.0183 LBO does not Granger Cause LEX 0.55357 0.5756 Table 15 shows a summary of a one-way causal relationship that was seen between the oil price and Gold price, which is statistically significant at 1.92%, as the p-value is less than 5%. It shows that Gold price has effects on the price of Brent oil, but price of Brent oil has no effect on the gold price. Table 15: Granger causality test of Brent oil price and Gold price Null Hypothesis Obs F-Statistic Prob L GP does not Granger Cause LBO 269 3.87116 0.0192 LBO does not Granger Cause LGP 0.45639 0.6347 Table 16 shows a summary of a one-way causal relationship that was found between the GBP/USD and Gold price, which is not significant, because the p-value is more than 5%. It shows that Gold price has no effect on LGBP/USD has no effect on Gold price. Kurdistan Journal of Applied Research | Volume 7 – Issue 2 – December 2022 | 105 Table 16: Granger causality test of Gold price and GBP/USD Null Hypothesis Obs F-Statistic Prob L EX does not Granger Cause LGP 269 0.16014 0.8521 LGP does not Granger Cause LEX 0.12959 0.8785 5. CONCLUSION In this research, we tried to investigate the nature of the relation between the GBP/USD exchange rate, the Brent oil price, and the gold price. Result shows that there are several possible channels influenced through which the dollar-pound rate affects in one way or another oil supply and demand and as a result oil prices. That is done through the analysis of the relations between study variables. Moreover, correlation coefficient values are given that there exists a positive explanatory correlation between the variables of the study. We have found a causal relationship between the gold price and the Brent oil price, which is unidirectional. This relationship demonstrates that the gold price has effects on the price of Brent oil, but not vice versa. In addition, when the exchange rate varies it leads to changes in oil prices. This is a unidirectional relationship from the GBP/USA towards oil prices which was shown by the Granger causality test. Finally, In this study, there is a co-integration relationship between the interpreting variables and the Brent oil price in US dollars per barrel (B.O), represented in GBP/USD Exchange Rate and the Gold Price in US dollars per ounce (G.P.). On the whole, there exists a positive long-term equilibrium relation between the GBP/USD exchange rate, price of oil and price of gold. Any change in the exchange rate of GBP/USD is causing the changes in prices of Brent oil. Consequently, the results are consistent with and not consistent with other researches that show opposite relationship. REFERENCES [1] H. Greene. Econometric analysis, 7th edition. Prentice Hall, 2008. [2] M. Pesaran,, Y. Shin,and R. Smith. Bounds testing approaches to the analysis of level of relationship. Journal of Applied Econometrics, 16 (3), pp. 289–326, 2001. [3] M. Pesaran, and Y. Shin. An Autoregressive Distributed Lag Modeling Approach to Cointegration Analysis, In: Strom, S., Holly, A., Diamond, P. (Eds.). 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